C5S.M0^,. C9 1/17 AilHtViS 18 I CO o o. o o en o o I— 00 o CVJ UJ C5 19 CM >-• Q 5 CE CD •8 O o I X 3 •8 o H 2 o -St: LJ LJ o m oc LJ _I Q. a. o a cs z o LJ c Q ° 0^ (£) 8 8 -S Q •s — I — 0*09 — T — O'K — r- O'O — I — O'OC- — T 09- 0*06 0-06- 3001 I lyi 20 o o S^313U c z- z- 21 I 1 r 00^ 00£ OCZ 001 Z^Oi 1 r 000^ 00£ 008 001 B < I— I lA Em T r 000^ 00£ OOE 001 ^>o S c 3 0) . o inly becau typically o bou (hid wit r all n ac CO *- Q. r all man CD ^ _Q) — O' CO 3 O o vp ^ S, 82 OO «fl c — CO e" ^•K e 2 oJ s: a. ^ t: egraded ma :y which is ree. position fix in slow mo curacy is av 1 rements. 0) o E o B with 24- ecified po orized use lized covei nterferenc e with 24- t to VLF e with 24 (graded pe 4-* > CO c .2 CO 23 CO — $5" .|o isd aint deg tween or use fix aci measu CO GC o rational world ther coverage. available to a ~ CO T3 3 >?• 131 z < CL o rational wil ited by sky rational wo System is malies. rational wo ther coverai olar areas. tion accura zimuth unc order of ±1 he interval be minutes. Fi etter position ual frequency "co r 0) c > CJ ss c 9) C a.E Ope age. anoi 0) CO a Q. Q) Q. O "t: 3 u u O $ 2 O-i O $.E h- C3> 00 T3 UJ CO CO March 1982 ' a Moderate A Range of Operation ■o o U.S. Coast, Continental U.S., Selected Overseas areas 0) o o •a T3 o ine of sight iresent air lutes) 0) O $ § $ _i^ if. $ c o 2 CO "*- CL U o § s s CO cc CJ > '5 r 2hrs er axis) > o c ■^§ f 2 CO to < o 3 <: 5 8 E O cu o 0) 0.8 afte (RMS p o 0} o 0) CD >4i- 0.1 ( axis) No V data No V data No V data No V data ladio N -IV, Ch C» < a. Dt 1^ ;:: .2 5 — Q. LU Q. UJ o LU O 1 max 1st (CEP a. IXI O Q. LU O 2dera NAC- ugust CO in9 s 8 ,500 fter our 8 8 U. LU < lU "- CO CN T- CO ^ t CM 1-^ CM -J E oP ^ C/5fN z^ ^J ' CO 2 $ c a> 3) 0} ? Q, < Q> 'm « Ui ^ CO a. CD Lora (Not Ome (Not Std 1 (Not TAC (Not Tran (Not 1- O z 25 The navigation accuracy that can be achieved by any user depends primarily on the variability of the errors in making pseudorange measurements and the instantaneous geometry of the satellites as seen from the user's location on Earth (Payne, 1982). Additional information on the navigation solution and navigation technique is given in Reference 3 (Milliken and Zoller, I98O). SYSTEM STATUS In December 1973 the Defense System Acquisition Review Council (DSARC) authorized a step-wise, design-to-cost development and test program which would lead, in successive phases, to an operational GPS. The system concept resulted from the integration of the best features of previous navigation satellite concepts being pursued independently by the U.S. Navy and the U.S. Air Force. The Navstar program is being developed in three phases: Phase I, concept validation; Phase II, full-scale engineering and development; and Phase III, production. The details of the schedule are shown in Figure 1. During Phase I prototype satellites were developed, a control segment was established, and advanced engineering models of user equipment were tested. Currently, the program is in Phase II. The main tasks of this phase include developing the prototype operational satellite, the operational control system, the prototype user equipment, and the completion of the developmental test and evaluation/initial operational test and evaluation (DT&E/IOT&E) . The current GPS constellation consists of a limited number of developmental satellites configured in two planes inclined at 63 degrees with respect to the equator. There are six good satellites (Navstars 3} 4> 6, 8, 9, 10) plus one satellite (Navstar 1) which is generally not being used for navigation because it is operating with a quartz crystal clock. The current constellation is shown in Figure 2. The plan is to maintain a minimum constellation of five satellites for the completion of the test and evaluation period for the system. It is currently projected that the last Block I test satellite will be launched in August 1985 to maintain the test configuration. The operational constellation is a 6-plane, uniform l8-satellite configuration plus three active spares. The spares are necessary to guarantee very high system availability for the l8-satellite constellation. The planes of the constellation are 60 degrees apart in longitude with each plane containing three satellites separated by 120 degrees. The phasing from plane to plane is 40 degrees so that a satellite in one plane has a satellite 40 degrees ahead (north) of it in the adjacent plane to the east. According to the current plan, the Block II (operational) satellites will be launched at a rate of eight per year beginning in October 1986. Two-dimensional coverage should be available by the latter part of 1987 and three-dimensional coverage, barring failures, should be available by the end of 1988. The Phase I control segment consisted of a master control station and antenna located at Vandenberg AFB, CA, and monitor stations located at Vandenberg AFB, Alaska, Guam, and Hawaii. The initial control system which will fill the control segment gap between Phase I and the final operational control system became fully operational in January 1983* The final operational control system (DCS) will consist of a master control station, three ground antennas, and five monitor stations. The master control 26 o > LU < o o a. Q. < UJ OC o ^™ ^ s^ 00 QJ:? 0) Q. ■^ «2 O z ii^ s o 00 i o t- CO \ o o o> \ UJ 3 Ul -1 T" \ Q o a eS < z K^ \ < Q. O OC 1- o 1 LJcs. //^/^^O^^^^Kv o >- 1^ 00 (/) Q. u. /^[y^ /■•. ^^m\ ASE III ERATH ABILIT O) z o 1- \ o o _l _l U. //^J>^KUN\ I 0- Q. (O OQ o \ u. 1 X ■R^l^^^H^ I 1 io< 00 a> ^^ 3 \ J^ Ar'^^*"*S^/^^NA A _i o _J < o \ \\y]\^^S><(/\s/J 3 ■■■ cc \ ■^" y\ljm<-'\. /^->— LX/ u. U) < a \ o o t- Q ■■■' \\\ ^\ / yf/ 00 — \ Oo d OC V >isO^*C-^^i^ ^~ < ' ■■" a. a \ H \ ■■■ z i^"" ^ UJ 00 UJ h- o UJ 11 CO 00 z o (/} UJ _l z Ul Q. o UJ > Ul e9 1- Q 1- 2 UJ ^B UJ Z9t ^^* Q. (0 CM 00 Q og "uj Z 2 CO O lU o> O O -J QQ * » '•^ _i ^ < Z) ^^ (0 u. Q IS. < ^■^^ ^»l ■M^ ■■■■ — 1- 00 Z UJ rs. UJ 0) o9 S O) S _l 1- < OC CD O CC Q. O) Q. o -1 UJ > UJ Q z UJ o Ul o o > UJ Q ^^x Z "" UJ Q. >- 1- o —1 Q // ^^ "^v,^^^ ^ lASEI DATIO (O is. UJ > UJ Q Q UJ O z ly^f^A^^ ^5 > U) 1- o OC < > Q 1 \v:^^^ ) Q. < 5 \ 3e^^^^^ y^ Q. ^ 3 ^v y^ UJ O Z ^ o OC < > — -1 o o> CO o UJ o T- Q UJ a 00 rs. <^ < Z UJ 1- (0 UJ o> (/) o = 1- 27 UJ z < o o CM 0) §1^ CM to 00 o O CM flC O 0)2 QC-I >z TO 0) E TO o OJ o > ^~ W. n OJ o 'c 4— ' a < o ■o 03 CL TO < z _j C ^^ TO > -1 ■■^ o CO ^ CD c o) E > O) c O C O) E 8 — QC if 3 03 > c)5 c LU OJ • • CO UJ oc O 0) c o 0) 3 O CO 0> DC TO (0 O) c 03 03 03 % c q 4-» E (_ 3 O 03 k- „i- u c 03 _l O DC rr- ~ C C LU (/) OJ 0) < 03 4-> O E 03 03 a O k- tatic ing/ x: o 03 o Q. a ceanic E omestic o: c E k_ 03 03 *-> Q. O o "03 S osition < O Q H oc J_ • • • • • • [L o3 C o a O ^ 03 Q. o c H— 03 03 o 03 T5 (D >- u -J 'JZ 03 < o > J3 03 4-* TO C c o 03 "D 03 03 V) c a o — 03 03 o o DC oc u u O) c 03 > c 0) ■>- 03 > c 03 o 3 o > i 3 CO ■♦-' 3 O 03 i- fD CO o 03 03 0) DC J 03 C ^ > "oj o n 03 c O 4-' 03 ^ 03 -' 03 o 03 o k_ o 4^ ■n 03 > 1 CO 4- a ■o F o 1 >+- X > (13 1 o LU I < h- CJ 30 navigation, which will in turn reduce fuel costs and transportation time. Search-and-rescue techniques can be enhanced because of the precision position identification capability of GPS. The mineral exploration and geophysical survey communities will be able to accurately locate potential petroleum bearing areas, ore bodies, and active fault belts in a shorter period of time. Other GPS applications to Mapping, Charting, and Geodesy have been given elsewhere (Senus and Hill, 1981). The GPS common grid feature will enhance many land-vehicle operations. Airborne collision avoidance systems and maritime hazard systems are also potential uses of the system. GPS time transfer applications include scientific, intra-system synchronization, and inter-system synchronization uses (Van Dierendonck and Melton, 1983). In addition to the potential applications given above, GPS has demonstrated performance in space applications and baseline determinations. Continuous 10 to 15 meter positioning in space without the use of ground tracking systems has been demonstrated on Landsat-4 using a GPS receiver (Birmingham et al. , 1983). Relative positions have been demonstrated to be accurate to within several centimeters over baselines varying from hundreds of meters to tens of kilometers (Counselman et al . , 1983). The potential applications for GPS are boundless. CONCLUSIONS The Navstar GPS is evolving into a highly accurate, worldwide, all-weather navigation/positioning system applicable to the needs of both the military and civilian communities. Since 1977 extensive testing has taken place which verified the established accuracy goals and the system operation under various mission-oriented conditions. There are numerous applications for which GPS can be exploited. Even though the system is not fully operational, it is being used by diverse civilian groups such as NASA for orbit determination onboard Landsat-4 and oil companies for geodetic positioning. As the system gains acceptance by the civilian community, more sophisticated uses for the system will be established. 31 REFERENCES 1. Birmingham, W. P., B. L. Miller, and W. L. Stein, I983, "Experimental Results of Using the GPS for LANDSAT 4 On-board Navigation," Proceedings of the ION Aerospace Meeting , Arlington, Virginia, pages 54-57. 2. Counselman, C. C, R. I. Abbot, S. A. Gourevitch, R. W. King, and A. R. Paradis, I983, "Centimeter-Level Relative Positioning with GPS," Journal of Surveying Engineering (ASCE) , Vol 109 , No. 2, pages 81-89 . 3. Milliken, R. J. and C. J. Zoller, I98O, "Principle of Operation of NAVSTAR and System Characteristics," in "Global Positioning System," Papers published in Navigation , Institute of Navigation, pages 3-14. 4. Payne, C. R., 1982, "NAVSTAR Global Positioning System, 1982," Proceedings of the Third International Geodetic Symposium on Satellite Doppler Positioning , Vol. 2 . pages 993-1021. 5. Senus, W. J. and R. W. Hill, 1981, "GPS Applications to Mapping, Charting, and Geodesy," Navigation , Vol. 28 , No. 2, pages 85-92. 6. U. S. Department of Defense, I983, Office of Assistant Secretary of Defense (Public Affairs), Washington, D. C, News Release, No. 328-83. 7. Van Dierendonck, A. J. and W. C. Melton, 1983, "Applications of Time Transfer Using NAVSTAR GPS," Navigation , Vol 30 , No. 2, pages 157-170. 9li .:C 32 CIVIL USE OF THE GLOBAL POSITIONING SYSTEM PRECISION POSITIONING SIGNAL (PPS) Col Phillip Baker/Lt Col Fred Zedeck Assistant Secretary of Defense (C^I) Pentagon, Washington, D.C. 20301 ABSTRACT. The Department of Defense (DoD) has established a policy that would allow limited use of the GPS PPS under certain conditions. An implementation approach is being developed by the DoD. The approach would include an application process which would filter applicants based on certain criteria. The USG or its agent would provide the cryptographic material and user equipment to approved applicants for a service fee. In order to complete the planning process, feedback from potential users of this service is being solicited. Specifically, DoD needs to know approximately how many groups or individuals would use the service and if the implementation approach is workable. As with many government projects in the area of defense, the civil sector is becoming increasingly aware of the positive benefits of certain defense programs in addition to the obvious advantages of having a strong defense posture. The world has changed dramatically since the first SPUTNIK went into orbit in 1957. Space and space-based technologies are affecting all of us in hundreds of differ- ent ways. NAVSTAR is just one of the more visible systems which, as it comes on line, will be used in more and more civil applications. The world community of Geodesy is attuned to the technological advantages of the system, but someday the average citizen will also be aware of GPS and use it to navigate boats, or light aircraft or even autos, which I understand we can expect to see by 1987. Although 1987 may seem a long way off, the DoD is rapidly approaching its goal of NAVSTAR final operational date. The space segment is under contract and ROCKWELL is off and running on building the 28 block-two satellites which are necessary to place NAVSTAR into full operation. We have a complete test cluster in orbit, and progress on the technical side of the program appears on track. The principal reason for GPS is to support the DoD and our overall defense program. The system was funded entirely by the DoD and virtually every major element of defense will benefit from the unique capabilities of this new system. Although I know this forum is sensitive to our nation's defense needs, your primary interests center on geodetic applications of GPS. As the tasks of the world's geodetic community (DoD included) continue to grow, these tasks get tougher to accomplish. As with Chinese pick-up sticks, the first ones are always easier to get at, than the ones at the end of the game. Although your industry is far from the end of its game, the sticks are getting harder to pick up. Geodetic applications are getting harder to accomplish and GPS will be a major player in helping your industry achieve its objectives. Three years ago, the National Ocean Industries Association submitted a request for civil access to PPS to the Secretary of Defense. DoD provided an interim 33 answer, but In matters of policy, final answers do not come quickly, I'm pleased to say however, that DoD has developed a position on PPS use in the civil commun- ity. It should not surprise you that NOIA was not our only request. The Texas Highway Department, and other informal requests for civil access to PPS require- ments were also received. The broad spectrum of national security issues in- volving access to GPS complicated the issue. Security and the protection of a sensitive DoD system had to be weighed against the benefits expected. The focus of the review centered on the question of whether there are valid defense-related national security applications for PPS access. The answer was hardly surprising. Of course there were. The challenge was to devise means to make this capability available in a manner both responsive to civil needs as well as to DoD require- ments for ensuring security of sensitive equipments, PPS is not the only approach open to improving location accuracy. Work is pro- ceeding in other areas such as differential GPS, to provide improved accuracies for GPS users in the civil community. Our objective is to provide the maximum accuracy level possible consistent with the security and integrity of the system. The more alternatives we can develop that do not involve sensitive technologies in providing PPS accuracy, the better it serves both communities. What I'm about to describe has not been set in concrete. As a matter of fact, we're open to suggestions as to how to improve on what we hope is a sound way to offer PPS access. The application process will be open to all civil users, both foreign and domestic. The review of applications will be conducted by the DoD position-navigation committee, expanded as needed to ensure comprehensive con- sideration of national security needs. Among the criteria that will be used to review the applications are the following: a. Is it in the national interest? b. Can the equipment be adequately protected? c. Is this the only way that the required PPS type accuracy can be obtained? Once an application has been approved, a certification will be issued based on geographic area and time frame. This certification will be forwarded to the activity which will provide the PPS service. An approved applicant will contract with the US Government or its agent for PPS access. Supporting services will be furnished under a contract arrangement. The product that will be delivered is positioning information necessary for your activities at the accuracy levels of the precise positioning signal, PPS equipment need not be purchased, since the agent will be responsible for providing the complete capability on your premises. Whether PPS is provided directly by the USG or its agent, certain unique respon- sibilities will be carried out by the government. The USG will continue to moni- tor the overall availability of PPS to the civil sector and develop PPS policy as required. We will assure that industrial security regulations are followed and we will be responsible for providing the necessary keying materials for use with the PPS capability. Should we designate a commercial agent to act in our place, it would provide the same positioning services as the USG, It would operate as will the USG, under a contract with the approved PPS applicants. As I mentioned earlier, the procedures and concepts outlined here are now being developed, A great deal of work remains to be done in developing this method into workable procedures. We invite your assistance in developing a system responsive to your needs and which also provides the security necessary to safeguard GPS, As 34 we gain more feedback from the civil sector and work out the procedures In more detail, your assistance will help develop a system that works, and Is supportive of your needs as well as ours. We are moving into uncharted waters here and there are few clear precedents. We want to be fully responsive to your needs and we are confident that the mutual requirements of service and system security can and will be met. With your help and comments I know they will be. 35 le d.1 I ON-ORBH FREQUENCY STABILITY ANALYSIS OF NAVSTAR GPS CLOCKS AND THE IMPORTANCE OF FREQUENCY STABILITY TO PRECISE POSITIONING Thomas B. McCaskill and James A. Buisson Naval Research Laboratory, Washington, D.C. 20375-5000 ABSTRACT: A description of the NAVSTAR Global Positioning System (GPS) and its primary mode of navigation will be pre- sented. This mode of GPS system navigation is then contrasted with that of the Navy Navigation Satellite System (NNSS) single pass mode of navigation, with emphasis on the relative importance of time synchronization and clock stability in the two systems. An on-orbit frequency stability analysis of NAVSTAR cesium, rubidium, and quartz clocks will be presented. The clock off- sets were obtained using smoothed pseudorange and integrated pseudorange-rate measurements, taken from the GPS monitor stations (MS). The MSs use high performance cesium clocks to drive their receivers, and to provide a ground-based time and frequency reference for GPS time. A smoothed orbit is used to separate the orbital and clock signals frcan the pseudorange measurements . Clock performance is characterized through the use of a time danain - frequency stability profile, which is evaluated for sample times of 15 minutes to two hours, and from one day to 10 days. Aging rate corrections were made for the quartz and rubidium clocks before computing their frequency stability. The sensitivity of frequency stability to small errors in the aging rate is presented for the NAVSTAR-8 rubidium clock. The frequency stability values obtained were processed to classify random noise process and modulation type, which are then com- pared with a generic frequency stability profile to separate GPS system effects from clock effects. Results of the GPS on-orbit frequency stability analysis are presented for quartz, rubidium, and cesium clocks. These results may then be used to predict GPS navigation performance and the potential for precise positioning. GPS SYSTEM DESCRIPTION The NAVSTAR Global Positioning System (GPS) is a tri-service Department of Defense (DOD) space-based navigation and time transfer (Easton 1972) system. GPS will provide a near-instantaneous, continuous navigation capability for user position and velocity, in all three coordinates. GPS TIME GPS time is operationally defined as the time scale used by the system which translates time, as derived from each NAVSTAR space vehicle (SV) clock, to a common time. Each NAVSTAR spacecraft carries clocks that are used as time and frequency references for GPS time, and to determine the epochs of the transmitted wave- forms. The on-orbit clocks run at a (nominal) rate of 38,500 nanoseconds/day fast, as predicted by Einstein's theory of relativity. The relativistic clock effect for orbiting clocks was verified by the first GPS satellite. Navigation 37 ■nOii •■li^jii'-^a^*!. Technology Satellite-2 (NTS-2). NTS-2 was the fourth in a series of NRL tech- nology satellites which demonstrated key GPS concepts, which included the first cesium clocks to be placed into Earth orbit. The frequency offsets, measured with respect to UTC(USNO) via satellite time transfer technique, are presented by figure 1. The relativistic clock effect for GPS was verified to better than 1 percent (Easton 1979). Because of this relativistic clock correction the rate of GPS time is nominally the same as UTC(USNO), except for leap second corrections. This is done through the use of hardware frequency synthesized offset of 4.443 parts in 10(10) to the transmitted frequency v^ich is continually applied to the output of each NAVSTAR atonic clock. This correction accounts for more than 99.6/J of the relativistic clock effect. Additional tuning adjustments are made, as required, by the MCS, to maintain each NAVSTAR clock to within +/- 1 msec in time, and +/- 1 part in 10(9) in frequency, to GPS time. GPS time is adjusted by the Master Control Station (MCS) to closely track United States Naval Observatory (USNO) Universal Time, Coordinated (UTC) using measurements taken with a GPS receiver located at USNO (Klepczynski 1983). The correction of GPS time to UTC(USNO) is performed in a three step procedure as follows : (1) A GPS user first measures the pseudorange using the signals broadcast by each NAVSTAR SV. The pseudorange measuronent includes the propagation delay, and other effects that must be removed in order to obtain the clock offset. Iono- spheric delay is measured by L1/L2 users; LI only users can use ionospheric model parameters contained in the navigation message. Tropospheric delay is corrected by measurement or model. (2) The second step requires a software computation by the GPS user to determine his clock offset with respect to GPS time. This computational pro- cedure is made using coefficients transmitted in the navigation message. The current procedure (Klepczynski 1983) requires the user to make a small rela- tivistic clock correction (Van Dierendonck 1980). The clock portion of the navigation message defines the NAVSTAR clock offset with respect to UTC(GPS) at a convenient epoch, and uses a quadratic model to predict GPS time at the time of measurement. This quadratic model is necessary due to the characteristic aging exhibited in both quartz and rubidium clocks. (3) The third correction is required for users who want to transfer time (Buisson 1976) via GPS spacecraft to LrrC(USNO). This correction from GPS time to UTC(USNO) is carried in the navigation message and is periodically updated using estimates obtained by USNO (Klepczynski 1985). GPS NAVIGATION The primary mode of navigation with GPS requires the user to make four simul- taneous measurements of time delay, taken between the user's clock and four GPS spacecraft. These measurements are called pseudorange (PR) because they contain the range between the user and a NAVSTAR SV, as well as clock offset and other effects. The four pseudorange measurements are then used with the orbital position, clock correction to GPS time, and other information contained in the broadcast ephemeris message to solve for the user's clock offset, latitude, longitude, and height. Velocity and frequency offset solutions may be obtained from GPS by making four additional simultaneous measuranents of pseudorange-rate, which may be integrated to obtain accumulated delta pseudorange. The frequency offsets may be calculated with respect to either GPS time or UTC(USNO). Instantaneous navigation is possible because each NAVSTAR clock is synchro- nized to a comnon GPS time, and at least four spacecraft can be continuously tracked from any place on Earth. The importance of GPS time, clock synchro- nization (Easton 1972), and clock stability (McCaskill 1983), will now be 38 described from the navigator's point of view. Each GPS PR measurement is obtained by correlation between signals derived from the navigator's clock and the onboard NAVSTAR clock (Dixon 1976). A single PR measurement would permit a determination of clock offset as has been previ- ously described. If four PR measurements were sequentially obtained from the same NAVSTAR three components of positions, and clock offset, could be determined (McCaskill 1976). But, due to the limited geometry, the accuracy of the solution would be highly degraded. If four widely separated NAVSTARs are used and one PR measurement is obtained from each, four different clock offsets would be determined. By synchronizing all four NAVSTARs to a corrmon GPS time at some epoch, and assuming the NAVSTAR clocks have sufficient clock stability to keep GPS time, the same four PR measurements allows clock offset plus three components of position to be accurately determined. The parameters for the size and placement of the GPS constellation has been extensively studied (Buisson 1972), and it has been shown that accurate world- wide navigation solutions for all three position coordinates and time, can be obtained with a 18 to 24 satellite constellation. The geometrical configuration of the four NAVSTARs used for the PR measurements, influences the quality of the navigator's solution for position (Buisson 1972). The performance measure used to evaluate the geometry is known as GDOP (geometrical dilution of position). GDOP is defined as the square root of the sum of the variances of the components for position and clock parameters, and is obtained from the equations relating position and clock offset to the four PR measurements (McCaskill 1971). GDOP is a pure number which is then multiplied by the UERE (user's equivalent range error) to obtain the estimated system accuracy. UERE is computed by the MCS to predict realtime GPS performance on a continuing basis. UERE may be used in a post-processed mode for estimating the accuracy of geodetic solutions. The instantaneous mode of GPS navigation requires that the NAVSTAR clocks be extremely stable because they are not continuously updated. The navigator's clock must be stable only for the time required to make the PR or PR-rate measurements. More stable user clocks can be used to advantage to improve the position solution. NNSS NAVIGATION The Navy Navigation Satellite System (NNSS) was the first space-based navi- gation system which was developed in the late 1950s. Applications for NNSS include static point positioning and surface navigation for slow-moving vehicles. Two techniques for accomplishing fixed point positioning by NNSS have been developed (Guier I960 and Stansell 1978). The first requires the user to track a single NNSS satellite for an entire pass, typically 15 minutes in duration. Multiple passes are used to obtain varying geometry and average certain types of error sources. These data are then processed to solve for user position. Other parameters of the solution include frequency biases and scaling parameters for residual tropospheric or ionospheric effects. The second technique is called translocation, and requires a reference station that is located within several hundred kilometers of the unknown survey station. This is a relative navigation technique which can improve the accuracy of the results, but it requires a communication link between the reference and unknown station. The frequency bias parameter (s) obtained from the NNSS position solution gives the estimated value of the difference between the NNSS frequency source and the user's frequency source, both of which are assumed to be constant during the 15-minute pass (McCaskill 1971). 39 GPS/NNSS COMPARISON Full comparison of the GPS and the NNSS space-based navigation systems would require a survey of the historical events and the technological requirements that have driven the development of these two systems (Hill 1979). Hence the comparison will be limited to the importance of time synchronization and clock stability in the two systems. Key GPS and NNSS features are sunmarized by Table 1. Table 1 GPS/NNSS SYSTEM FEATURES FEATURE GPS NNSS .NAVIGATION INFORMATION SOURCE .NAVIGATION CAPABILITY .ACCURAa VELOCITY TIME UTC(USNO) ABSOLUTE FREQUENCY .precise TIME/FREQUENCY .15-ininute frequency stability .GPS timeCsynchronized clocks) req'd for spacecraft & user .1 NAVSTARs (multiple access) .1 NNSS pass INSTANTANEOUS .l»D x,y,z,t .continuous velocity •precise frequency 15m SEP 0.1 KNOT (3 AXIS) < 100 NS < 1 PART IN 10(11) .2D lat,lon£ 35m CEP < 1 KNOT (N VELOCITY) 50 vS .TIME TO FIRST FIX 1 MINUTES .NAVIGATION GEOMETRY .SPACECRAFT CONSTELLATION HD GDOP (INSTANTANEOUS) 2.5 METERs/METER 18-21 NAVSTARs 35-100 MINUTES 2D PDOP 5 NNSSs .ALTITUDE .PERIOD REPEATING GEOMETRY 10,900 NMI 12 HRS YES 575 NMI 105 MINUTES NO .SPACECRAFT aOCKS .PRESENT .FUTURE .MM)ULATION C/A P QUARTZ, RUBIDIUM, CESIUM QUARTZ CESIUM, HYDROGEN SPREAD SPECTRUM CW 2 MHZ BW NARROW BW 20 MHZ BW .TRANSMITTED FREQUENCY 1575.n2 MHZ 1227.6 MHZ 150 KHZ 400 MHZ .RELATIVISTIC CLOCK CORRECTION .MAJOR ORBIT PERTUBATION .ORBH PREDICTION GROWTH RATE YES RADIATION PRESSURE ORBIT ADJUSTMENTS 5-25 m/D DRAG 2-25 m/D 40 LAUNCH DATE CLOCK TYPE 2/22/78 QUARTZ 10/7/78 RUBIDIUM 12/11/78 RUBIDIUM 2/9/80 CESIUM 4/26/80 CESIUM/RUBIDIUM 7/14/83 RUBIDIUM 6/13/84 CESIUM 9/10/84 CESIUM Comparison of the key features presented by Table 1 does not include the many technological factors which contributed to the development of both GPS and NNSS. Developments such as space-qualified atomic clocks, long-term orbit prediction and Kalman estimation algorithms, have all contributed to the evolutionary development from NNSS to GPS. Two of the most critical factors are the ability to maintain precise time and frequency synchronization through atomic clocks, and the simultaneous access to four NAVSTARs through spread spectrum techniques. Table 2 GPS NAVSTAR CLOCKS ANALYZED NAV ID SV ID 1 4 3 6 4 8 5 5 6 9 8 11 9 13 10 12 GPS ON-ORBIT CLOCK ANALYSIS The Naval Research Laboratory (NRL) has determined on-orbit clock performance for the vehicles shown in Table 2. The goal of this technique is to separate the clock offset from the orbit and other system effects that are present in the GPS signal in order to determine the on-orbit clock performance (McCaskill 1975). This procedure utilizes a highly redundant set of PR and PR rate measurements that are collected from all four present MSs. This redundant set of measurements allows the determination of clock and orbit states that are independent of the MCS's realtime Kalman estimates of NAVSTAR clock and orbit states (Varnum 1982). The on-orbit results have been used to determine the NAVSTAR clock performance, and provide improved clock process noise parameters for the Kalman clock/ ephemeris estimation. The on-orbit clock analysis flow diagram is depicted by figure 2, and has been described in detail (McCaskill 1983). Outputs from the clock analysis include frequency histories, frequency stability profiles, time domain noise process analysis, and anomally detection. Key features of this technique are (1) use of a high-performance reference clock at each monitor station, and (2) use of a smoothed reference orbit to separate the orbital and clock signals from the pseudorange and pseudorange rate measurements. The smoothed reference ephemer- ides used in this analysis were computed by the Naval Surface Weapons Center (Swift 1985). On-orbit frequency stability analysis accuracy is primarily dependent on four factors. Those factors are (1) the measurement precision, (2) orbital accuracy, (3) MS reference clock stability, and (4) the number of samples analyzed. The measurement precision is on the order of 18.5cm for a 15-minute smoothed PR measurement (IBM 1981). The post-processed orbital accuracy is typically better than 5 meters. The MS reference clocks are typically stable to 6 parts in 10(14) for a 1-day sample time, and the length of the data set analyzed is at least a factor of 10 greater than the sample time. Frequency histories are calculated using pairs of clock offsets separated in time by 1-day, which is called a 1-day sample time. Sample times which vary from 41 15-minutes to 2-hour s, and from 1- to 10-days are used for the frequency sta- bility calculations. Data sets of up to 1-year are used for this paper. For example, for a 1-year data set using four-station MS ensemble averaging, the number of samples for a one day sample time is on the order of 1400 samples; for a 15-minute sample time the number of samples is on the order of 36,500 samples. These choices result in high confidence estimates for the on-orbit stability results. The set of frequency stabilities is then used to plot a frequency stability profile (sigma-tau plot) for each clock. The clock's frequency sta- bility profile is then compared to the GPS specifications to insure that each on-orbit clock is maintaining proper GPS performance. The model used is the IEEE reconinended measure of frequency stability in the time domain (Barnes 1971). The equation that relates this variance to a power -law random noise process is presented by Eq . ( 1 ) . a ^y(T) = a(T)" (1) whereayCx) is the limiting case of the two-sample variance, t is the sample time, "a" and "u" are constants associated with the random noise process types. The application of this model to analysis of orbiting clocks has been presented in detail (McCaskill 1983). A generic frequency stability profile for a clock is presented in figure 3. This profile includes all of the five recognized types of clock noise processes that can occur, and their behaviour as a function of sample time in the time domain. The types of noise processes expected from a normally behaving clock, for these sample times, are a subset of the following types: white noise FM, flicker noise FM, and random walk FM. Any departure from the expected behaviour for each of these random noise processes is investigated, and could be attribut- able to other system factors besides the clock. Once a clock has been characterized through a frequency stability analysis, the frequency stability profile may then be used to estimate a clock's time prediction performance. A set of time prediction curves is presented by figure 4, using an optimal two point prediction algorithm. This algorithm, and other models for estimating time stability have been presented (Allan 1974). Each of these optimal time prediction models has one thing in common — namely that the long-term time prediction performance is ultimately driven by the product of the clock update time and the frequency stability. Therefore the frequency stability is a fundamental measure of time prediction performance, or time stability. The length of time between NAVSTAR clock updates is determined by system performance requirements, hence improved frequency stability is the parameter that will improve time prediction performance. The NRL on-orbit analysis represents total system errors superimposed on the clock results. System influences may either enhance or detract from actual clock performance. Figure 5 presents GPS system clock specifications as a function of sample time. ON-ORBIT RUBIDIUM RESULTS On-orbit clock analysis results will be presented for the rubidium clock currently in use on-board the NAVSTAR-8 SV. This rubidium clock is the best performing rubidium of those that have been launched and used. This device is the first to be operated onboard a NAVSTAR SV using a temperature controlled baseplate which compensates for the temperature sensitivity well known in rubidium clocks. Clock offsets between the NAVSTAR-8 rubidium clock and the Vandenberg MS clock are presented in figure 6. These clock offsets were computed using post- 42 -processed data. The clock offset for each point was evaluated at the time-of- -closest-approach (TCA) of NAVSTAR-S to the Vandenberg MS. Reference to figure 6 indicates a sequence of smooth curves for the clock offsets, with an occasional adjustment that to keep the clock within the GPS time specification limits, or for other reasons that will be discussed in this paper. This set of clock off- sets were further processed to compute frequency offsets, using sample times that vary from 1- to 10-days. The frequency history for the NAVSTAR-8 rubidium clock, with respect to the Vandenberg MS, is presented in figure 7. A linear trend in the frequency offsets is the most dominant feature present in the frequency history. Reference to figure 7 indicates that during 1984 the NAVSTAR-8 rubidium clock experienced a total frequency change of 1.05 parts in 10(10). A linear change in frequency, as a function of time, corresponds to a constant aging rate in the NAVSTAR-8 rubidium clock. If the aging rate of the on-orbit clock was constant and accu- rately known, an exact correction could be made before calculating frequency stability, or in predicting future values of GPS time. Careful visual inspection of the data presented in figure 7 indicates small departures from a constant aging rate. Frequency offsets for the NAVSTAR-8 rubidium clock were fit to a linear fre- quency model as a function of time, and the frequency linear residuals are presented in figure 8. The statistics of this fit are presented in the enclosed box, and includes the aging rate value used for calculating the linear frequency residuals. The residual behaviour from January until mid-July 1984 follows a linear trend, followed by an abrupt change to a new linear frequency residual trend after mid- July through the end of 1984. Figure 9 again presents the NAVSTAR-8 rubidium frequency linear residuals, with the inclusion of potentially significant events that could influence the clock's behaviour. The clock temperature step of 3 degrees centigrade in mid- July is readily seem to occur at the time of an abrupt change in frequency linear residuals. No other significant change was known to have occurred at this time, hence changing the temperature setting is the most likely cause of this abrupt change in the NAVSTAR-8 rubidium clock's behaviour. The remaining factors that were noted during 1984 have either a small, or a no impact effect on the rubidium clock's performance. The behaviour of the NAVSTAR-8 rubidium clock's frequency residuals after the temperature setting change are presented by figure 10. These residuals indicate an anomalous behaviour that lasted from mid- July until October 1984. The fre- quency residuals from the other three MSs were analyzed to determine whether this behaviour was due to the NAVSTAR-8 rubidium clock, or the MS reference clock. Correlation of the residuals indicated that it was indeed the NAVSTAR-8 rubidium clock which experienced an anomalous behaviour. The frequency history was used to partition the rubidium database before calculating the aging rate correction for the frequency stability determination. Two partitions were used for the 1984 database, with the segmentation occur ing during mid-July, corresponding to the temperature adjustment. Quadratic curves were fit to the clock offset data for each partition, and the coefficients to the quadratic fit were then used as corrections to the rubidium clock offsets before computation of the frequency stability. A subset of the NAVSTAR-8 database used for the frequency stability determi- nation was used to explicitly compute the influence of aging rate errors on frequency stability, and is presented by figure 11. The stability profiles were computed with an increment of 2 nanoseconds/day/ day. These parametric aging rate curves indicates a low sensitivity to aging rate errors for a 1-day sample time, with dramatically increasing sensitivity as the sample time approaches 10 days. The importance of this analysis can be seen if GPS were to be used in a long-term prediction mode. 43 Frequency stability computations were made for sample times of 1- to 10-days for each of the four monitor sites. The frequency stability profile referenced to the Vandenberg MS clock, is presented by figure 12. A composite frequency stability profile for each of the four monitor sites is presented by figure 13. Agreement between the monitor sites is on the order of 2 parts in 10(14) for a 1-day sample time, and degrades to 4 parts in 10(14) for a 10-day sample time. A four-station ensemble average was computed and is presented by figure 14. Comparison of this frequency stability profile with the theoretical frequency stability profile (figure 3), is used to classify the random noise process type. ON-ORBIT CESIUM RESULTS NAVSTAR-9 was launched on 13 July/ 1237 UTC, 1984 and the first clock on-board to be activated was a cesium clock. This type of cesium clock was developed by the Frequency & Time Systems Corporation (FTS), under contract to NRL, as part of the NRL Clock Development Program for GPS. The frequency history for the clock with respect to the Vandenberg, MS is presented in figure 15. Inspection of the frequency offsets indicates no anoma- lies. The frequency offsets were computed using a 1-day sample time, and reach a maximum of 5.3 parts in 10(12) and a minimum of 4.4 parts in 10(12), for the entire data span. Frequency stability with respect to each of the individual monitor sites, are presented in figure 16. No aging rate correction or par- titioning of the data was necessary before computing the stability results, because cesium clocks have no appreciable aging. Comparison of the measured stabilities from the four monitor stations indicates a range of stabilities of 1.2 parts in 10(13) to 1.7 parts in 10(13), for a 1-day sample time, and 4 parts in 10(14) to 6 parts in 10(14), for a 10-day sample time. The stability profile indicates an unexpected departure from a normal clock model which has peak effect for a 6-day sample time at all monitor sites except Vandenberg. This suggests that other factors beside the cesium clock may be causing this effect. A four-station ensemble average was computed using the stability data from each MS, and the result is presented in figure 17. The profile indicates a white noise FM process for 1- to 4-days sample time. The stability profile for 10-day sample time approaches the linear extension of the noise process present in the 1- to 4-day results which suggests that effects other than clock could be con- tributing to the 4- to 9-day deviation. Stability results during a NAVSTAR pass can be determined by using the smoothed clock offsets, which can be sampled once per 15 minutes, using the smoothed PR 15 minute measurements. Highly significant statistical results can be obtained for sample times of 15^ninutes to 2-hours. Because of the length of the data set, stabilities can be averaged and evaluated as a function of time (as well as a function of sample time), by partitioning the data base into statistically significant subsets. Results for 5-day sets have been analyzed and presented (McCaskill 1983). These results are called "short term" because they are evaluated for sample times that are relatively short as compared to sample times of 1- to 10-days. Short term stability results referenced to all four monitor stations, have been analyzed from initial turn-on until the end of 1984. The individual stabi- lity samples referenced to the Vandenberg MS clock, and a 900-second sample time, are presented in figure 18. Each data point presented in figure 18 was computed using three successive clock offsets that are separated in time by 15 minutes. For a 6-hour pass a total of 25 samples would be possible. Using a maximal-use-of data overlapping sampling technique results in 23 stability samples per pass. The stability variances may be averaged to obtain value for the entire data span. The sample time is then varied from 900-seconds up to 44 2-hours and connected to produce a stability profile which is shown in figure 19. Canparison of this profile with the theoretical profile (figure 3) indicates a white noise FM process for 900-seconds up to 2700-seconds, with a transition to flicker noise FM for 1- to 2-hours sample time. This departure is not expected of a cesium clock. ON -ORB n SUMMARY RESULTS Frequency stability profiles for orbiting quartz, rubidium, and cesium clocks are presented by figure 20. These results are all referenced to the MS cesium clocks. In most cases four-station ensemble averaging was used to improve the confidence of these stability profiles by (1) decreasing the importance of any one individual MS, and (2) increasing the number of on-orbit samples by a factor of four. The rubidium and cesium clocks indicate three of the five possible types of random noise process, with anall exceptions that will be discussed. For sample times of 15-minutes to 2-hours a white noise FM process is the dominant process. For sample times of 1- to 10-days three types of noise processes are encountered. The rubidium clocks indicate flicker FM and random walk FM processes. The cesium clocks indicate a near -white noise FM process, flicker noise FM, but no random walk FM. For 15-minute to 2-hours sample times the expected result, for the NAVSTAR atonic clocks, is a white noise FM process. The departure of the NAVSTAR-3 rubidium (McCaskill 1983) clock is possibly due to temperature- induced effects. The NAVSTAR-6 rubidiian clock (now deactivated) showed a flicker noise FM process for 15-minutes to 2-hours sample time. The renaining atomic clocks followed white noise FM trends, with a transition to flicker noise FM. The on-orbit clock stabilities currently available from NAVSTAR atomic clocks represents a significant improvement over previous space-based time and frequency standards. Future GPS enhancements that relate to precise clock and ephemeris are an advanced cesium and hydrogen maser clock currently being developed under con- tract by NRL for the Space Segment. In addition MS reference hydrogen maser clocks are being developed for the Operational Control Segment (OCS) and are planned to directly support operational requirements. These improved clocks will also improve post-processed clock/ephemeris solutions, which will result in improved positioning with GPS. REFERENCES Allan, D.W., Gray, J. E., and Machlan, H. E., 1974, "The National Bureau of Standards Atomic Time Scale: (feneration. Stability, Accuracy and Acceptabilty, NBS Monografti No. page 226. Barnes, J. A., Chi, A. R., Cutler, L.S. , Healey, D. J., Leeson, D. B. , McGunigal, T. E., Mullen, J. A., Snith, W. L., Sydnor, R., Vessot, R.F.C., and Winkler, G.M.R., 1971, "Characterization of Frequency Stability", IEEE Transactions on Instrunentation and Measuronents, IM-20, No. 2, pages 105-120. Buisson, J. A. & McCaskill, T.B. , 1972, "TIMATION Navigation Satellite System Constellation Study", NRL Report 7389. Buisson, J. A., McCaskill, T.B. , Snith, H. , Morgan, P., and Woodger , J., 1976, "Precise Worldwide Station Synchronization via the NAVSTAR GPS, Navigation Technology Satellite (NTS-1)", Proc. 8th Annual Precise Time and Time Interval (PTTI) Applications and Planning Meeting. Dixon, R.C., 1976, "^read ^ectrum Systems", John Wiley & Sons Easton, R.L., 1972, "The Role of time/ frequency in Navy Navigation Satellites", Proc IEEE, May, 1972, pgs 507-563. 45 Easton, R.L., Buisson, J. A., McCaskill, T.B. , Oaks, 0. J., Stebbins, S.B. , Largay, M. J., 1979, "The Contribution of Navigation Technology Satellites to the Global Positioning Systems", NRL Report 8360. Guier, W.H. & Weiffenbach, G.C., I960, "A Satellite Doppler Navigation System", Proc IRE, vol 48, pg 507-516, Apr, I960. Hill, R.W., 1979, "An Overview of the NAVSTAR Global Positioning System and the Navy Navigation Satellite System", Proc. of the AAS/AIAA Astrodynamics Conference, Vol 40, Part I, pages 21-32. IBM, 1981, "GPS Critical Design Review", Book 2 of 3, Section 5.1 User Accuracy, pages 1-3. Klepczynski, William, 1983, "Modern Navigation Systems and Their Relationship to Timekeeping", Proc. of the IEEE, pages 1183-1198. Klepczynski, W. , and Kingham, K. A., Morikama, T. , and Yoshio, Y. , 1985", Time from GPS", First International Symposium on Precise Positioning With the Global Positioning System. McCaskill, T.B. & Buisson, J. A., 1976, "A Sequential Range Navigation Algorithm for a Medium Altitude Navigation Satellite", J. Inst. Navigation, 23(2), Summer, 1976. McCaskill, T.B. , & Buisson, J. A., & Lynch, D.W. , 1971, "Principles and Techniques of Satellite Navigation Using the TIMATION II Satellite", NRL Report 7252. McCaskill, T.B. & Buisson, J. A., 1975, "NTS-1 (TIMATION III) Quartz and Rubidium Frequency Stability Results", Proc. of the 29th Annual Symposium on Frequency Control, pages 425-435. McCaskill, T.B. , Buisson, J. A., and Stebbins, S.B. , 1983, "Frequency Stability Analysis of GPS NAVSTARs 3 and 4 Rubidium Clocks and the NAVSTARs 5 and 6 Cesium Clocks", NRL Report 8778. Oaks, O.J., Buisson, J. A., and Lister, M.J., 1985, "Time Transfer and Clock Analysis via the Global Positioning System (GPS)", Measurements Science Conference. Stansell, Thomas A., 1978, "The TRANSIT Navigation Satellite System", Magnavox R-5933/Oct. Swift, R.S., 1985, "NSWC's GPS Orbit/Clock Determination System", First International Symposium on Precise Positioning with the Global Positioning System" . Varnum, Fran, and Chaffee, James 1982, "Data Processing at the Global Positioning Master Control Station", Proc. of the Third International Geodetic Symposium on Satellite Doppler Positioning, pages 1023-1040. Van Dierendonck, A.J., et al, 1980, "The GPS Navigation Message", Institute of Navigation publication "Global Positioning System", pages 55-73. 46 > JO' 2t 3_ Ou. UO 10 •' HIGH -^lOJl 10" NTS2 LAUNCH 6/23/77 QUARTZ -UTC (USNOl- CESIUM RELATIVITY CORRECTION 170 200 220 250 CFIELD TUNE NAVAL RESEARCH LAB (NRL) CLOCK ANALYSIS FLOW CHART FOR NAVSTAR GPS DVniMMlNATION ft MS h 1\ l\. ¥JU«M*rsiiiO MCS '\ -^ J iV MAWMI MS V H^ \ OUAM MS -I L ^ MS -J 280 300 320 MCAtunFMEnm r •• mulMPIANOI ItMCl « niUDO-MANOfl PnCPROCtSSINO ■ ANTHROIAflOM ■OinTMtMT DtlATS K»T-FM>CIUIO lAMPLI RATI CONVinSION *o« lACM onsAnmn coMnnAnoM NAVAL OtSf RVATORV NRL OPS CLOCK ANALYSIS • svtiiM mmwMAMCt • ALIAM VAUAMCI • IHMC OOMAIM HOtH PHOCIH 4WALVI > MtOUIMCV HtCTORT ■ ANOMAir prricnoN TIME DOMAIN FREQUENCY STABILITY PROFILE ^ \ — ^ WM)Tt PHASE FLICKER PHASE t 1 WHITE FRED FLICKER FRCO 1 RAND WALK FREQ 1 LOG (SAMPLE TIME r I ricoiK 3 1000 CLOCK PREDICTION PERFORMANCE VS FREQUENCY STABILITY I I I I 1 1 ii| lO"'-" 10" FREQUENCY STABILmr o, (t) ricmE 4 CPS SYSTEM ANALYSIS rREOUEHCV STPBILITY SPECir ICATIOHS le' SflfPLE TIME IN SECONDS [nrTI START INC m MY B .0 TO DM 363.24 1984 ,,,„,, . e9-fiPR-8^ 47 RUBIDIUM OSaiXATOR (NO. 34) PHASE OFFSET NAVSTAR e Vaodanbarff Uonttar SUUoB HOOinEDJUUAM DAYS RUDIDIUM FREQUENCY OKreCT COKKECTEU AND PURGED NAVSTAK Vanilcnbcrf Mooltsr SUtioo ■ •■ fi» Hat tn Bit Htm ml •»• nr mt ■•• kic RUDIDIUM OSaLLATOR (NO. 34) FREQUENCY OFFSET UNEAR RESIDUALS NAVSTAK 8 Vandcnbcri MonltAr SuUon b. ito \ X •• / ,^••.^, MmS Jrrar •/ f MOO MM MOO MM MM aiM RUBIDIUM OSCIUATOR (NO. 33) FREQUENCY OFFSET UNEAR RESIDUALS NAVSTAR 6 V*ndenbcr| Uonllor SUUon RUDIDIUM OSaiXATOR (NO. 34) FREQUENCY OFFSET UNEAR RESIDUALS NAVSTAR B Vandenberg Monitor Station m 2 •■ ae u b. 12 i;. ^ aU •..■;■ -^ -«.•• jf<»r -•«»' W"'V,4 J-rif ■••UK al I»«« »I.l(«r«« « „ «•■• s>» atiw-iaK m/4 Iron OIl.t m/4 -li- aM* aiaa 48 NAVSTAR a RUBIDIUM - VAr«0£Net.HC MS> OAT 270- 36S 1083 FREOueNCT STABILIIT 36 34 32 30 ."28 o I" -22 ^20 -32 NS/0-2 26 NS/0-2 M NS/0-2 ■28 NS/0-2 J 1 1 1 1 t _ I I I I I 2 3 4 S 8 7 H U IL TAU (OArs> QPg SYSTEM ANALYSIS NOVSTfiR 8 VS nOMlTOR ST0T10N5 IB' 18* 9W«>t.C TlIC IN SECONDS _ IllRLJ START INC «T DBT 16 ,« TO VM 363.4 1984 W-tf>R-e5 Ob • i SYSTEM ANALYSIS VnNKNBERC VS NAVSTOR 8 le' 10'- SBtPLE TIME IN SECONDS ricHC i: CPS SYSTEM ANALYSIS STATION ENSEMBLE VS NAVSTAR 8 SfirPLE TIME IN SECONDS ricuti !• CESIUM FREQUENCY OFFSET NAVCTAR 9 Vandenberf Monitor Station i»f — «•• nr Ml ■•t (IC I!* ' ■ . r"! iff' "I «'" ■=. Wa'.ii.''"; 7 : i»/'jVt'>^^'' ,\ >■<■*!* H ■< I < ^. H i^ I [ED je' MODinED JULIAN DAYS eooo aoM aiae 49 CPS SYSTEM ANALYSIS MOVSTOR 9 VS nOHlTOn STOTIONS le* le- SWfLE nrC IN SECOUDS STORTINC OT DOT 191.2 TO DOY 363 10 1981 f^ CPS SYSTEM ANALYSIS STnTlOM EMSEMBLE VS NOVSTOR 9 -T e9-flPR-85 10" le- SRrfLE TIME IN SECONDS DTfiRTINC OT DRT 132.1 TO BOr 363 , 1<» I98t 10" e9-«=R-e5 10^'- 1 r 1 g UJ 10' GPS SYSTEM ANALYSIS VPNDENBERC VS N0V3T0R 9 -1 —I 1 1 1 1 1 T— I -1 r -r -1 r -1 r-r 36 7^ 108 114 180..216> 252 2B8 32<( "360 TIME 3H DftYS.lSS-v . • • •' ' |nRL | 3Fn=Lc TIME see ssc riCUBK IS 10 y ic GPS SYSTEM ANALYSIS VONDENBERC VS NRVSTOR 9 ^: 10 ' le ' SfirPLE TIME IN SECOKDS 10' le'-i—f IB' CPS SYSTEM ANALYSIS STATION ENS VS NflVSTOR 1/3/4/3/6/8/9/ 10 i^ i^ 10" 10' SS«*LE TIME IN SECONDS ricuKi >o IB" InrlI 50 NSWC»S GPS ORBIT/CLOCK DETERMINATION SYSTEM Everett R. Swift Space and Ocean Geodesy Branch Space Systems Division Naval Surface Weapons Center Dahlgren, VA 22^148 ABSTRACT. NSWC has provided the GPS predicted reference trajectories to the Master Control Station since the launch of the first GPS satellite in 1978. Single- satellite weighted least-squares orbit fits using range difference data derived from smoothed range data for the four original monitor sites are used in making these predictions. The resulting fitted trajectories have been made available to the GPS geodetic community. To improve the accuracy of the GPS orbit/clock estimates, NSWC has developed a system of computer programs implementing a multi-satellite filter/smoother procedure for GPS data reduction. An overview of this GPS orbit/ clock determination system is given including the estimation concepts employed, the orbit and clock models chosen, and the output produced. Results of applying this procedure to several weeks of GPS monitor site smoothed data augmented by data from two Defense Mapping Agency tracking sites is presented. These results are in the form of after-fit residual statistics, station navigations, and comparisons between the filter/smoother-derived trajectories and those obtained from the standard four- station batch fits. Future NSWC GPS orbit/clock determi- nation investigations will be discussed including plans to augment Operational Control Segment tracking using the TI 4100 geodetic receivers. INTRODUCTION NSWC has provided the predicted reference trajectories to the GPS Master Control Station since the launch of the first satellite in 1978 under the sponsorship of the Defense Mapping Agency (DMA). These trajectories are used as references in a linear Kalman filter estimation program to provide current estimates of the vehicle states which are then used to predict future states. These predictions, after being functionalized, are then broadcast by the satellites in the form of navigation messages. All tra- jectories are computed using the World Geodetic System- 1972 (WGS-72) gravity field model and tracking station coordinates. 51 Single- satellite weighted least squares orbit fits using range difference data derived from smoothed range data for the four GPS monitor sites (Vandenberg, Guam, Hawaii, and Alaska) are done to provide the predicted reference trajectories. Over the years both force and clock model and software system improvements have reduced the average along-track error growth to usually less than 10 meters/day (Beveridge, 1985). Periodic variations about this linear or sometimes quadratic trend also exist. The fitted portions of these trajectories have been made available to the geo- detic community. Additional orbit fits and studies have been conducted at NSWC using this data augmented by data collected at DMA tracking sites in Australia, Seychelles, England, and Argentina. NSWC has also provided extensive analysis support to the GPS Joint Program Office and Master Control Station. With the final transition from the Interim to the Operational Control Segment (ICS to OCS), NSWC's reference generation responsibility ends. At this time NSWC will retain the task of providing highly accurate fitted GPS trajectories and clocks to the geodetic community under sponsorship of DMA. These fits will be based on data from the five OCS monitor sites, DMA tracking sites, and possibly data provided by NGS and NASA. Transfer of the production GPS ephemeris and clock generation responsibility to the Defense Mapping Agency Hydrographic/Topographic Center (DMAHTC) is currently planned for sometime in 198?. To improve the accuracy of the fitted trajectories and clocks a system of computer programs implementing a multi-satellite filter/smoother proce- dure for GPS data reduction has been developed. A Kalman filter was selected to try to account for unmodeled accelerations (e.g., force model errors attributed to model deficiencies in the gravity field, radiation pressure, and thermal radiation models and control system induced effects) and random clock variations characteristic of atomic clocks. A fixed- interval smoother was selected because processing is done after the fact so that estimates at a given time can be based on both past and future data. A multi-satellite approach was adopted to allow for optimal separation of satellite and station clock offsets, to allow for multi- satellite station navigations, to accommodate use of a doubly differenced data type involving two satellites simultaneously, and to accommodate the proposed cross-link ranging data. This system of programs will be referred to as the Multi- Satellite Filter/Smoother (MSF/S) in the rest of this paper. MULTI- SATELLITE FILTER/ SMOOTHER OVERVIEW GPS Data Flow Figure 1 gives a simplified flow of GPS data starting after preprocessing and smoothing of the data. Either ICS or OCS data are merged with the DMA data and possibly other data to give a time-ordered smoothed observation file. Smoothed pseudo- range data is usually available every 15 minutes. 52 / INITIAl \ IcONWTIONSr"^ C0«RK10«/ EDITOI MuiusATfiirre FIlTtR/SMOOTHK Figure 1. GPS Data Flow The integrated Doppler data is not smoothed but sampled every 15 minutes or less. Any further processing requires the generation of a reference tra- jectory for each satellite using NSWC's orbit computation program called CELEST (O'Toole, 1976). These trajectories must be within the linear region of convergence relative to the true trajectory since a linearized estimation process is used. The Corrector/Editor is executed next and operates in a single- satellite mode. The Corrector adjusts the observed value as required to account for time transmission effects, tropospheric refraction effects, the periodic component of the relativistic effect, the effect of the displacement of the electrical phase center of the antenna system from the center of gravity of the satellite, and the effect of solid earth tides on station heights. ICS data have had all corrections except for solid earth tides previously made. OCS and DMA data have not been corrected at all. The Editor does polynomial fits to residuals formed by differencing a computed value based on the reference orbit with the observed value. Consistency checks of the after- fit residuals are used to identify bad points. Only range and range difference (integrated Doppler) data types can be edited. Byproducts of the editing procedure are nominal clock offset estimates for all clocks relative to a master clock and the approximate times and magnitudes of planned or anomalous clock events such as Z-count adjusts, C-field adjusts, and time or frequency jumps in either the satellite's or stations' clocks. The result of the Corrector/Editor is then an edited file of observations with all known deterministic corrections made except removable of nominal clocks. Finally the Multi- Satellite Filter/ Smoother is executed to provide the precise ephemerides and clock estimates. In addition to the reference trajectories, corrected and edited data, and nominal clock information 53 including events, the MSF/S system of programs requires various input including the overall program flow, quantities defining the time spans for the fit and each data type, lists of satellites and stations to be pro- cessed, the solution parameter set and a priori statistics, master station selection (if any), inertial-to-earth-fixed transformation information including earth orientation information, and the diagnostics and output desired. The MSF/S system produces both inertial and earth-fixed trajec- tories, satellite clock offsets from GPS time (actually both time and frequency offsets), earth orientation solutions, and diagnostics in the form of plots of the corrections and their sigmas, after-fit residual plots, and correlation coefficient matrices. The MSF/S system can also be executed in a mode in which previously computed orbits and satellite clocks are input and held fixed, and stations are then navigated, i.e. station coordinates and clocks are solved for. Data for stations at known locations both included and not included in the orbit fitting procedure can be used to evaluate the accuracy of the fitted orbits and clocks. Estimation Concepts The MSF/S system utilizes a linear Kalman filter (assumes linear state equations and measurement model) followed by a smoother as the form of the estimation equations. Linearization is done about the reference trajectory, nominal clock offsets (which may contain jumps), and nominal values for all other parameters. This of course means that the filter states are actually corrections to nominal states and the measurements are processed as residuals. Therefore partial derivatives are required that relate the states at one time to a previous time (state transition matrices) and that relate the measurements to the states (measurement matrices). All partial derivatives are evaluated based on the nominal trajectory and parameter values. There is no relinearization of the measurement model about the estimated states. The mini-batch concept is also employed in the MSF/S system. In this concept all measurements in a specified interval (typically 1 hour or less) are processed in a batch mode. This is based on the assumption that the process noise contribution to state uncertainties can be ignored over intervals much shorter than the time constants of the linear system model. This essentially averages out the random effects over the interval chosen, which primarily affects the clock estimates for GPS. Another effect is that solutions are only available at the mini-batch steps. However, the form of the stochastic state equations relating to the trajectory was chosen so that deterministic propagation of the trajectory corrections between steps is exact. Both the orbital element and clock states are treated as pseudo-epoch state parameters. This means that they are the epoch state corrections which would have occurred had the process noise been zero. These states can then readily be mapped to current state corrections using the state 54 transition matrices. This definition was adopted so that the partial derivatives generated simultaneously with the reference trajectory generation could be used directly as in a batch fit and so that the clock model would reduce to a polynomial function of time if its process noise terms were zero. The square root information implementation of the estimation equations was selected for the MSF/S system (Bierman, 1977). These equations are mathematically equivalent to the classical Kalman filter/ Rauch-Tung-Streibel smoother equations (Rauch, et al., 1965). A square root approach was selected because of its accuracy and stability characteristics in handling large state and measurement vectors. The information form (as opposed to the covariance form) was selected because the smoother results are of primary interest (in this implementation filter solutions never need to be computed), the measurements have been previously edited, and covariance information is required only occasionally. Parameter Set and Models Table 1 provides a list of the possible parameters by type, name, and the assumed models. The stochastic state equations in discrete form are given by (1) where j refers to the j-th mini-batch time step and (wj) is a white noise vector with covariance Qj. Only the stochastic (p) parameters are being driven by white noise. However since the x parameters (pseudo-epoch orbital elements) are dynamically related to the orbit-related stochastic parameters through the Vpj matrix, both the p and x parameters are smoothable. This form of the state equations was selected for the MSF/S system for effi- cient handling of the multi-satellite capability within the square root information formulation and maximum utilization of the available partial derivatives and other precomputed quantities from CELEST. When the orbit-related parameters are viewed together several comments apply. With just one set of orbit- related stochastic parameters and pseudo- epoch orbital elements states being solved for, the orbit model is equiva- lent to solving for position, velocity, and acceleration corrections with the acceleration corrections constrained to be zero mean Gauss-Markov or random walk processes. The radiation pressure and unmodeled acceleration parameters are not solved for simultaneously. If radiation pressure parameters are chosen, they can be viewed as solving for acceleration corrections along the satellite-sun line and y-axis directions. This is 55 Table 1 MSF/S Parameter Set and Models Parameter Type Stochastic (p) Orbit-related Measurement- related Time-varying (x) Bias (y) Station-related Orbit- related Parameter Name Radiation pressure Unmodeled accelerations Tropospheric refraction Satellite clock Station clock Pseudo-epoch orbital elements Station coordinates Polar motion Radiation pressure Thrust Gravity model coefficients Model Scale factor for radiation pressure and y-axis acceleration- both states modeled as 1st order Gauss-Markov (or random walk) processes Radial, along- track, and cross- track accelerations - states modeled as 1st order Gauss- Markov (or random walk) processes Zenith refraction- state modeled as 1st order Gauss-Markov (or random walk) process 3rd order linear system with white noise inputs 2nd order linear system with white noise inputs a, e sin oj, e cos oj, I, M<-a), fi Local- vertical system (ENV) Pole coordinates, length of day Scale factor for radiation pressure and y-axis acceleration Radial, along-track, and cross- track components Unnormalized Same as MCS Partials from CELEST because the radiation pressure acceleration is almost constant throughout the orbit (except during eclipse) so that the scale factor parameter is just scaling this acceleration. If unmodeled acceleration parameters are chosen, the acceleration corrections solved for are just resolved into different directions. The bias radiation pressure parameters can be used with either of the stochastic orbit-related parameters to account for non-zero mean values for these parameters. A continuous thrust would serve the same purpose. These bias orbit-related parameters would primarily be used to emulate batch fits using the Filter only. 56 The stochastic model for the satellite clock in current state variables is given by A¥ = frequency drift At = frequency offset (2) At = time offset where At = t. (mini-batch step interval) and the w. 's are white 'J+1 ' ^3 noise terms with spectral densities q^'s. Typical use of this model assumes that q^ = 0, i.e. frequency drift is modeled as a constant. Under this assumption the model for the frequency offset state, Af f is equivalent to a constant plus the integral of the frequency drift state, A¥, plus the integral of white noise (a random walk). The model for the time offset state, At, is then equivalent to a constant plus the integral of the fre- quency offset state, Af, plus the integral of white noise. Therefore the noise contribution to the At state consists of the integral of the sum of white frequency noise and random walk frequency noise. The term called frequency offset is therefore not an instantaneous value because it does not include white frequency noise effects. All of this implies a one-to-one correspondence between the white noise spectral densities q^ and q^ for the clock model and an Allan variance profile as given in Figure 2. The Allan variance corresponding to the model is the sum of the individual white frequency noise and random walk frequency noise Allan variances. 10 -11 10 -14 10 ALLAN VARIANCE Gy^ (T) = ^ + ^L , q, = .3 10 10' 10" 10" AVERAGING TIME T (SECONDS) Figure 2. Correspondence Between Clock Model Spectral Densities and Allan Variance 57 Measurement Model As mentioned in the GPS Data Flow section above, all data to be used in the MSF/S system have been corrected for known deterministic effects. Therefore the observation equation is considerably simplified. For pseudo- range data the nonlinear observation equation is given by Do«»« -J^ —"'^^'l. Ik nom. . nom.\ Range = T ^ - r ^ + c(At ^ - At ^ I sat. sta.l V sta. sat./ ,_. (AT At ^ -At ^ W R sta. sat. 7 o-ir, TT ref. sin E where ^hsl-l. - ''eference inertial satellite position T|f|; = reference inertial station position ATsPai = nominal station time offset ATsat.' = nominal satellite time offset I all at the ATsta. = station time offset solution parameter / observation ATgat. " satellite time offset solution parameter y time ACr = zenith tropospheric refraction solution parameter E = elevation angle c = speed of light The linearized measurement model then requires that residuals and partials of data with respect to solution parameters be computed. The residual is computed by evaluating this expression with ATsta. » A^sat.' ^^^ ^^R ^®^ to zero and subtracting this result from the observed value. To obtain the measurement partial derivatives, explicit partials with respect to ^sat.» "^sta.» A^sta.' A^gat. ^^^ ^^R ^^^ computed first then the chain rule is applied to obtain the partials with respect to the solution parameters. The nominal clocks may contain jumps as determined in the editing procedure mentioned above. Adjustment of the clock state noise covariance matrices is done at mini-batch times in the neighborhood of these jumps to account for the uncertainty in their estimates. In a navigation- type run the satellite clock terms are replaced by the total clocks (nominal plus smoother solution) obtained previously. The MSF/S system can also process integrated Doppler data in the form of correlated range difference data. Both pseudo-range and correlated range difference data can also be processed interferometrically accounting for the correlation of measurement errors that results from differencing. This is accomplished without actually differencing by properly adjusting the satellite clock model statistics (station clock model statistics also if double differencing is desired) to solve for an appropriate clock parameter for each group of measurements. A complete mathematical description of the MSF/S system is contained in Swift, 1985. 58 RESULTS Six weeks of data for a period starting in late June of 1984 have been processed using the orbit/clock determination system just described. Each fit span was a week in duration and contained data for four satellites (SV06, SV08, SV09, and SV11) for the first 2 weeks and five satellites (+ SV13) for the other 4 weeks. The data consisted of smoothed pseudo-range data from the four GPS monitor sites and DMA's Australia tracking site and integrated Doppler (range difference) data from DMA's Seychelles tracking site. Only 4 weeks included Seychelles data and SV13 was not tracked by Seychelles during this period. Data from the DMA tracking sites in England and Argentina were not usable during this period. The data were processed in 1-hour mini-batches and minimum observation uncertainties of 60 cm on the pseudo-range and 20 cm on the range difference were assigned. For each satellite the solution parameters were: 1. Radiation pressure with steady-state uncertainties of .01 on the scale factor parameter and 10""^^ km/sec^ on the y-axis acceleration parameter and both with decorrelation times of 4 hours 2. Pseudo- epoch orbital elements 3. Clocks with state noise covariances based on the Naval Research Laboratory's clock analysis Allan variances (McCaskill, et al., 1983,1985) For each station, except for the master station, the only solution parame- ters were clocks with state noise covariances based on the specifications for the station Hewlett-Packard cesium clocks. In addition the pole coordinates were solved for. After the orbit/clock fits were done the updated orbits and clocks were held fixed and the same data reprocessed but this time solving only for the station coordinates and the station clocks, now including the clock for the master station. The station coordinate solutions are referred to below as navigations and are one of the three diagnostics used to summarize the fits. The other two are the after-fit residuals and the RMS trajectory differences between those estimated by the MSF/S system and the fitted portion of the standard four-station references. Table 2 is a summary by satellite and by data type of the after-fit residuals RMS'd over all the weeks processed. All satellites were using rubidium clocks during this period except for SV13 which was using a cesium clock. Range measurement uncertainties computed in the smoothing process at the MCS are typically on the order of 60 cm. The range difference measurement uncertainty is on the order of 4 cm (Hermann, 1981). Low-level systematic trends are present in the after-fit residual plots for both the pseudo-range and range difference data. These trends probably indicate a residual orbit error in addition to station coordinate and earth orientation errors. 59 Table 2 After-Fit Residuals Satellite Ranee SV06 103 SV08 89 SV09 78 SV11 85 SV13 65 Overall 85 RMS RESIDUALS (cm) Ranee Difference 11 12 21 18 — 16 Table 3 is a summary by station and component of the navigations averaged over all the weeks processed. The standard deviations indicate that the navigation solutions are consistent from week-to-week especially for the horizontal components and for range data. The actual navigations values are consistent with the one-sigma WGS-72 coordinate uncertainties of 1 m per component except for Australia. The possibility of an Australian station height coordinate error is being investigated. Table 3 Navigations Navigation Components fern) East North Vertical Station Me^n §.D, Mefm §,D, Me^rj 3,D, Vandenberg -6 5 10 5 145 26 Guam -49 29 27 8 -5 20 Hawaii -35 16 -32 15 -14 45 Alaska 14 7 -19 5 -3 28 Australia -136 10 24 25 450 84 Seychelles -70 49 -192 58 46 39 Table 4 is a summary of the RMS (and peak) differences by satellite and by component between the MSF/S-derived earth-fixed trajectories and the fitted portion of the standard earth-fixed reference trajectories RMS'd over all the weeks processed. These results indicate that the two orbit-fitting procedures produce significantly different trajectories. These differences in conjunction with the above residual and navigation results indicate an as yet unquantified orbit accuracy improvement. Additional analysis using station data not included in the orbit/clock fits is required to evaluate the actual accuracy obtained. 60 Table H RMS and Peak Differences Between the MSF/S-Derived Trajectories and the Fitted Portion of the Standard Reference Trajectories Trajectory Differences (m) Sat^lUte Radial Tangential Normal RMS Peajc £MS Peak RMS peak SV06 1.6 3.8 14.8 42.0 10.1 24.5 SV08 1.0 3.2 8.3 23.7 6.6 19.1 SV09 1.8 5.6 15.3 43.3 9.8 24.8 SV11 .8 2.6 7.9 23.3 6.8 18.2 SV13 1,0 3.^ 9,0 27.1 10.5 25.2 Overall 1.3 5.6 11.5 43.3 8.9 25.2 FUTURE WORK NSWC plans to process an additional 10 weeks of data from last year using the procedures summarized above. When OCS takes over control of the GPS constellation all of NSWC's ephemeris and clock estimates will be produced using this new software system. All processing is currently based on WGS-72 but will be converted to WGS-84 when the OCS converts in July 1985. Starting this summer DMA plans to start deploying fixed-site tracking equipment utilizing the TI4100 geodetic receivers. The first three receivers will replace equipment currently in use in England, Australia, and Argentina. Further units will be deployed as available to as yet to be defined locations. Both the OCS monitor site receivers (built by Stanford Telecommunications, Inc.) and the TI4100 receivers will provide smoothed pseudo- range and integrated Doppler measurements. This should provide a worldwide set of highly accurate measurements for orbit/clock determinations. Studies will be conducted using this data to determine the optimum way to determine the GPS orbits and clocks. Other studies will be conducted to evaluate the earth orientation data obtained using GPS. ACKNOWLEDGMENTS The author gratefully acknowledges the programming support provided by D. Clark, H. Ball, M. Eward, E. Durling, L. Gordon, J. White, and L. Hawkins, and the analysis support provided by W. Gouldman, M. Breslin, P. Beveridge, J. Carr, V. Curtis, and M. Thomson. 61 REFERENCES Beveridge, P.E., 1985: Private communication.. Bierman, G.J., 1977: Factorization Methods for Discrete Sequential Estimation ,, Academic Press, New York. Hermann, B. R., 1981: Formulation for the NAVSTAR Geodetic Receiver System (NGRS), NSWC TR 80-348, Naval Surface Weapons Center, Dahlgren, Va. McCaskill, T. B. , Buisson, J. A., and Stebbins, S. B. , 1983: Frequency Stability Analysis of GPS NAVSTARs 3 and 4 Rubidium Clocks and the NAVSTARs 5 and 6 Cesium Clocks, NRL Report 8778, Naval Research Laboratory, Washington, D.C. McCaskill, T.B. , and Buisson, J. A., 1985: "Orbit Frequency Stability Analysis of NAVSTAR GPS Clocks and the Importance of Frequency Stability to Precise Positioning, " Proceedings of the First International Symposium on Precise Positioning with the Global Positioning System, Rockville, Md. O'Toole, J.W. , 1976: CELEST Computer Program for Computing Satellite Orbits, NSWC TR 3565, Naval Surface Weapons Center, Dahlgren, Va. Rauch, H.E. , Tung, F. , and Striebel, C.T. , 1965: "Maximum Likelihood Estimates of Linear Dynamic Systems," AIAA Journal, Vol. 3, No. 8, pp. 1445-U50. Swift, E. R., to be published: Mathematical Description of the GPS Multi- Satellite Filter/ Smoother, NSWC TR, Naval Surface Weapons Center, Dahlgren, Va. 62 INTERFEROMETRIC DETERMINATION OF GPS SATELLITE ORBITS R.I. Abbot, Y. Bock, C.C. Counselman III, R.M. King Department of Earth, Atmospheric, and Planetary Sciences Massachusetts Institute of Technology Cambridge, Massachusetts 02139 S.A. Gourevitch and B.J. Rosen Steinbrecher Corporation 185 New Boston St Moburn, Massachusetts 01801 ABSTRACT. One-way phase observations of GPS satellites at three ground stations were differenced between stations to form interf erometric observations. These single-difference observations were differenced between satellites to form double-difference observations. We analyzed the one-way, single-, and double-difference observations by least-squares to determine the orbits of the satellites. In most cases the formal standard errors of the estimated satellite positions ware of the order of several meters — equivalent to a few parts in 10 of the orbit radius. The actual errors of the estimated orbits are unknown, but we were able to test the day-to-day precisions by using these orbits to analyze observations from an independent pair of stations, to determine the baseline vector between them. The results of this analysis confirmed the uncertainty estimate of a few parts in 10 . Further confirmation was obtained from a comparison of orbits estimated from disjoint, but interleaved, spans of observations. 63 INTRODUCTION If the NAVSTAR Global Positioning System (GPS) is to be useful for crustal motion monitoring, the orbits of the GPS satel I i tes^wi 1 1 need to be known with uncertainties of the order of 1 part in 10 or less. This level of accuracy has not been achieved. A major problem has been the instability of the cesium-beam frequency standards which are employed in most of the present tracking stations. To show that interferometric observations by stations equipped with hydrogen-maser frequency standards can yield better accuracy, we have installed the dual-band tracking receivers of the Air Force Geophysics Laboratory at the NEROC Haystack Observatory in Florida, and at Harvard College Observatory's George R. Agassiz Station errors, then we conclude that the rms errors in the orbits are no worse than 3-4 m in any component. These errors, like the formal uncertainties, are about a factor of two smaller than the orbital errors deduced for the January analysis. DISCUSSION AND CONCLUSIONS The post-fit residuals from a typical set (day 219> of single-difference and double-difference observations from the August observations are shown in Figure 2. The appearance of systematic, common-mode variations in the single-difference residuals suggests that the largest source of error in our 66 analyses is the unmodeled fluctuations in the local oscillators. Although we can't rule out a contribution from the receivers themselves, we have independent evidence that much of the fluctuation is due to the variations in the relative phases of the hydrogen maser frequency standards at the sites. These variations should cancel in double-differences. Other potentially significant sources of errors are variations in the tropospheric path delay, any uncorrected cycle slips, and unmodeled accelerations of the satellites. We conclude that we have not yet reached the accuracy goal of 1-in-lO . With a more complete constellation of satellites, and perhaps additional tracking stations, it will be possible to use only double-difference observations to determine the orbits. Since double-differences are free of the effects of receiving-site frequency-standard instability, it should be possible to determine the orbits more accurately than we have been able to do. In our January and August experiments we had too little double-difference data because there was too little two-site, multiple-satellite, mutual visibility. ACKNOWLEDGEMENTS Research at N.I.T. has been supported by the U.S. Air Force Geophysics Laboratory (AFGL>, Geodesy and Gravity Branch, under contract F19628-82-K-0002. 67 REFERENCES Bock, Y., R.I. Abbot, C.C. Counselman III, S.A. Gourevitch, R.M. King and A.R. Paradis, 1984: "Geodetic Accuracy of the Macrometer Model V-IOOO", Bulletin Geodesique. 58 . pp. 211-221. Bock, v., R.I. Abbot, C.C. Counselman III, S.A. Gourevitch, and R.W. King, 1385: "Three-Dimensional Geodetic Control by Interf erometry with GPS: Processing of GPS Phase Observables", these proceedings. Lerch, F.S., S.M. Kiosko, and G.B. Patel, 1982: "A Refined Gravity Model for Lageos (GEM L-2>", Geophvs. Res. Lett.. 9 . pp. 1263-1266. Seppelin, T. 0., 1374: "The Department of Defense World Geodetic System", Canadian Surveyor. 28 . pp. 436-506. 68 ITT ~y^ •ft I I — -c£^ — I — I— o in o ID O O ID o in* o o ID o ID o m f f 1 EH 1 tn 1- •r 1 ^ T in 1 4J I 0) u 00 69 INTERFEROMETRIC PHASE RESIDUALS HAYSTACK — RICHMOND EQUIV. RANGE (CM) 10 - -10 - SINGLE DIFFERENCES (P O.OOh. 6^ <^e\»^vji.^4s; a NS 1 O NS 4 ^ NS 6 + NS 8 y NS 9 ■<^ X 10 - oo '^^^.-Jt^^ A'^ + ++ -x- -10 - DOUBLE DIFFERENCES a NS 1 - NS 9 O NS 4 - NS 8 ^ NS 6 - NS 8 + NS 9 - NS 6 -T- 20 -1— 22 18 MRS UTC on 6 - 7 AUGUST 1984 (DAY 219) Figure 2. Single-difference and double-difference phase residuals from the Haystack-Richmond baseline, day 219. 70 Table 1: Estimated uncertainties in satellite orbital positions between orbits determined from A (days 215,217,219) and B (days 216,218,220) data sets. Sate 1 1 ite Radial Al ong- track Ac ross-track NSl 1 m 6 m 4 m NS4 2 11 2 NS6 2 11 1 NS8 1 7 1 NS3 1 4 2 72 GPS ORBIT IMPROVEMENT AND PRECISE POSITIONING by E.J. Krakiwsky, B. Wanless, B. Buffett, K.P. Schwarz, M. Nakiboglu Division of Surveying Engineering The University of Calgary Calgary, Alberta, Canada Positioning accuracy using GPS satellites is limited by, among other factors, the precision with which the orbits are known. In the event of GPS ephemerides degradation for civilian use, the capability of orbit improvement takes on a higher level of importance. The authors outline a method for improving the accuracy of orbits, where perturbation theory is used to characterize the orbit. Corrections to the satellite pass initial conditions are obtained to improve the orbits, which can in turn be used to achieve precise positioning results. Mathematical models and resulting adjustment equations for rigorous orbit improvement and precise positioning are given. A simulation scheme is outlined for orbit improvement over Canada, and the results of this investigation are presented. INTRODUCTION The spectrum of GPS researchers is delimited on one end by those who do orbit determination and on the other end by those who investigate how to obtain point positions. In this paper we report on research that is directed towards the dual task of orbit improvement along with precise positioning. By orbit improvement we mean the correction of an orbit over a short arc of about four hours. With the estimation method reported herein it is possible to improve orbits which are in error as much as 200 m. The motivation for this research is two-fold: (1) GPS ephemerides may be degraded for civilian use; and (2) present discrepancies in reported results for independent solutions of station coordinates range from 5 to 18 cm [e.g. Goad and Remondi, 198A; Beutler et al., 1984; Beck et al., 1984], which, for the lengths of lines encountered, implies orbit errors ranging from 20 to 50 m. Clearly, before the full potential of GPS can be realized, orbit errors, along with other biases like timing errors, must be incorporated into the adjustment model and estimated along with station coordinates. The underlying philosophy of The University of Calgary's approach to solving this problem is that a judicious amount of orbit modelling should be done so that only a limited amount of orbit correction would be forthcoming from the adjustment process itself. The extent of the orbit modelling is discussed first. Then the adjustment process is described for three distinct modes: orbit improvement mode; positioning mode; and the mode in which both positions and orbits are part of the solution. The roles that different GPS observables 73 (ranges, range differences - Doppler, and phase) play in orbit improvement is described. Finally, a possible network configuration is given for improvement of GPS orbits over Canada. GPS ORBIT MODELLING AND COMPUTATION GPS orbits first need to be appropriately modelled and then their compu- tation can be made. At the outset it was determined that to support a relative baseline accuracy of 1 X 10 , an orbit accurate to 2.5 m is needed [Nakiboglu et al., 1984]. Hence, any force model must include all perturbing forces which meet or exceed this accuracy for an orbital arc of about one- third of a revolution. The investigation of the force model is based on a linear first order perturbation solution of the Lagrange planetary equations [Kaula, 1966]. Table 1 contains the perturbing forces that significantly influence the motion of GPS satellites over time intervals of four hours. They include the non-central component of the earth's gravitational potential C- and higher order geopotential coefficients, the gravitational influence of tne sun and the moon (third body effects), and solar radiation pressure. Other perturbing forces such as those due to atmospheric drag, albedo radiation and tidal effects can be neglected from the analysis due to the high altitude of the GPS orbits and the short orbital arcs being considered. The detailed descriptions of the perturbing forces are given in the following [Kaula, 1966; Kozai, 1963, 1973; Lala, 1971; Gaposchkin, 1973; and Giacaglia, 1973]. It is worthwhile noting that the along track perturbation is dependent upon(a), M) , the radial component on (a, e) , and the out of plane component on (i. fi). Table 1 Typical Orbit Perturbations ^v,^,^^ Perturb. Perturbations in Metres ^*>v.^^ Effects Higher Orbital^ V,^^^^ Order Lunar 3rd Solar Elements ^^•V,^^ So Geopot. Body Radiation* a 2600 20 220 5 e 1600 5 140 5 i 800 5 80 2 fi 4800 3 80 5 w+M 1200 40 500 10 —7 — '' *Assuming an acceleration of 10 ms Even though the force models have been chosen to yield an orbit accurate to 2.5 m with reference to the geocentre, we can still expect large unaccounted for orbital errors to occur in the three principle directions mentioned above. This is mainly due to the limited number of permanent tracking stations. This information is used in the context of the adjustment process. Once having modelled the orbit, the next task was to investigate ways to compute it. Two approaches were examined - the analytical solution and the numerical solution. The analytical solution represents a straightforward extension of the linear perturbation theory used in the analysis of the force 74 model. In general, linear solutions are sufficient to yield orbits to an accuracy of 2 m for all components of the force model excluding the predominant effects due to C-_ [Gaposchkin, 1973]. Investigation revealed that second order perturbations due to C _ were about 30 m, and hence, were included in the analytical solution using a Taylor's series approach in orbital elements accurate to about one metre. It should be noted that the second order development requires only a marginal increase in computation time and consequently will not significantly affect any conclusions made about the relative efficiency of analytical methods over numerical so- lutions. Second order effects of C _ can be reduced by an order of magnitude through the use of Hill variables [Butfett, in prep.]. The numerical method of solution adopted for computing the orbit is based on the direct integration of the equations of motion in Cartesian coordinates, often referred to as Cowell's method [Conte, 1962]. Cowell's method has the advantage of a simple formulation for the equations of motion. Consequently, a shorter step size is required, although this is not a serious restriction given the short arc lengths being considered. A comparison of the analytical and numerical approaches results in the conclusion that the numerical approach is computationally more efficient. ESTIMATION MODEL The unknown parameters to be estimated have been partitioned into three groupings: (1) The first set comprises tracking station coordinates [x., y , z.] and are denoted by the vector x. (2) The second set are the sextuplets of Keplerian orbital elements [a, e, i, fi, 0), M] corresponding to the initial conditions for each short-arc observed and are denoted by the vector z . (3) The third set being those nuisance parameters corresponding to: (i) unaccounted for tropospheric refraction (C„); (ii) corrections to satellite clock polynomial coefficients (a , a^ , a.) ; (iii) receiver clock polynomial coefficients (A , A^ , A-); (iv) range at lock on time (r , for Doppler only) ; (v) the single phase difference ambiguity parameter (N^ , one for each tracking station relative to a master station and satellite pass) ; and (vi) an unknown scale factor to account for solar radiation pressure in the force model. In the present prototype program package, this third set has been included in the vector of unknowns x. In a future version of this package, it is contem- plated that the nuisance parameters will be divided into those that are pass dependent and included within the z vector, and those that are station depen- dent will be included in the vector x. The observables, denoted by the vector I, are ranges, range differences and single difference phases. Covariance information is assumed available for the observables and is denoted by C . As well, the model has, as an option, the possibility to include a priori information on the vectors x and z , and the corresponding covariance matrices are C and C . ° x z 75 The estimation model used is comprised of two sets of functions f. and f- relating the vector of ground station Cartesian coordinates x, satellite Cartesian coordinates x' , and the initial state Keplerian elements z , to a vector of observables I, In equation form we have f^(x, x', il) = , C^ . Cj^ (1) f2(x' + s, z^) = , C^ , C^ (2) where f. corresponds to a pure geometric mode model, while f_ is the relationship between the initial conditions and the satellite state vector at an arbitrary epoch. That is, f- is the explicit solution of the equations of motion in terms of the initial conditions. Note that incorporated into the model is the provision to treat f_ as imperfect, and that this imperfection is regarded as a signal. This means that an a priori covariance matrix C will have to be provided at the beginning of the estimation process. The results presented in this paper, however, do not consider the signal component. The linearized form of the models are: A 6x + A ,6x' + w = r , (3) X x' where 6x' = B6z 'h 'h A = X x' 8x * ~ 3x' ' (4) w = f^(x%x'°,)l) B = B, B„ = 9x' 3z(t) 1 2 3z(t) * az o and fix, 6x' and r are corrections to the approximate values of the unknowns x°,x'**, and the observations !i. The pure positioning mode is obtained by inserting very small elements on the diagonal of C and delete the matrix C . The orbit determination mode is obtained by inserting very small elements in C and relaxing the elements in C or by deleting C altogether. When C and C are both relaxed, the improve- ments will be made to both the ground stations and orbital parameters. To incorporate orbit improvement capabilities into the least-squares adjust- ment, the six initial conditions (z ) used in the solution of the equations of motion are introduced as weighted parameters (C ). In addition, a solar radiation pressure constant is also included as a weighted parameter to resolve the uncertainty in the solar radiation component of the GPS force model. For 76 present purposes, the initial conditions are expressed in terms of the Keplerian orbital elements z , although it should be noted that this choice is not unique. The solution of the differential equations of motion using the first ap- proximation of the initial conditions is found using the numerical integration method. For GPS orbits, the numerical procedures have the advantage of accuracy and computational efficiency. For the subsequent solutions of the differential equations of motion using the updated initial conditions, the analytical method of solution is utilized in a perturbation scheme where the errors in the initial state vector (6z ) are propagated forward in time. The analytical solution, based on a linear perturbation theory, is used in the evaluation of the linearized constraint imposed on the observation equation. The constraint 6z(t) = B_6z (5) z relates the changes in the Keplerian initial conditions, 6z to the changes in the osculating Keplerian e]ements, 6z(t) at time t. This is further transformed into satellite Cartesian coordinates by 6x' = B^6z(t) , (6) which is needed to evaluate the misclosure term w during the iteration process. Due to the high altitude of the GPS satellites, the Jacobian matrix can be constructed using a linear perturbation theory that incorporates only the second zonal harmonic. Consequently, the resulting elements of the Jacobian matrix can be computed efficiently by comparison with the computations required to numerically re-integrate the differential equations of motion using the com- plete force model [see Nakiboglu, et al., 1984]. Comparisons of the results obtained from numerical integration using the complete force model with those based on the linear perturbation theory using C only, indicate that errors in the initial conditions of approximately 200 m can be propagated rigorously to within 1 m for orbital arcs of up to four hours. The comparisons demonstrate the limitations in the use of a non-varying Keplerian orbit in propagating initial condition errors even for the high altitude GPS satellites. ROLE OF DIFFERENT OBSERVABLES ON ORBIT IMPROVEMENT The ability to resolve errors in GPS orbit elements is mainly dependent upon the tracking network geometry, the observation accuracy and the observational inner geometry. Computer simulations were run to analyze the different influences of pseudorange, Doppler and single difference observations on orbit improvement. The results of these tests are presented in this chapter. Pseudorange measurements produce intersecting spheres, and have geometric strength in the line connecting the satellite and observing station. Alterna- tively, Doppler measurements produce intersecting hyperboloids and have strength in the direction of satellite velocity. The geometric strengths of pseudorange and Doppler measurements are orthogonal to each other, and this property has been presented in previous studies [e.g. Hatch 1982; Jorgensen 1980]. Single difference phase measurements produce intersecting hyperboloids, intuitively resembling Doppler measurements in their geometric strength. 77 The eighteen satellite, uniform GPS constellation was simulated using typical orbital parameters. Ground traces produced by the eighteen satellites are shown in Parkinson and Spilker, [1984]. The three satellite arcs CI, D3 and E3 used in the simulations are depicted in Fjwijre 1, . yx Figure 1: Satellite Constellation Ground Tracks from Parkinson and Spilker, [1984] 78 The adjustment program 'astro' [Wanless, in prep.], developed under this research, was thoroughly tested using observations simulated in program 'difgps', developed at the University of New Brunswick [Davidson et al., 1983]. Test runs were made with true satellite and ground station parameters and perfect observations. These tests produced adjustment residuals equal to zero, indicating the formulation was programmed correctly. Test runs were also made with satellite or ground station parameters changed by known amounts and observations corrupted with random error. These tests converged to the correct solutions, indicating the adjustment formulation was working correctly. Pseudorange, Doppler and single difference observations were simulated for the three satellite arcs over Canada from Network A (see Figure 2). The three observation types were processed independently in 'astro' to enable a compari- son of the effect each type has on orbit determination. The default one sigma observation accuracies used were 2.0 m for pseudorange and 0.1 m for Doppler and single difference phase. These accuracies reflect receiver random error, atmospheric modeling error, satellite group delay and multipath, and are taken from Martin [1980]. The one sigma values were also chosen to agree with those of Varnum and Chaffee [1982], who state the ratio of Doppler to range accuracies is 20 to 1 for GPS satellites. The observational inaccuracies due to satellite position errors and oscillator instability are not included in the values used since these inaccuracies are explicitly propagated into the solution through a priori covariance information. The ability of each observation type to detect an error in the , satellite initial conditions was tested by inserting a 50 m bias (1.8 x 10 radians) in one orbital element at a time. The a priori standard deviation for the biased element was increased to 50 m to reflect this error. Observations for Network A and corresponding to four hour passes of satellites CI, D3 and E3 were simulated at 60 second intervals with an elevation angle cut-off of 7.5 degrees, resulting in approximately 900 measurements per pass. The detailed solution outputs for single orbit element perturbations are given in Nakiboglu et al. [1985] and are summarized in Table 2. Listed for each observation type are the orbital element that was changed, the absolute error remaining in this element after convergence and its standard deviation, the maximum absolute error induced into another element and its standard deviation, and the number of iterations needed for convergence. The same simulation scenerio was used with satellite E3 to test the capability for resolving errors in multiple orbit elements. Three typical samples of these tests are given in Table 3. 79 NETWORK A Stations : 1, 2A, 3A. 4 NETWORK B Stations : 1, 2B, 33, 4 Figure 2 : Tracking Networks 80 Table 2: Single Orbit Element Errors - £ ;atellite Pass E3 Element Error a of Maximum of Biased by Remaining Element Error Maximum Number of 50 metres in Element Induced Error Iterations (metres) (metres) (metres) (metres) Fseudorange Observations a 0.00 0.09 e 0.00 0.03 6 0.09 0.15 a 0.01 0.03 5 0.84 0.05 e 0.25 0.01 6 0.09 0.05 a 0.24 0.01 6 S^ 0.08 1.23 0.0 N/A 2 0.83 0.05 e 0.22 0.01 6 Doppler Observations a 0.22 0.03 a 0.00 0.01 2 e 0.19 0.01 a 0.37 0.02 3 0) 0.01 0.15 0.0 N/A 2 i 0.09 0.19 a 0.03 0.02 2 a 0.06 0.13 a 0.01 0.02 2 M 0.13 0.15 a 0.03 0.02 2 Single Difference Observations a 0.07 0.07 e 0.12 0.03 2 e 1.68 0.11 a 0.22 0.03 2 0) 0.14 0.30 a 0.01 0.03 2 i 0.24 0.27 a 0.01 0.03 2 fi 0.10 0.14 a 0.01 0.03 2 M 0.08 0.30 a 0.00 0.03 3 The default pseudorange accuracy of 2.0 m had to be decreased to O.IO m to enable these tests to converge. 81 Table 3: Multiple Orbit Element Errors - Satellite Pass E3 Elements Error of Maximum a of Biased by Remaining Element Error Maximum Number of 50 metres in Elements Induced Error Iterations (metres) (metres) (metres) (metres) Pseudorange Observations a e Q 0.40 0.05 4.07 2.96 iMSCCE 7.0 0.09 0.39 1.21 2.59 0.0 2ASCCE 1.0 N/A a 0.12 0.03 b) 0.16 0.19 i 0.16 0.25 n 0.06 MSCCE 0.3 0.19 Doppler Observations e 0.01 0.02 a 0.01 0.11 b) 0.31 0.35 i 0.04 0.33 n 0.20 MSCCE 0.3 0.23 ASCCE 0.2 Single Difference Observations 0.0 ASCCE 0.8 N/A ^ MSCCE = Maximum satellite Cartesian coordinate error. 2 ASCCE = Average satellite Cartesian coordinate error. Multiple orbit element errors were tested in other combinations. Pseudorange observations were unable to resolve simultaneous errors in a i M; a fi M; aeojifi; aewiftM. It is apparent from these tests that multiple angular errors cannot be resolved by pseudorange observations. The combinations of orbit elements in Table 3 were chosen to represent along-track, radial and out-of -plane errors. In terms of sensitivity, the solutions with pseudorange measurements tend to take longer to converge than both Doppler and single difference phase solutions; This is likely due to the relative observation accuracy of pseudoranges being 20 times weaker. The ability of each observation type to solve particular orbit element errors is evident. Pseudoranges appear to recover elements 'a' and 'e' more accurately than the other observations, but have problems resolving errors in 'co', 'i' and 'M' .Doppler and single difference solutions are less accurate 82 and 'e' are in error, but are generally at the one metre level or better for all other combinations. This difference in sensitivity can be attributed to both the observation accuracy, and the different geometry of observations. A distinct advantage in combining the different observation types simultaneously in a single adjustment is evident from the results. The combination of pseudorange and Doppler measurements should provide the ability 'e'. •w to resolve a group of four or five orbit elements, for example 'a', 'i' and *Q\ with a high degree of precision and confidence. This particular combination of observation types is in fact used at the System Master Control Station to compute and predict GPS orbits [Varnum and Chaffee, 1982; Franslsco, 1984]. EFFECT OF TRACKING NETWORK GEOMETRY AND ACCURACY The effect of tracking network geometry on orbit improvement was analyzed by repeating multiple element tests using network B (see Figure 2) . The results of these tests for pseudorange and Doppler observations are given in Table 4. Table 4: Network B Multiple Orbit Element Error Solutions Pseudorange Observations Element :s Error of Maximum of Biased bv Remaining Element Error Maximum Number of 50 metres in Elements Induced Error Iterations (metres) (metres) (metres) (metres) a 0.65 0.16 e 0.42 0.38 (D 1.43 1.16 0.0 N/A 7 i 2.27 0.96 12 0.51 MSCCE 4.0 2.67 ASCCE 1.5 Doppler Observations a 0.25 0.04 n 0.02 0.16 e 0.02 M 0.05 0.14 MSCCE 0.3 ASCCE 0.3 0.02 83 The results using network B are superior to network A, most noticeably in the pseudorange solution, since this combination would not converge using network A. The effect of inaccuracy in the tracking station coordinates was analyzed by treating the coordinates as weighted parameters in the adjustment. The a priori variances for station coordinates were increased and random error commensurate with this variance was applied to the coordinate values. This procedure was applied in steps until the orbit solution was degraded beyond the 2 metre accuracy level. The results of these tests are given in Table 5. Table 5: Effect of Tracking Station Coordinate Inaccuracy Doppler Observations - Satellite Pass E3 Elements Error of Maximum a of Biased by Remaining Element Error Maximum Number of 50 metres in Elements Induced Error Iterations (metres) (metres) (metres) (metres) (1) Stations 1,3,4 o = 0.10 m, random coordinate error applied Relative Accuracy Approximately 0.1 ppm a 0.08 0.09 (D 0.18 0.23 i 0.07 0.57 e 0.01 Q 0.A7 0.62 MSCCE 0. ,5 ASCCE O.A 0.03 (2) Stations 1,3,4 a = 0.50 m, random coordinate error applied Relative Accuracy Approximately 0.5 ppm a 0.31 0.33 0) 0.32 0.41 i 1.89 1.77 n 2.72 MSCCE 2.8 2.53 e 0.01 0.03 3 ASCCE 1.5 The results of these tests indicate that tracking stations must be known to a relative accuracy of 0.1 to 0.4 ppm for orbit improvement to a 2 m accuracy level. These results are generally in agreement with those of Stolz et al. [1984]. CONCLUSIONS The results presented in this paper show that it is possible to do short arc orbit improvement to an accuracy level of 2 metres from four regional tracking stations,' if the stations are known with a relative accuracy of 0.1 to 0.4 ppm. Similarly, orbits of this accuracy will give relative station positions to 0.1 ppm. The force model analysis demonstrated that perturbations due to the non-central component of the earth's gravitational potential, the third body effects of the sun and moon, and solar radiation pressure have to be modelled to achieve this level of accuracy. 84 The simulation studies for orbit improvement over Canada show that a subset of satellite initial conditions can be resolved to produce accurate orbits. The results also indicate that an optimum solution would involve a combination of pseudorange with either Doppler or single difference phase observations. ACKNOWLEDGEMENTS This project is supported by a contract from the Geodetic Survey of Canada, Department of Energy, Mines and Resources under the scientific authority of D. Delikaraoglou. REFERENCES Beck, N., D. Delikaraoglou, K. Lockhart, D.J. McArthur, G. Lachapelle, 1984: Preliminary results on the use of differential GPS positioning for geodetic applications, IEEE 1984 PLANS. Beutler, G. , D.A. Davidson, R.B. Langley, R. Santerre, P. Vanicek, D.E. Wells, 1984: Some theoretical and practical aspects of geodetic positioning using carrier phase difference observations of GPS satellites, Mitteilungen der Satellitenbeobachtungsstation ZJmmerwald No. 14. Buffett, B., in preparation: Short-arc orbit determination for the global positioning system, M.Sc. thesis. The University of Calgary. Conte, S.D., 1963: The computation of satellite orbit trajectories. Advances in Computers, 3, 1-76. Davidson, D., D. Delikaraoglou, R. Langley, B. Nickerson, P. Vanicek, D. Wells, 1983: Global positioning system differential positioning simulations. University of New Brunswick Technicl Report No. 90. Francisco, S.G., 1984: Operational control segment of the global positioning system, lEE 1984 PLANS, 51-58. Gaposchkin, E.M., 1973: Smithsonian standard earth (III) Smithsonian Astrophys. Obs., Special Report 353. Giacaglia, G.E.O., 1973: Lunar perturbations on artificial satellites of the earth, Smithsonian Astrophys. Obs., Special Report 352. Goad, C.C., B.W. Remondi, 1984: Initial relative positioning results using the global positioning system. Bulletin Geodesique, 58, 193-210, Hatch, R. , 1982: The synergism of GPS code and carrier measurements, Magnovax Technical Paper, MX-3353-82. Jorgensen, P.S., 1980: Combined pseudorange and Doppler positioning for the stationary NAVSTAR user, IEEE 1980 PLANS, 450-458. Kaula, W.M., 1966: Theory of satellite geodesy, Blaisdell Publishing, Waltham Massachusetts. Rozal, Y,, 1963: Effects of solar radiation pressure on the motion of an artificial satellite, Smithsonian Contr. Astrophys., 6. 85 Kozai, V. , 1973: A new method to compute lunisolar perturbations In satellite motions, Smithsonian Astrophys. Obs., Special Report 349. Lala, P., 1971: Semi-analytical theory of solar pressure perturbations of satellite orbits during short time intervals, Bull. Astron. , Czechoslovakia 22, 63-72. Nakiboglu, M. , B. Buffett, K.P. Schwarz, E.J. Krakiwsky, B. Wanless, 1984: A multi-pass, multi-station approach to GPS orbital improvement and precise positioning, IEEE PLAN 1984, 153-162. Nakiboglu, M. , E.J. Krakiwsky, K.P. Schwarz, B. Buffett B. Wanless, 1985: Contract report for Energy, Mines and Resources, Surveys and Mapping Branch, Ottawa. Parkinson, B.W., J.J. Spilker Jr., 1984: GPS overview and differential operation, IEEE PLANS 1984, Tutorial notes. Stolz, A., E.G. Masters, C. Rizos, 1984: Determination of GPS satellite orbits for geodesy in Australia, Australian Journal Geod. Photo, Surv., No. 40, 41-52. Varnum, F., J. Chaffee, 1982: Data processing at the global positioning system master control station. Proceedings of the Third. Int. Geodetic Symposium on Satellite Doppler Postioning, 1023-1040. Wanless, B., in preparation: A prototype multi-station, multi-pass satellite data reduction program, M.Sc. thesis. The University of Calgary. 86 FORCE MODELLING FOR GPS SATELLITE ORBITS C. Rizos A. Stolz University of New South Wales, P.O. Box 1, Kensington, 2033, AUSTRALIA ABSTRACT The forces acting on a GPS satellite include those due to the earth's non- sphericity, the direct attraction of the sun and moon, the gravitational attraction of the tidal bulge, and the non-gravitational forces arising from the direct and reflected solar radiation pressure. The effects of these forces on the orbits of GPS satellites have been studied in order to ascertain the level of sophistication of force modelling necessary in GPS processing software. For high precision orbits, up to a few days in length, only the earth's geopotential, the attraction of sun and moon, and the direct solar radiation pressure need be considered. The essential features of each of these models is discussed. INTRODUCTION Although the primary function of the NAVSTAR Global Positioning System is as an all-weather, continuous-availability navigation system, it is also represents the natural successor to the ageing TRANSIT system for surveying and geodesy. GPS will drastically change the v/ay in which many routine surveying tasks are carried out because it will permit the determination of position with higher accuracy, at lower cost and in less time than TRANSIT, and may even rival the traditional EDM- theodolite methods. Unlike TRANSIT, the two functions of real-time navigation on the one hand, and high precision geodetic positioning on the other, are to a large extent, separated in GPS. An essential element of real-time navigation with GPS is the technique of simultaneous pseudo-ranging to 2 to 4 satellites with the aid of C/A and P codes that are modulated on the GPS signals (e.g. Spilker 1978, Payne 1982). However for most surveying applications it is the measurement of the phases of the satellite signals themselves that is the desired observable and an explicit knowledge of the codes is not essential. Therefore, in the surveying and geodesy context it is adequate to visualise the GPS satellite system as a constellation of highly stable orbiting benchmarks equipped with precision clocks. All measurement and processing techniques require the input of GPS ephemerides in order to determine user position. For navigation users the ephemerides are readily available in the navigation message, also modulated on the basic GPS signals (the GPS "broadcast ephemeris"). The accuracy of these ephemerides is presently estimated to be at the 40 - 100 metre level, with occasional sudden degradations in accuracy. Using P code pseudo-ranging and the "broadcast ephemeris", positioning accuracies of 10 - 15 metres are obtainable, while C/A code ranging satisfies navigational accuracy requirements at the hundred metre level. 87 Using GPS carrier phase measurements taken over an observation period of from a half to three hours (to resolve the ambiguities due to the unknown number of whole carrier wavelengths in the satellite-receiver distance), positioning accuracies at the few metre level have been obtained with the "broadcast ephemeris". However as with TRANSIT, higher accuracies are obtained from pro- cessing observations made simultaneously at two ground stations. Operating in this "translocation" mode, relative positional accuracies of a few decimetres over 100 km are obtainable (or a few parts per million in baseline length). The GPS "broadcast ephemeris" does not lead to superior accuracy over that currently provided by the TRANSIT system although accurate results are obtainable in less time and for any length baseline. V/here the so called "codeless" receivers are used, the GPS orbital information has to be provided from an external source because such receivers lack a built-in navigation message deciphering ability. It is the lack of precise GPS ephemeris information that will be the major limiting factor on the accuracy of differential positioning using the carrier phase observable. An adequate rule-of-thumb for estimating the effect of orbit error on position differences (baselines) between two receivers operating in the translocation mode is that a given error in the satellite coordinates introduces an error in the baseline reduced by the ratio of the baseline length to the satellite's altitude. For example, a 2 m orbit error will limit the baseline accuracy to 0.1 part per million of its length, or 1 cm in 100 km, while a 20 m orbit error results in an error of 10 cm in 100 km, and so on. The analyst has to ensure that GPS ephemerides of adequate precision, valid for the observation period in question, are available to perform the task of position determination. In most cases however, only the coordinates of the satellites at widely spaced intervals of time are provided. Under such circumstances orbits needs to be predicted for the time span of the observations using the solution of the relevant initial value problem based on the equations of motion. If the initial values are of poorly known an orbit improvement procedure may be attempted. The solution of the equations of motion requires that the perturbing forces operating on a satellite be modelled. This force modelling capability is necessary for the task of both (a) orbit improvement, and (b) position determination/orbit prediction, or, as is usually the case in high precision applications, a combination of both. The aim of this paper was therefore to investigate the nature of the forces operating on GPS satellites to ascertain the degree of sophistication necessary for modelling both short arcs (a few hours duration) and longer arcs (a few days), to satisfy baseline accuracies of 0.1 - 1 parts per million (or 2 - 20 m in terms of orbit accuracy) . FORCE MODELLING INVESTIGATIONS The perturbing forces investigated were: ^ (1) the earth's non-sphericity (acceleration Rg ) ^ (2) the third body effects of the sun and mooiC(acceleration Rig ) (3) the earth's tidal potential (acceleration R^) (4) the ocean tide potential (acceleration Rq ) 88 (5) the solar radiation pressure (acceleration Rg) (6) the earth's albedo pressure (acceleration Rg) The total perturbing acceleration vector, expressed in an inertial Cartesian coordinate system, is therefore: S = tg + fi3 + S^ + to + tg + tg (1) The equations of motion of a satellite may therefore be written, also in the inertial Cartesian system, as: ^ GM r r = l^^l 3 + t (2) where the first term represents the central force or 2-body motion, r and r are the acceleration and position vectors of the satellite respectively, and R is the perturbing acceleration (equation 1). Models for R have been developed and the solution for the vector r at any time t requires the integration of the three second order differential equations given above, using the initial values of roand roat some time toto define the constants of integration. Direct analytical solution of these equations is not possible. However, by transforming the equations of motion to a more desirable form (e.g. using Keplerian elements in the Lagrangian planetary equations), restricting the com- plexity of the perturbation model and by truncating high power expansions, it is possible to obtain approximate analytical solutions (Kaula 1961, Kaula 1966, Goad 1977). These solutions are useful in order to gain an insight into the effects of the gravitational forces, (l)-(4) above. Nevertheless, they are not usually used for routine orbit computations. For high precision applications, the direct solution of equation 2 by numerical integration using a multi-step Cowell type predictor-corrector is recommended. The main advantage of this approach is that all the perturbing forces can be accounted for (equation 1) and modelled as accurately as possible. The non- analytical surface forces, such as solar radiation pressure and albedo, can be readily included. Furthermore the numerical approach is computationally more efficient than the analytical methods. To understand the behavior of GPS satellites in response to various perturbing forces, we generated four different test orbits, each separated from each other by 90 degrees in longitude, for periods of up to two days duration. Each orbit was integrated first with and then without the perturbing acceleration under study and the satellite position differences were obtained and plotted. The perturbing forces and their effects on GPS orbits are discussed below. 1. The Earth's Gravitational Potential The non-central part of the geopotential which varies as a function of the latitude, longitude and geocentric distance, is usually represented as a spherical harmonic expansion involving the coefficients C ,S . The gravit- nm nm 89 ational acceleration vector Rg is then computed by differentiating the geo- potential with respect to the Cartesian axes (see Cappellari 1976, p4-9 to 4-14 for formulae). The coefficient C2o» representing the earth's flattening, is responsible for the slow precession of the line of nodes of a satellite's orbit around the equator, as well as causing perturbations in its elliptical motion. C20 is approximately three orders of magnitude larger than any other harmonic coefficient. The acceleration due to the central force term in equation 2 is 0.56 m/s , while C20 results in a perturbing acceleration of about 5 x 10 ^m/s^, and all the other terms in the geopotential model only contribute approximately 3 X 10 m/s to the total perturbing acceleration vector. Zonal geopotential coefficients produce primarily long period satellite per- turbations (periods > 1 day), while the even degree zonals produce mainly secular perturbations. The non-zonal terms (those representing the geopotential variation with longitude) give rise primarily to perturbations with periods of less than a day. The case of "resonance" when successive groundtracks of the satellite are exactly separated by an interval equal to the wavelength of the geopotential harmonic deserves special mention. After a certain number of sate- llite revolutions, the groundtrack repeats itself and the satellite's motion is perturbed in an identical manner thus magnifying the earlier perturbations. In the case of GPS orbits, the coefficients of even order lead to resonances of very long period and significant amplitude, but their effects on arcs of up to two days in length is moderated. Because GPS satellites are in high stable orbits of about 20 000 km altitude, they are much less affected by short wavelength features in the geopotential than satellites at lower altitude. A number of gravity field models, complete to degree and order 20 and beyond (for a (20,20) model there are 441 coefficients), have been developed (Lerch et al 1983, Reigber et al 1983). For computing GPS orbits some subset of these model coefficients need only be used. The task is therefore to identify the minimum subset that still satisfies the orbit accuracy requirements for arc lengths of a few days. We find that orbits generated with a geopotential model complete to degree and order 8 (81 coefficients) do not deviate from those generated using a much more complete model by more than a centimeter after two days. Therefore, an (8,8) model can be considered to be a "reference" model for GPS satellite arcs of a few revolutions. In FIGURE 1 we show the effects on two GPS orbits of truncating the geopotential model to degree and order (4,4) as opposed to degree and order (8,8). Also shown are the reduced orbital errors that result when the (4,4) model is augmented with zonal and even order coefficients to degree 8. The two orbits were selected from the four tested to illustrate the high sensitivity of individual orbits to truncated geopotential models. Note the large improvement on using the augmented (4,4) model for orbit A, but only a slight change in the case of orbit B. A (4,4) model is adequate if 20 m accuracy orbits over two days are required. However, the (4,4) model is generally not accurate enough for 2 m orbits, except for arcs of a few hours duration. Gravity field modelling for high precision GPS orbits is not a great problem because available orbit generators, based on the numerical integration principle, can easily accommodate geopotential models of degree and order 10 and above. The 90 effect of errors in the model coefficients was not studied, but these are not expected to be significant for the low degree and order terms. The analytical approach for integrating the GPS orbits appears to be adequate, but only for the short arcs considered by Nakiboglu et al (1984), Nevertheless, the latter technique does not possess the flexibility to account for the non-zonal geo- potential terms which are needed to generate ephemerides for longer arcs. 2. Direct Effect of Sun and Moon The perturbing acceleration vector for the sun and moon is (Cappellari 1976, p4-7): iLzii - Is 1 fiiizii _ h Ks = ^^s ilMr l^si^J *'^ilMr I \t (3) where G is the gravitational constant, M /M-. and Rg/R-|^ are the ^sses and the geocentric position vectors of the sun and moon respectively, and R is the geoj- centric position vector of the satellite. The magnitude of the acceleration Rjg acting on the GPS satellites is of the order of 5 x 10 ^m/s^. The point mass effects of the other planets are negligible. The perturbations of the satellite position due to luni-solar attraction, although mainly of long period, are nevertheless significant. Position errors of the order of 1 to 3 km can result if the luni-solar effects are ignored. After only 3 hours, errors of 50 - 150 m in each of the radial, crosstrack and alongtrack components of the orbit are produced, the variation being mostly due to the orientation of the GPS orbital plane in relation to the sun and moon. Although luni-solar perturbations can be adequately modelled analytically (Kaula 1961), the expressions are cumbersome to program. The coordinates of the sun and moon as a function of time, in an inert ial geocentric Cartesian reference system, are required. Readily accessible analy- tical expressions for the luni-solar ephemerides are given in the Astronomical Epheraeris (Gurnette & Wooley 1974, p98, pl07). But are they accurate enough to be used with GPS orbits? FIGURE 2 shows the orbit discrepancies that result when a typical GPS orbit is generated from the abovementioned analytical expressions for the luni-solar ephemerides compared to those derived numerically (Standish 1985). The discrepancies are of the order of 100 - 250 m after two days. Even after 3 hours, the GPS orbit errors arising from the luni-solar ephemeris errors are almost 10 m. 3. Earth and Ocean Tidal Effects Earth and ocean tides change the earth's gravitational potential, in turn producing additional accelerations on the satellite. In its simplest form, the perturbing acceleration due to the solid earth tides caused by either the sun or moon, is given by: „ k GM , iRdl^Rl C3-15cos^e) - + 6cose -d 1^1 l^dl' (4) 91 where k2 is the Love number of degree 2, M^j is the mass of the disturbing body, R^ is the geocentric position vector to the disturbing body, ag is the mean earth radius, is the angle between the geocentric position vectors R and R^j and the remaining quantities are defined in equation 3. The magnitude of the acceler- ation is of the order of 10" Ws^. By neglecting the earth tide effect orbital errors of 0,5 - 1 m result after two days. This is well below the error toler- ances considered here. The ocean tide effect is more difficult to model. The potential at A, due to a mass load dm at P arising from a tide height of h, is: Gdni- p r U = a^^ ^ (1 + k;^) P^^cosij) (5) kl are load deformation coefficients of degree n, ij^ is the geocentric angle between A and P, PjiQare the associated Legendre functions of degree n and dmp = p^ h(P,t) da (6) where p^ is the average ocean density, t is time and da is the element of surface area. The total oceanic potential at A is the global integral of eqn.5. A model of the ocean tide height h(P,t) as a function of time and place is required. Schwiderski (1980) gives one such model in which the individual Darwinian tidal constituents are expressed in terms of spherixal harmonics. We have used this model to generate the perturbing acceleration Rq , Perturbing accelerations of the order of lO'^'m/s^ are obtained. Moreover, the contribution of the ocean tides to the orbital perturbations of GPS satellites varies from around the submetre level to over 2 ra, after an integration period of two days. 4. Direct and Reflected Radiation Pressure The non-graviational and non-analytical forces arising from the sun's direct radiation pressure and that portion of it that is reflected back from the surface of the earth are the most difficult to model. The perturbing acceleration due to direct solar radiation pressure is usually expressed as follows (Cappellari 1976, p4-62) : s s r m ' s (7) where u is an eclipse factor such that u=0 when the satellite is in earth's shadow, u=l when it is in sunlight and 0< X X X ♦ « I I I I I I 100 200 300 400 500 TIME IN MINUTES ' 600 700 Figure 3 -lb ORBIT APPROXIMATION FOR NAVSTAR 1 . MJD(START) = 45725.2187 RESIDUALS RADIAL(+), ALONG TRACK(X),OUT OF PLANE(X) EARTH POTENTIAL COMPLETE UP TO DEGREE AND ORDER 4 GM(SUN)- 0.13271250D+21 GM(MOON)- 0.49027890D+13 SOLAR RADIATION PRESSURE CONSTANT- -0.9558D-07 0.3-5 0.2-: 0.1-:% 0.0-. R E S I D U A L -0.ii s I -0.2- N n -0.3-5 -0.44 X X X X ^ + + + + 5 * + X * * ^ ■¥ >* X 5 ! ♦*♦♦♦♦ - ♦ * w 100 200 300 400 TIME IN MINUTES 500 600 700 103 Figtore 3.2a 0U3IT APPROXIMATION FOR NTAVSTAR 1 . MJD(START) = 45725.2187 RESIDUALS RADIAL(+), ALONG TRACK(X).OUT OF PLANE(*) EARTH POTENTIAL COflPLETE UP TO DEGREE AND ORDER 8 Gn(SUN)- 0.1327lSSeD-«-Sl GHCnOON)- e.490S789eD-t-13 SOLAR RADIATION PRESSURE CONSTANT- -e.9685D-e7 2: ^ R 1- E S I D e- U A L S -1- ^ -*Table 4.1 used as a priori variances for elements. Soluti on B : Element Set C (Table 4.2) used as a priori orbi ts. Set B/Table 4.1 used as a priori variances for elements. Point solution Estimated-Ground Truth RMS x(m) y(m) 2(m) x(m) y(m) z(m) P 226 X -2.776 -3.378 -1.056 .323 .125 .092 P 230 X -.698 1.154 1.512 .255 .127 .079 P 232 X -.108 -.718 -2.170 .025 .019 .023 P 233 X 2.477 1.824 -.122 .223 .127 .068 P Z2 two observation equations can be set up for the orbit improvement: /6/ /7/ In these equations the clock rate is ignored but proper terms csui be added to each of them. Notation to above expressions is explained on the Fig.1 AB '''7 1 / k / I Ws T Jb B Fig.1 Let us consider more closely the geometry of the elementary set of these observations. As it was pointed out in Zielinski, 1983 it is convenient to apply the double /two-armed/ interferometer as an ele- mentary configuration in SRI. Measuring the time delay is equivalent to the distance measurement 122 As we know, the determinat locus for points with a constant difference of distances to two other points is a hyperbola and in three-dimensio- nal space a hyperboloid. Thus for each pair of observations of the double interferometer we have an intersection of two hyperboloids connected with baselines AB and AC. This intersection gives a spatial curve line on which the satellite is located. /Pig. 2/ In this way the interferometric observation from three points is some- how similar to the direction observation where the satellite is loca- ted on the St right line determined by o( and 6" . Here the curve line SS'is determined by the positions of points A, B and C aM ^7 t^B''^AC • Now, if the additional parameters are involved, e.g. Auaq and Auy^C resulting from clock differences, then the line SS' is dis- placed and changes a bit its shape. The second observable r can be interpreted as a difference between radial velocities observed from two ends of a baseline. Hence 't is a function of the orbital velocity l^g and geometry /Pig. 3/ Let us new discuss the problem of the stations coordinates. As the three stations constitute the minimum configuration, we can consider them as a single "observing unit". This "unit" is defined by 9 para- meters: either cartesian coordinates for each station or other para- meters /e.g. position vector of one station, direction cosines of the plane AJBC and distances between 3 stations/. There c€ui be a number of such observing units distributed over the Earth. However they can also form a network similar to the well known triangulation network. For an N-station network there are N (N-1) /2 possible baselines / but only N-1 independent/. 123 Fig. 3 Now, if we have an orbit high enough that the substantial orbital arc can be observed from one triangle, there is no reason why we could not find all unknown parameters with one reservation - the origin for geographical longitude or for the right ascension of the node must be set up arbitrarly. In this situation we have following number of para- meters : 6 orbital parameters 3N - 1 coordinates of stations _N_-^1^_ clock correction differences 4N + 4 parameters in total So, for N = 3 it is necessary to have at least 16 independent observa- tion equations of type /!/• The SRI solution comprising observations of T and X is in effect the combined geometrical-dynamical solution. It can be compared with the solution in which the satellite triangulation by simultaneous observations is combined with dynamical orbit improvement. Therefore we can expect the strong solution for orbital parameters as well as for station coordinates. Co variance analysis In the process of the orbit improvement we have to do with the equa- tion system AX = L + V /9/ since X = (A'fpA)-' A^PL /'°/ In this study we are not so much interested in the solution vector X as in the variance-covariance matrix of the parameters 124 Two essential characteristics have been investigated: coefficients of mean errors of parameters YEii and correlation matrix. The matrix A consists of the derivatives with respect to f and X . For P the unit matrix has been applied. Vector ARq of corrections to orbital elements can contain. correc- tions to keplerian elements or to rectangular elements Rq and ^^ In the second case the derivative vector Jl consists of components If , ^ etc • It is practical to evaluate xnese derivaties by means of nu&erical integration, using variable initial conditions. For other derivatives there are th« following expressions: 3X^ " Ar,3 ^h ' ^r^B Z^^/ Xs- •X, A "■ab Vs- Y, A -"ab ^s- ■^A 3r Zs~^A 9t . -(^s"'^b) aZ, - Ar^3 aZB ■ Ar^B Numerical experiments Using expressions /?/ we made some model calculations of the orbit of the imaginary satellite with orbital parameters analogous to GPS sate- llite. We have improved the orbit assuming different stations configu- rations and different sets of parameters to be determined. At least one station has been assumed fixed in each case, but in same cases, when short baselines have been taken /up to 300 km/ more stations have been assumed as geodetically known. The same assumption has been done concerning the clock corrections: for short distances they have been assumed as known, for longer distances they have been determined in the adjustment process. Typically 24 hour orbit has been calcula- ted. In each case the correlation matrix and the weight coefficients of errors of parameters have been obtained. As the separate problem we have analysed the perturbations for GPS orbit, Probabely the most interesting result concerns the influence of the Earth gravity field harminics , It is shown in the Table 1 , There are effects of individual zonal harmonics as well as of sums of tesseral harmonics of the given degree, after 24 hours of integra- tion. We can see that the harmonics higher then n s 7 have negligible influence. Conclusions In general we can state that with the SRI data we get stronger solu- tion then with optical, laser or doppler separately. We can always get a good solution providing that the station positions are known. The orbit can be determined with an accuracy of few cm with assumed stan- dard deviations 30 cm and 0,3 mm/s for r and X , However, the assu- mption of the known coordinates for all stations is not realistic, 125 n especially for long "baselines. Therefore it is necessary to include into solution the station coordinates. Then the solution becomes stron- gly dependent on geometry. We can get the optimal solution when the ratio of the baseline length to the orbit hight should be about 1 : 10 For G-PS satellites it requires baselines longer them 1500 km. Table 1 Influence of the Earth gravity field harmonics on GPS satellite motion Harmo nics Position, difference after 24 hours radial along track cross track total m m m m J2 -152.786 -24947.667 -7305.177 25995.673 J3 0.489 -1.611 0.083 1.686 J4 -0.007 -3.345 0.498 3.382 J5 0.008 0.001 -0.003 0.009 •^S J6 -0.005 0.134 0.006 0.134 g J7 -0.003 0.046 -0.000 0.046 S J8 0.002 0.004 0.001 0.005 J9 0.002 0.006 0.001 0.006 J10 -0.001 0.021 0.001 0.021 T2" -14.945 69.237 55.928 90.253 T3 6.835 -50.620 2.268 51.130 d T4 0.379 1.616 -0.426 1.713 2 T5 -0.064 0.490 -0.100 0.504 S T6 -0.032 0.176 0.048 0.185 o T7 0.005 0.146 0.010 0.147 5 T8 0.001 0.020 0.001 0.020 T9 -0.002 0.029 0.001 0.029 T10 0.001 0.017 0.001 0.017 References 1 , Y, Bock, 1980, A YLBI variance-covariance analysis interactive com- puter program, OSU Dept, of Geodetic Science, Rep, No 298, 2, Y, Bock, 1983, On the time delay weight matrix in VLBI geodetic parameter estimation, OSU Dept, of Geodetic Science, Rep, No 348 3, A, Dermanis and E, Grafarend, 1981, Estimability analysis of geo- detic astrometric and geodynamical quantities in very long baseline interferometry. Geophys, Journal of RAS, 31-56, 64. 4» A, Droiyner, 1981, Geometric interpretation of a covariauice matrdlx. Artificial Satellites - Plsuaetary Geodesy, No, 3, 16 5. P,J, Pell, 1980, Geodetic positioning using a Global Positioning System of Satellites, OSU Dept, of Geodetic Science Rep, No 299 6. V,S, Gubanov, N*©, Umarbajeva and P,A, Fridman, 1982, primienien metoda RSDB v geodynamicheskih issledovaniah, Pres. at INTERCOSMOS Symp, of Satellite Geodesy, Suzdal, 7. J,B, Zieli]4ski, 1983, Potential possibilities of the satellite radio interferometry in dynamical mode, Pres, at lAG Symp, "The future of terrestrial and space methods for positioning", Hamburg, 126 An alternative concept for the design of a low cost C/A code Navstar GPS receiver M T Allison and P Daly Department of Electrical and Electronic Engineering University of Leeds Leeds LS2 9JT United Kingdom ABSTRACT The Navstar Standard Positioning Service (SPS) is intended to play a primary role in civil navigation providing position, velocity and timing information on a global basis 2A hours a day. A complete prototype single channel C/A code receiver capable of fulfilling the requirements for a low dynamic environment is described. Novel features in both hardware and software design are detailed which have contributed towards the realisation of a cost effective system without compromising navigational accuracy. A highly structured and efficient software package written in the "C" programming language enables the use of a single multi- tasking microprocessor which controls all receiver functions in addi- tion to navigation processing. The receiver still achieves a low time between fixes - an important performance criterion. The package also provides software portability crucial in the exploitation of new microprocessor technologies. Results are given for both two and three dimensional position fixing which qualify the receiver and indicate clearly accuracies typical of the C/A code in Western Europe. Since it is likely that the C/A code navigation accuracy will be deliberately degraded when Navstar reaches its operational phase, it is important to establish the full capability of the system now. This also enables the subse- quent implementation of differential Navstar techniques (Beser and Parkinson 1984) . Factors influencing navigational accuracy are dis- cussed. RECEIVER DESCRIPTION An overview of the receiver is shown in Figure [1]. A planar microstrip antenna (Wood 1980) of approximate dimensions 10 X 10 cms feeds a filter and LNA in the mast unit. This is followed by two stages of down conversion. A fixed local oscillator at 1700 MHz derived directly from the 10 MHz master clock produces the first i.f. at approximately 124 MHz. This is further mixed by a VHF local oscilla- tor under processor control down to the final 10.7 MHz i.f. at which point the 127 signal is still 'spread spectrum' with 2 MHz bandwidth. AGC is provided for in the subsequent gain block. It can be seen that both the AFC and the AGC loop are closed in the software - feedback in terms of frequency and power being obtained from the carrier tracking and code tracking loops respectively. The choice of 10.7 MHz as the second i.f. was made for reasons of convenience allowing the use of off-the-shelf items in the code and carrier loops - for example crystal filters- to reduce the overall cost. The signal is now de-spread in an early-late delay-lock loop incorporating three loop bandwidths. The bandwidth remains wide for code aquisition and is closed down whilst pseudo-ranging. If the processor has no prior knowledge of the expected code phase, aquisition may take up to 30 seconds during which time the locally generated C/A code if shifted across the received code, until the correla- tion peak pulls the loop into lock. However, once the satellite's position is known, the processor can offset the code phase to within a few chips of the correct phase, reducing the signal aquisition time to under one second. This occurs whilst navigating. The carrier loop recovers a 10.7 MHz carrier for coherent demodulation of the BPSK de-spread signal. The 50 baud data stream output is matched filtered for optimum processing gain in the presence of Gaussian noise, and interfaced to the processor. The final section is the pseudo-range module. The C/A code epoch timing mark together with a 50 MHz reference from the master clock enables the measurement of pseudo-range, truncated to ±3 meters. Examination of range-rate from space vehi- cles at various elevations determines the noise on the range measurement due to receiver phase noise. This was found to be similar in magnitude to the truncation noise. It was thus decided that increased resolution of the pseudo-range measure- ment would not enhance receiver performance, whilst the configuration used had the advantage of limiting the pseudo-range representation to a convenient 16-bit word simplifying hardware. A simulated Navstar signal forms the basis of the built-in test equipment (BITE). This can either be injected into the receiver at 10.7 MHz under processor control enabling a fault diagnosis to be presented on the user VDU, or used to modulate an L-band carrier to test system integrity from the antenna input onwards. SOFTWARE CONSIDERATIONS The software complexity in a GPS receiver implementation can exceed that of the hardware - which in fact can be considered a consequence of good design approach. For this reason, the choice of programming language is quite critical. In the receiver described, the "C" language was used predominantly. This virtually eliminated the need for assembly language routines. The resulting software package is thus fully portable, which enables the receiver to be updated to use a more powerful processor as required. In addition, the software development time was substantially reduced and software maintenance simplified. The software was developed using a mini-computer under the UNIX operating system and the final code down-loaded into the receiver in RAM enabling alterations to be carried out quickly throughout the development cycle. A single Z80 microprocessor provided both receiver control and navigation pro- cessing. Its advanced interrupt structure allowed the one multi-tasking processor to execute many program segments, each one controlling part of the receiver as an Interrupt service routine. Should the code and carrier loops be implemented 128 digitally, the necessary additional software will take the form of further routines using the same processor. Although the Z80 was used here to prove the system, due to the amount of floating point arithmetic necessary to produce a navigational solution, a 16-bit processor (possibly with arithmetic co-processor) would provide fix updates every few seconds using the receiver described. The following processor/co-processor combinations are being evaluated for use in an updated ver- sion of the Leeds University receiver : 8086/8087; 80286/80287; Z8000/Z8070; 68000/68881. However, the 18 second fix update time (200 fixes per hour) obtained here using three satellites would be quite adequate for many applications where low price is to be prefered to speed. RECEIVER OPERATION User interface is via a VDU through which various modes of operation can be selected. If a cold start is performed, a single satellite will provide the almanac. Following this, the receiver is able to select a constellation of three satellites minimising HDOP from a subset of healthy satellites above 5 degrees elevation. The availability of GPS from Leeds with the present six satellite test constellation is shown in Figure [2] . Once the precise ephemeris has been col- lected from the chosen three, navigation may proceed. Each satellite is sequenced in turn and dwelled upon for three seconds for pseudo-ranging and position calculation. Should a satellite drop below 5 degrees or become masked from the user, a new constellation will be selected. These func- tions are fully automatic with no operator intervention necessary. At present the receiver uses three satellites (2D navigation) by default. The user may select a fourth using the status display which gives a list of available satellies together with health status and elevation. Choosing a fourth satellite at high elevation will reduce VDOP. A GDOP algorithm will be included in the next software update. During navigation, user latitude, longitude and height are displayed together with details applicable to the satellites being sequenced. Many other receiver opera- tion modes may be invoked. POSITIONING RESULTS Figure [3] indicates results typical for two dimensional position fixing whilst Figure [5] represents three dimensional fixing. (Three and four satellites respectively) . The cartography resident in the software depicts the Engineering buildings at Leeds University. Associated with these scatter-plots are the corresponding graphs of latitude and longitude (and height for the 3D case) error versus time. Figure [4] and Figure [6]. The time scales of the experiments are of the order of 40 to 50 minutes. It must be emphasised that the scatter-plots show independent fixes using new pseudo-range data from each satellite and do not incor- porate any filtering or smoothing. The zero error position has been normalised to conincide with the average position produced by the receiver. The precise position has yet to be established in WGS72 coordinates from an independent survey. The average latitudes, longitudes (and height for the 3D case) with one sigma values are given. It has been observed that whilst using the same constellation in similar experiments over periods of many weeks, the average results differ by less than 10 meters in all three dimensions (maximum deviation) . However, a change of constellation produces a shift in average position - this is evident in the results 129 submitted. Thus, repeatability is shown to be good although there are still fac- tors affecting absolute accuracy. The factors believed to be most Influential include : (i) the accuracy of the transmitted satellite ephemeris and clock parameters which are subject to degrada- tion by the time satellites are visible to users in Western Europe; (ii) uncorrected ionospheric effects for this single frequency set; and (iii) an incorrect estimate of height above the reference ellipsoid for 2D positioning. In the first case, an improvement is expected once the Operational Control System (OCS) replaces the Initial Control System (ICS) (Bowen 1985) . In the second, the ionopheric model obtained from transmitted parameters could be employed. There have recently been some doubts as to the improvement these provide with the present transmitted parameters (Ashjaee 1985) - explaining their omission here. A better estimate of height will be obtained by averaging results from 3D positioning and this will be fed back into the 2D solution. CONCLUSIONS A low cost GPS receiver has been described which indicate present accuracies obtainable using the C/A code with the Navstar test constellation in Western Europe. The operational constellation and control segment is expected to be capa- ble of achieving better accuracies than those presented. Should the system be deliberately degraded, these will only be obtainable using differential techniques. REFERENCES Ashjaee, J M, 1985: Improving the Accuracy of C/A Code Systems, The Institute of Navigation National Technical Meeting, San Diego 15 - 17 January Beser ,J Parkinson, B W, 1984: The Application of Navstar Differential GPS in the Civilian Community, Navigation (Special issue on GPS), Vol 2, 167 - 196 Bowen, R Swanson,P Winn,B Rhodus,W Feess,B, 1985: GPS Operational Control System Accuracies, The Institute of Navigation National Technical Meeting, San Diego 15-17 January Wood,C, 1980: Improved Bandwidth of mcrostrip Antennas using Parasitic Elements, lEE Proc, Vol 127 Pt H No. 4, 231 - 234 130 THE UNIVERSITY OF LEEDS : EXPERIMENTAL NAVSTAR QPS RECEIVER ■trt MHi .130 dS* Itt I.I. 2nd l.f. 1-^ ^-f 124 MHi T^ ii lO.r MHl MASTER CLOCK to MHz I UJ > O * < CO UJ u 2 3 w 5 * FREQUENCY QENERATION UNIT 7\ 80 MHi PSEUOO- RANQE A— Y BUILT IN H TEST EQUIPMENT CODE TRACKING LOOP \—\ C/A CODE GENERATOR 7\ CARRIER TRACKING LOOP 7V~ DATA rH RECOVERY 7^^ — CONTROL AND NAVIGATION PROCESSOR v.o.u. PRINTER FIGURE 1 NAVSTARS VISIBLE FROM LEEDS ON APRIL 15 1085 (SPACE VEHICLES 6. 8. 0. 11. 12. 13) 1 2 3 4 6 e 7 a • 10 I 1 12 13 14 IS 16 17 16 19 20 21 22 23 TIME (HOURS) FIGURE 2 131 Ill o a >- tJ I- (B — -o in X □: - a ujin LUOO I— a ■< o o a ox I— (N tn — > . <> 0! O E •> L » (Tin ■o e — C1.-D 3 .> o- (DLTi en o ~r - «Ln w win oo— ra -0 . II n L CT) •O C ^ • % 0- \ > 6 ai „ c o 01 (0 L kJ CTICTI « c T) o -N. (N o. B LHO f\)(ri UJ oc 3 o (•.MtMf) apntit*-) 132 oc o 1 II I I * I I I I ^ SCRIQoiQSer s: en o > - (8- <^ 1 X - I •1 E S E o-ino in oioj •I u c - . • o • 1 0) OD - e o *> A 9 jcS-Se Sin II II II II 14. • 5 • O— '— 'X 8S Ui OC 3 O 133 CAPABILITIES OF THE TR5S SERCEL GPS RECEIVER FOR PRECISE POSITIONING C. BOUCHER Institut Geographique National 2, Avenue Pasteur, 94160 Saint-Mande, France G. NARD Societe d'Etudes, Recherches et Constructions Electroniques (SERCEL) BP 64, 44471 Carquefou, France ABSTRACT - Recording receivers and data processing equipments for GPS NAVSTAR satellite signals have been developed in France by the French company SERCEL. They are currently under experimentation. These equipments aim to investigate differential and absolute positioning techniques in real time, in view of offshore explorations which require a very high ship positioning accuracy. The characteristics of this equipment fulfil the requirements of differential and absolute precise geodetic surveys. Using the C/A code, this 5 channel receiver allows pseudorange and Doppler measurements on LI frequency with high accuracy and records the GPS message. Moreover, a large research program on processing methods and softwares applied to surveying and geodesy has been undertaken. A description of the equipments is given with precise characteristics and calibration methods together with the results of experiments at sea, compared to accurate reference fixes given by the SYLEDIS system. Preliminary results concerning land surveys are also described. 1 - INTRODUCTION The use of the NAVSTAR Global Positioning System (GPS) for geodetic positioning is presently investigated by several groups. Its tremendous impact on geodesy and other fields has been now extensively demonstrated (Anderle 1984, Bossier 19B3, Boucher 1985). Several manufacturers and organizations are performing hardware and software developments in France. This paper presents a GPS receiver built by the Societe d'Etudes, Recherches et Constructions Electroniques (SERCEL), and its applications to surveying. SERCEL has been active for thirty years in the design and manufacturing of field equipements for precise marine positioning (TORAN, SYLEDIS, for which 1000 units are in use), and land surveying (16.000 EDM equipments, distributed by WILD). The necessity of a future ground system for highly reliable and precise positioning is clearly a consequence of technical, economical and political reasons. This is why SERCEL has recently developed a long range and accurate radiopositioning system GEOLOC, using spread spectrum techniques. 135 Nevertheless, it is also. an opinion that the major tool for surveying, geodesy and navigation will be based upon a specialized satellite system. The GPS system is the first of this kind to provide a highly accurate, almost permanent and universal positioning. SERCEL has therefore decided to develop a receiver which should fulfil, alone or coupled with performant ground systems, the high level of accuracy and reliability of the future requirements in positioning. The objectives of these developments are : - high accurate dynamical positioning at sea (1 to 10m level) - land surveying and geodesy (1 to 10cm level) - time transfer and synchronization (1-lOns level) A series of ten GPS receivers named TR5S model has been built and receives presently its first applications. SERCEL has acquired for ten years a well recognized experience in differential use of OMEGA, and plans to apply a similar approach to GPS, providing rapidly methods of real time or delayed differential positioning. Several French agencies are using such a receiver in order to develop their own applications. Institut Geographique National (IGN, France) has acquired a first unit in January 1985. IGN has undertaken a program covering the 1985-1986 period which comprises : + establishment of specifications for field GPS surveys + establishment of related specifications of accuracy for absolute or relative positioning + development of software for operational GPS data analysis + use of GPS positioning for various projects in or outside France + participation to ancillary activities which can provide useful information (ionosphere, ephemerides) This research and development activity will be done with the cooperation of other agencies (CEA, ONES, INSU ...), particularly by sharing receivers for pilot experiments. 2 - DESCRIPTION OF THE SERCEL TR5S RECEIVER The SERCEL TR5S GPS equipment can receive and process simultaneously the signals coming from up to 5 satellites, using a C/A code generator to perform pseudorange and phase measurement on the LI frequency (1.57542 GHz). This 5 channel receiver can fulfil two tasks, namely field data recording and real time position estimation. 2-1) Overview of the equipment The receiver comprises an antenna and its preamplifier, a receiving-processing unit, a colour screen unit and a control and display unit (fig. 9). 136 ANTENNA Preamp 1575.42 MHz UHF AMP. and Conversion 21.42 MHz ^7^ jL. THT :ij£: CO TT ^TT 2LkL ^TFT Multiplexed time counter :?F Channels and I/O control processor Navigation solution processor Int. Osc 10 MHz Common circuits and Synthesis 21.36 MHz -Optional ext. osc. POWER SUPPLY 24 V 2 X RS 232 I/O - rough data - processed data /keyboard^ FIG. 1 • TR5S GENERAL SYNOPSIS CARRIER PHASE TRACKING LOOP Doppler Ooppler set (4 bits) Code ielection set (8 bits) Hybrid circuits FIG. 2 - CHANNEL DESCRIPTION IT 20m( Channal i Data Doppler period 8 bits Integer dopptar count 1 6 bits Fractional doppler count 8 bits 8 bits aet Racurrance . 137 Fig. 1 shows the synopsis of the receiver. The antenna is connected to the receiver by a unique coaxial cable. The receiving circuit has 3 steps of frequency conversion (1.57542 GHz, 21.42 MHz, 20 KHz). The second IF (21.42 MHz) is supplied to 5 parallel channels which perforin most of the signal processing. A bus connection perform I/O exchanges between these channels and the common units. These units comprise a time counter, an I/O control processor, a navigation processor, and interfaces with a keyboard and video screen. A RS 232 output is used to collect data, usually with a Tandberg cartridge tape recorder. Fig. 2 shows the diagram of a channel. Each channel is equipped with an automatic gain controller, a C/A code correlation loop and a carrier phase tracking loop which is also used to extract broadcast data. Pseudorange and phase readings are performed every 0.6s. Each channel provides dense and precise measurements. The electronic delays of each channel are very stable, which is a necessary condition for accurate positioning. A 24 V power supply enables standard field or sea measurements. The antenna can be equipped with an anti-reflection screen and can be mounted on a standard tripod (fig. 10). Fig. 11 shows the current design for a ship or a vehicle. 2-2) Mechanical and electrical characteristics Receiver - Size : 360 x 525 x 445mm - Weight : 27kg - Environmental temperature : to 40° C - Waterproof - Power : 24 V, 10 A CPU - Size : 160 x 240 x 75mm - Weight : 1 .6kg - Waterproof Antenna (land) - Height : 300mm - Size of the screen : 600 x 630mm - Size of the preamplifier : 160 x 160 x 100mm - Weight of the antenna, screen and preamplifier : 11kg - Environmental temperature : -20 to 50° C - Hemispheric diagram - Right circular polarization - Noise factor : 4 dB - Maximum gain : 3 dBic - Length of the cable : 30m The ship antenna has a size of 480 x 180 x 200mm. The keyboard, screen and tape recorder are non waterproof. 138 2-3) Technical characteristics Receiver - 5 channels - L 1 - C/A code - range, phase and data Frequency standard - 10 MHz (possible external input) - crystal oscillator - lO'^Vday Dynamical limitations - velocity < lOOkra/h - acceleration < 0.5g Sensitivity - minimum level for acquisition : - 132 dBm - minimum level for tracking : - 141 dBm - acquisition time : 60s at 90% Pseudorange - rate : 0.6s - resolution : 0.12m - noise : 2m (S/N 45 dB-Hz) 8m (S/N 29 dB-Hz) - interchannel noise : 0.5m (S/N 45 dB-Hz) 2m (S/N 29 dB-Hz) - accuracy of interchannel calibration : 0.5m (S/N 38 dB-Hz) Phase - rate : 0.6s - resolution : 1.5mm - noise : 3mm (S/N 45 dB-Hz) 6ram (S/N 29 dB-Hz) - interchannel noise : 4mm (S/N 45 dB-Hz) 8mm (S/N 29 dB-Hz) - accuracy of international calibration : 2mm (S/N 45 dB-Hz) 3 - PRECISION AND CALIBRATION The necessity of guaranteeing very stable group and phase delays for each tracked signal is an important feature to allow centimetric accuracy. Compared to multi- plexed receivers, multichannel receivers will provide more dense information, but the above requirement must be carefully checked, A careful design can provide almost identical and stable delays for each channel. It is then possible to check the corresponding performances by a suitable calibration. First, laboratory tests with a GPS signal simulator can be done. The 5 channels receive the same signal, the strength of which can be modified. Fig. 3 shows the 1 min. average and the 0,6s individual pseudorange. Fig. 4 shows similar results on phase. Fig. 5 and 6 show interchannel comparisons for pseudorange and phase respectively. These figures illustrate the quality of the channels and the low sensitivity to a decreasing S/N ratio. A second step which can be performed is to assess a same GPS satellite signal 139 Prototyp* : il level dB Ev«lu«tlon Ou :8 tun 1985 2sAl Harga S (dal Cy.lu.Uan *t •■ Mm IBM Pseudorange : average/1 min 10. i Hsy IPr e] (a) ; 3 Idiv = 1 meter Tmin Pseudorange : average/0. 6$ec. 10^ BraUT S] (a) T Y Idiv = 1 meter Tmin FIG. 3 - Pseudo range calibration f (input level) (from G.P.S. signals simulator at receiver antenna input) Separate channels Integrated doppler. Average : 0.6sec. M\.OfB (UuN^at (channel 1) ■■-122dBm Tmin. FIG. 4 - Separate channels integrated doppler evaluation f (level) from G.P.S. signals simulator Prototypt : 11 Igygl^g Evaluation du : B Napa ISes 2b4l Marga 4 (dB) -122 dBm iLJUJULJJUIllUH -132 dBm -140 dBm it/Mf^ , I 1 I lIUlfMllMII Ml lIljUPi Differential pseudo range : average / 1 min. 10^. Xoy tPr <- Pr C (al Tmin. 1 div. = 1 meter Tmin. Differential pseudo range : average / 0.6 sec. 10— dFalPr 4- Pr tl (a) I 1 div. = 1 meter k ^ im** » rt n ,>^m ^ Y>^' •9'.. |> » V '*** " r»ntV^)y V '»V»M>ii ^ if|[ ^ , I* nm tMB Average / 0.6 sec. f-tura Channels : 2-1 ::_-122 I 1-132 -140 dBm i». . dBm 1 div. = 4 millimeters Channels : 4—3 f^NflflWllIlt 1 div. = 4 millimeters FIG. 6 - Channels difference integrated doppler f (level) from G.P.S. signals simulator 140 SV Sigrial Prolotirp. : 12 level dB^"""""" '" -^ *'"'* "*^ is: . Harg* 4 (aBI If 10. • "''^''''''''^^^'^Wn,, ,^ -134: dBm ■ 1 1 » — 1 1 ^>■ Differential pseudo range : average / 1 min. lof MoytPr <- Pr 11 M Tmin. H 1 div. = 1 meter -«.. Differential pseudo range : average / 0.6 sec. iof Brmtpr 4- Pr 1) (•) . 1 div. = 1 meter Tmln. Tmin. FIG. 7 - Channels difference pseudo range calibration from actual S.V. signals processing (S.V.6) Protetypa ; 12 tv4iu.cion du :2o H.r« lUM Avorago : 0.6 sec. ^ oea j-1 (tour/ioo) Channels 2—1 :. T 1 div. = 4 millimeters 2«^ OOP 4-1 (tour/iooi Channels 4—1 div. = 4 millimeters FIG. 8 - Channels difference integrated doppler evaluation from actual S.V. signals (S.V.13) FIG. 9 -TR5S EQUIPMENT VIEW 141 FIG. 10 - TR5S Antenna Set up for topography FIG. 11 - Typical ship antenna mount Target center : 47*38' 1.4ee-N r27'44.357"H oct 25,1984 4h53B47.4s ♦R 250 3G32274 3009 •1 88455982360 303106G0 12 15 6 38 FFBD5500 - •2 88558945364 62018230 08 1 1 fl 38 FFBflDC00 «3 88549992879 48349234 06 1 1 C 38 FFBE8100 S »4 88519763231 02817246 11 14 6 38 FFBR4300 £ •5 88569860422 03930296 13 10 3 38 FFB7EF00 = Mode :3D*T PR*Dp Bovlng user 5 Dop 1.7/T .1.6/H 3.2/fl I r-ms er : 24.7n$ IB.Bm 13.7»i Clod : 1.3735079581s -2.94038E-009s/s se.ete [lev R 2 1 m Pange i m Doppler • m 12 51.636 278.095 -2.279 -9.315 2.993 3.463 8 12.449 20.361 3.238 0.545 9.966 6.936 14.110 65.132 -2.512 -0.210 8.890 6.973 -e.822 5.428 5.575 ihilt te) 24.896 7.320 70.756 131.594 -0.206 -10.324 -0.418 16.075 8.705 Jserpos: 47*30'12.473"N 4*27'37.492"H 60.18« 4.4ffi/s 26.2' Vh : -0.16m/s User P FIG. 12 - TYPICAL TR5S OPERATION DISPLAY 142 to all 5 channels. Fig. 7 and 8 illustrate the results. The residual noise on differences is 0.5in for pseudorange and 2iran for phase. The bias can be obtained in 1 min. of calibration which should be done before and after each session. 4 - DATA ANALYSIS 4-1) Real time processing A software package has been developed by SERCEL for two purposes : - static or dynamic single point positioning (Kalman filter or least squares; 3D + T, 2D + T, 3D or 2D solution) - utility programs (AZ-EL diagrams of GPS satellites for a given site, GDOP-TDOP- HDOP-VDOP diagrams) These softwares are available in the real time microprocessor, and also on HP9836. 4-2) Data analysis for geodesy IGN has undertaken the development of a software named GDVS which will be able to perform a semi-dynamical adjustment of range and range-rate data (Transit, GPS, DORIS) for a regional network of stations. This software can also be used for simulations. The various types of raw data are preprocessed on a HP9836 and converted to standard data files (for measurements, ephemerides , auxiliary data ..), The main GDVS routines are run on DEC VAX 11/780. Concerning GPS, this software accepts pseudorange, Doppler, phase, 1st, 2nd or 3rd differences. In a second step, a special operational GPS software will be installed on HP9836, depending on the results of the research phase using GDVS. 5 - PRELIMINARY RESULTS Various field tests have been performed. For land applications, IGN has establ- ished a test network for space systems in Britanny, with sides from 2 to 300km. Two 3 day sessions have been realized with TR5S receivers, the first one in January 1985 with 2 sets (30km), the second in March with 3 sets (triangle of 30km) WGS 72 coordinates come from standard conversion of the French datum NTF (Boucher 1981). SERCEL has performed navigation solutions (see fig. 13). Instantaneous accuracy at 15m level has been shown. Results with geodetic software will be available later on this year. SERCEL has also performed dynamical positioning at sea. Fig. 14 shows results compared to SYLEDIS (dots). This system has a 10m accuracy. A 20m bias can be seen, due to system instantaneous bias and WGS 72 datum local discrepancies. 6 - CONCLUSIONS The TR5S receiver is considered as a suitable tool for the three major applic- ations mentioned before, namely dynamical positioning at sea, land surveying and time transfer. Presently good results can be obtained with the preliminary constellation, although the useful window is short. For the operational phase, the anticipated system degradation will seriously limit real time absolute positioning. Nevertheless, differential techniques should largerly remove this limitation. The geodetic community can now begin to consider GPS as a major technique for horizontal and vertical network establishment (Hothem, 143 FIG. 13- Fixed point plot Ta qet center ; 47*3r 6.159"N 4*26'56.568"H ae.Ma H^ ^ Oct 25,1984 ^^ ^ 5h 3a 6.6s -Mi -Mi -IM ■i -| • h- — • 1 rtt to) ■i 1 1 A ■i — • • 1 m 3- ■ i:-^;at t 1 - - / 'tm . » ./ « 1 k ^^^^H se-p-s: 47'3ri7,515"H 4*26'54.273"H 67,98« User P FIG. 14 - G.P.S. NAVSTAR VERSUS SYLEDIS actual venal track* diffarancas 144 Goad, Remondi 1984). The necessary cooperation implies compatibility of systems. Standardization on terminology and data formats is therefore desirable (see report to SCS by Paradissis, Wells 1984). With adapted hardware and software techniques, it is our opinion that the GPS system will fulfil widely the mentioned applications. It finally shows the capability of spaceborne radiotracking techniques, which is also considered by other space projects, such as the DORIS system on SPOT-2 (CNES 1984) or the PRARE system on ERS-1. References ANDERLE (R.J.) - 1984 - Prospects for Global Positioning System - Cincinnati BONIN (G.) - 1985 - Exemple de realisation frangaise d'un recepteur NAVSTAR/GPS - Navigation 129, pp. 58-73 BOSSLER (J.D.) - 1983 - The impact of VLBI and GPS on Geodesy - EOS 27 BOUCHER (C.) - 1981 - Definition des systemes geodesiques utilises en France (NTF, ED 50, WGS 72) - IGN/DTIG, RT/G n° 7, Saint-Mande BOUCHER (C.) - 1985 - Le systeme NAVSTAR GPS et ses applications geodesiques - Navigation, IFN 12^, pp. 17-30 C.N.E.S. - 1984 - Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS) - Toulouse GOAD (C.C.) REMONDI (B.W.) - 1983 - Initial relative positioning results using the Global Positioning System - XVIIIth General Assembly of lUGG, Hamburg HOTHEM (L.D.), GOAD (C.C), REMONDI (B.W.) - 1984 - GPS satellite surveying. Practical aspects - CIS 1984 annual convention, Quebec PARADISSIS (D.), WELLS (D.E.) - 1984 - GPS standardization-status and problems - Meeting CSTG/SCS, Sopron 145 THE FIRST WILD-MAGNAVOX GPS SATELLITE SURVEYING EQUIPMENT: WM-lOl By Thomas A. Stansell, Jr. Steven M. Chamberlain MAGNAVOX ADVANCED PRODUCTS AND SYSTEMS COMPANY 2829 Maricopa Street Torrance, CA 90503 and Fritz K. Brunner WILD HEERBRUGG LTD. CH-9435 Heerbrugg Switzerland ABSTRACT. This paper begins with an overview of typical surveying requirements. Consequently the design concepts for the development of the portable and fully self-contained GPS Satellite Surveying Equipment WM-101 are described. The principal features are: C/A code receiver, simultaneous phase measurements of the reconstructed carrier signals of the LI frequency from several GPS satellites, and recording of the processed GPS satellite signal data on tape cassette in the field unit. Precise position differences are calculated by post-processing of the recorded data in a separate small computer. INTRODUCTION Wild Heerbrugg and Magnavox have entered into a joint venture in order to deve- lop, produce, and market an entire range of satellite surveying equipments which employ signals from the Global Positioning System (GPS) satellites. Each party to this joint venture brings its own perspective and unique expertise. Beginning with the AN/PRR-14 Geoceiver, Magnavox was the first company to provide a portable geodetic surveying instrument using satellite signals. In 1978 Magnavox introduced the MX-1502, which has become the most widely used satellite Doppler instrument in the world. The advent of GPS presents Magnavox with the challenge and the opportunity to continue its leadership in this field. GPS can provide centimeter accuracy in less than an hour. Thus it will be used far more extensively than satellite Doppler systems which require at least twenty- four hours of data collection per site. Therefore, it is expected that thousands of GPS instruments will be used by the land survey community. Although Magnavox understands the GPS technology and many of the geodetic applications, it is not as well positioned to serve the vast land survey market made possible by GPS. 147 However, as the world's leading maker of conventional survey instruments, Wild Heebrugg clearly understands the full range of geodetic and land survey require- ments. To continue its leadership in this field, it is necessary for Wild Heerbrugg to offer the best possible GPS surveying instrument. By combining the technical, production, and marketing strengths of both organisa- tions, the intent is for both to expand their present positions of leadership. It is clear that GPS will have a significant and perhaps even revolutionary impact on surveying. The new joint venture will be able to serve the needs of this market far better than either partner alone. Not being first into a market is never comfortable. On the other hand, we have had the time to observe what others have done. We acknowledge their significant achievements but intend not to repeat their mistakes. Furthermore, Magnavox has had the advantage of participating in the military GPS program for many years, gaining valuable insight into how to obtain the best results. Our first joint venture product, the WM-101, takes full advantage of this experience. This paper highlights the design principles for achieving optimum performance from the WM-101. After a discussion of important aspects of GPS surveying, we give a brief overview of the WM-101 characteristics. Next is a section which describes how to take best advantage of the GPS satellite signal structure. The sections which follow focus on the principal design objectives of accuracy, portability, special features, assurance of success and the post-processing capability. THE GPS SURVEYING ENVIRONMENT It is the considered opinion of geodesists worldwide that GPS satellite surveying has started to revolutionise their profession. Indeed, never before have geodesists been so enthusiastic and ready to accept a new technique. Figure 1 shows the approximate accuracy performance of various modern geodetic techniques as a function of distance. It is obvious that GPS satellite surveying has the potential of superior accuracy compared with most other techniques over a wide range of di stances. However, Figure 1 shows the accuracy performance only. GPS satellite surveying offers many other significant advantages orver conventional surveying methods: 3D vector components are determined directly, line-of-sight between ground stations is unnecessary, sites may be selected by survey requirements rather than by geodetic network configuration, observation towers are unnecessary, low skill required by the operator, and continuous measurements made easily, e.g. deformation surveys. Even today when GPS is still in its test phase (several hours of useful observation time per day) these advantages result in significant cost savings. The following is a summary of the requirements of GPS satellite surveying equipment for geodetic surveying and off-shore positioning as seen by the user community. Naturally the requirement for small size and portability is yery high; equally important are reliability and price. The antenna unit should be robust, but allow for unambiguous pointing to it for eccentric survey measurements. The precise height measurement of the antenna's phase centre above the ground mark must be considered crucial for high precision surveying applications. The receiver unit should allow for unattended satellite signal reception whilst the operator is 148 occupied with other local surveying work. After returning to the receiver unit the operator should be able to assess the quality of the received data. It should be possible to preprogram the receiver unit for routine work, so that it may be used by relatively unskilled operators. GPS satellite surveying equipment should combine basic navigation capabilities with high accuracy performance for static positioning of single points and differential measurements. Thus the satellite orbit information needs to be acquired in the field. In addition the operator should be assured that the measurements are valid. Furthermore, it is considered tedious to synchronise receiver clocks before and after each observation period. Post-processing of the collected data is considered an important phase of GPS satellite surveying, although the capability to calculate baseline results in the field is strongly recommended. The first GPS satellite surveying applications were the re-surveying of classical triangulation networks. In most future applications a mutually supportive combina- tion of GPS satellite surveying equipment and conventional surveying instruments will provide the most efficient solution to the surveying problem. Nevertheless, it is not difficult to foresee how this novel technology will impact and change geodetic surveying. The GPS satellite surveying equipment WM-101 is designed to serve the needs of the surveying profession by taking its present requirements into account. However, it is also designed to incorporate future features and technological developments with ease to the user when upgrading the WM-101. WM-101 OVERVIEW Figure 2 shows that the WM-101 consists of two major components: the antenna unit and the processor unit. The antenna unit, shown mounted on a tripod, is housed in a moulded polycarbonate case. The bottom surface of the antenna is flat with a center hole threaded to accept a standard 5/8-th inch tripod mounting stud. The top of the antenna is shaped to serve as an unambiguous survey target. The height of the anten- na unit is 0.18 m, and its maximum horizontal diameter is 0.21 m. The volute antenna receives the 1575.42 MHz satellite signals, which are filtered, amplified, down- converted to lower frequencies, and then sent via cable to the processor unit. The standard cable length is 10 m of RG-223, with an option for up to 120 m of RG-214. The processor unit is housed in a briefcase style, moulded polycarbonate case. This provides both ease of carrying and shock resistance. It is environmentally sealed, weighs approximately 14.4 kg, and has dimensions of 0.17 x 0.51 x 0.39 m. The hinged dust cover protects the control panel during transport but is removed during operation. A plate on the inside of the dust cover provides all the necessary field instructions. The control panel provides 43 alphanumeric and function keys for entering data and controlling system operation, and a 3 line by 20 character vacuum fluorescent display for showing results and status information. A toggle switch controls main power. A meter displays internal or external battery voltage, internal temperature, or the power state of the unit as selected by 3 small pushbuttons. Two LED indica- tors provide status/warning information. Two dessiccant cans control the humidity of the main electronics compartment and of the tape deck respectively. They also 149 contain automatic pressure-relief valves to compensate for changes in atmospheric pressure. A digital tape cassette reader/recorder is mounted under a hinged protec- tive cover. It is used to record both raw satellite data and internally computed position fix results. The tape recording process has been designed to optimize reliability and efficiency. At the lower front of the unit are connectors for the antenna and optionally for external power, a modem interface, an RS-232 serial interface, an RS-422 serial interface, a second antenna, and an external oscillator. Power for the unit may be supplied either by an internal, rechargable, nickel cadmium battery pack or by an external source. The internal battery pack typically will operate the unit for 4.5 hours. The external power source may range from 10.5 to 15 volts. An optional AC/DC power accessory can be used to operate the unit while charging the internal battery. The main processor within the WM-101 is the Intel 8086 with an 8087 arithmetic coprocessor. This powerful 16-bit computer controls virtually every function of the system. Its power is used to compute satellite visibility predictions, navigation solutions, and point positioning results including transformations in the field. It is able to control power to major functional elements to minimize battery drain. It controls the self-test function and reports the source of any error found. Having a powerful computer makes possible many future improvements through software insertion. The receiver card of the WM-101 provides four independent code correlation chan- nels, i.e., four satellite signals can be tracked simultaneously. These channels are sequenced so that up to nine satellites can be tracked without losing cycle count and so that interchannel biases are observed and removed. TAKING MAXIMUM ADVANTAGE OF GPS SIGNALS It seems axiomatic that GPS satellite surveying equipment should take maximum advantage of the signals provided. Therefore, it is curious that some equipment makers have touted "codeless" receivers. Pseudorandom digital codes are the very basis of the GPS signal structure and are used not only to make pseudorange measure- ments but also to provide access to the underlying carrier signal, the satellite message, and precise time marks. These are valuable resources which we believe should be exploited rather than discarded for the sake of "codelessness". By using the C/A code structure, the WM-101 obtains the full GPS LI signal strength, thus minimizing phase measurement noise. In contrast, "codeless" receivers typically experience a 16 dB squaring loss when processing the LI GPS signal, and the penalty becomes worse, dB for dB, if the signal fades due to multipath, antenna pattern, shading, or additional signal filtering. Because accuracy depends on making high quality, low noise measurements we believe it is best to begin with the strongest possible signal by using code correlation techniques. Because the satellite message is transmitted by modulating the code, "codeless" receivers discard this valuable message. The almanac part of the message tells which satellites are available and healthy, and allows prediction of when they will appear and at what angles. When a new satellite is put into service, equipment capable of reading the almanac will know and begin to use the signals immediately. The ephemeris part of the message permits the user to navigate, to calculate point 150 positions in the field, and to have immediate access to orbit parameters for post-processing. We believe it is important to take maximum advantage of this resource. The C/A code also is a valuable source of time synchronization. Codeless recei- vers not only must have some other source of time signals to set the internal clock, but all equipment participating in a survey must be physically interconnected prior to deployment in order to achieve precise synchronization. The same process must be repeated after the survey to assure that time synchronization was maintained throughout the data collection interval. We believe in taking full advantage of the precise time marks inherent in the C/A codes, not only to set the clock but to synchronize the measurements. The GPS signal structure permits real-time navigation and on-site point position- ing. Although not vital to a survey mission, these capabilities are a significant benefit. Navigation is helpful when attempting to find an unknown marker. Point positioning helps verify that the proper site actually was occupied. Furthermore, the quality of the data being recorded is made evident through this process. Perhaps even more important is the confidence gained by the surveyor that his equipment in functioning properly in the field. The WM-101 GPS satellite surveying equipment has been designed to take full advantage of the GPS signal structure. This design philosophy: (1) minimizes measurement noise, especially under adverse conditions, (2) permits access to the satellite message for prediction of satellite availability, real-time navigation, on-site point positioning and immediate, free access to orbit parameters for post processing, and (3) obtains precise time marks for data synchronization without the need to interconnect WM-101 receivers either before or after a survey. These capabilities optimize the probability of success and give assurance while in the field that the equipment is working properly. We see no disadvantage in making full use of the GPS signals. ACCURACY Although many characteristics of a survey set are important, dependable accuracy is vital. Because field test results are not yet available for the WM-101, the design factors which contribute to excellent accuracy will be reviewed. Survey accuracy ultimately depends on the precision with which an instrument measures the phase of the received GPS carrier signals. As stated in the previous section, use of the C/A code aids this objective by providing the best possible signal-to-noise ratio. The WM-101 measures the phase of these strong signals with a precision better than one degree. Because multiple correlation channels are used, it is necessary to observe interchannel phase biases. One of the four receiver channels is dedicated to this function, sequentially observing all of the same signals tracked by the other three channels. Thus, the WM-101 is able to determine the relative phase of the observed satellite signals with sub-millimeter precision. The accuracy of determining one point with respect to another also depends on the number of satellite signals tracked simultaneously at both sites and the duration of these simultaneous observations. Although it is desirable to place the antennas so as to achieve an unobstructed view of the hemisphere, there are practical 151 limitations imposed by terrain or by nearby structures. Therefore, a signal may be tracked at one site which cannot be received at the other. Furthermore, this lack of intervisibility will not be known until the data are returned for post processing. To minimize this problem the WM-101 warns the operator when an expected satellite signal is not being received. Also, the satellite predictions define the azimuth and elevation angles to all satellites for assistance when establishing the antenna location. Even so, there will be many instances in which satellite signals can be seen at one site and not at the other. To compensate, we believe it is best to track every potentially useful satellite signal at both sites, which is why the WM-101 is capable of tracking and recording data from up to nine satellites at once. Even if one or two signals are blocked, others may be available to compensate. In post processing, it is better to obtain an acceptable answer from less than an optimum set of signals than to obtain no answer because the optimum four satellite signals were available at one site but not at the other. Multipath (the reception of reflected signals) is another source of error. For- tunately, the effects tend to average out, but reflected signals should be avoided if at all possible. There are three methods of avoiding multipath signals. One is to shape the antenna pattern to attenuate signals received below the minimum acceptable elevation angle. Large ground plane structures can achieve this effect, but at the sacrifice of portability. The WM-101 antenna pattern, as shown in Figure 3, reveals that the objective has been achieved without adversely affecting portability. The second factor is polarization. The GPS signals are right-hand circular polarized, but reflected signals are left-hand circular polarized. Therefore, an antenna which maintains its right-hand circular polarization over the entire sphere is a yery effective way of attenuating multipath signals. The WM-101 antenna attenuates reflected signals by at least 7 dB at all angles. Finally, the process of correlating with the C/A code also attenuates reflected signals. This is because the path length of the reflected signal is longer than that of the direct signal. If the extra path length is over 300 meters, the reflected signal is attenuated by at least 30 dB. If the extra path length is 150 meters, the attenuation is only 6 dB. Overall, the combination of a shaped antenna pattern, excellent polarization circularity at any angle, and receiver correlation to attenuate delayed signals assures minimum interference from multipath signals. Another significant error source is unmodeled tropospheric refraction. To reduce this error the WM-101 is designed to record local weather parameters along with the satellite measurements. Although the weather parameters may be entered manually, automatic entry from an external weather sensor package is permitted. Automatic weather sensing may seem like a small detail, but such details are important to achieving ultimate survey accuracy. It is important that no information be lost when measuring the satellite signal phase. Therefore, the WM-101 not only measures the precise phase at periodic inter- vals but also the accumulated phase change between these precisely defined time marks. Continuously integrated phase data permit non-ambiguous solutions in the shortest possible time. The WM-101 is a single-frequency instrument. Therefore, errors due to ionospheric refraction differences between survey sites are not observed. However, because ionospheric errors dominate long distance survey results, provision has been made for adding an L2 receiver in 1986. This option consists of a dual -frequency antenna 152 unit and an L2 receiver board which fits within the WM-101 card cage. It is impor- tant to note that the L2 receiver will provide precise carrier phase measurements whether or not the P-code is denied to civil users. The proprietary technique being used provides a substantially better signal-to-noise ratio than the current genera- tion of "codeless" L2 receivers. This section has described characteristics of the WM-101 which permit it to obtain the best available accuracy both now and for years to come. Excellent accura- cy requires that a survey instrument be designed to optimize each and every parame- ter affecting its ability to measure precise carrier phase from as many satellites as possible and to apply appropriate ionospheric and tropospheric corrections. SPECIAL FEATURES OF WM-101 Portability Because of its small size (0.17 x 0.51 x 0.39 m), light weight (14.4 kg), and robust construction, the WM-101 processor unit is easily transportable by hand and naturally by back pack, helicopter, jeep, or pack animal. The briefcase configura- tion is easy to carry with one hand, and it is designed to fit under an airplane seat. Four metal feet on the bottom of the case have tapped holes for securing to a backpack, table top, or other mounting surface. The hinged, removable dust cover protects the control panel during transport. The moulded polycarbonate structural foam case protects the unit against rough handling. The unit can withstand a drop of 0.60 m onto a hard surface during trans- port. The internal components are designed to accept vibration from 5 to 2,000 Hz during transport and 5 to 55 Hz while operating. Two-way automatic pressure relief valves prevent over-or under-pressurization due to altitude changes of -200 to +15,000 m during transport. The unit is built to operate under harsh environmental conditions such as wind driven rain, sleet, snow and dust. Sealed construction is used throughout. Not only is the unit weatherproof and waterproof, but it also is buoyant. The unit can withstand temperature extremes of -40 to +70°C during transport and -25 to +55°C while operating, with humidity between and 100 percent. Desiccant is used to control humidity inside the case. All connectors are ruggedized and equipped with protective caps to prevent damage during transport. A shipping case is provided for long distance transport as baggage or freight. The antenna unit is likewise easily transportable due to its small size (0.18 x 0.21 diameter), light weight (1.5 kg), and robust construction. It is encased in a moulded polycarbonate housing which is pressurized and sealed. This housing protects the unit from both shock and the environment. The unit is submersible in water and can be transported or operated at temperatures ranging from -40 to +70°C. The antenna unit also can withstand the same atmospheric pressure changes, shock and vibration as the processor unit. An antenna shipping case is provided which also houses accessories required in the field. In most cases it is not necessary to carry external batteries into the field. The processor unit contains a rechargeable nickel cadmium battery pack. A fully charged battery pack can operate the unit for about 4.5 hours, which provides more than 153 enough time to collect sufficient satellite data for a precise differential position survey. For other operational scenarios, spare battery packs may be taken to the field, or an external power source (10.5 to 15 volts) may be used. On average the unit consumes only about 20 watts. A rugged spare parts kit also is available. The kit may be taken to the field so that immediate repair is possible. The WM-101 has been designed for portability. Small size, robust construction and low power consumption permit this instrument to be used in practically any desired location. Multiple Data Ports The processor unit contains three data ports: an RS-232 serial port, an RS-422 serial port, and a modem port. These ports will be used for several types of data communications, as selected by operator keyboard commands. Some of the uses will be: a. Printer Output. ASCII format data will be output to a port for printing. The output can be programmed at intervals or immediate when the PRINT DISPLAY key is pressed. b. Tape Dump. Data previously recorded on tape cassette will be output to a port. This feature allows the processor unit transfer data to an external computer either by direct wire connection or via a communications link. c. Weather Input. It is desirable to enter weather parameters (i.e. temperature, pressure, and humidity) for tropospheric refraction correction. These data may be entered either manually via the keyboard or automatically via inputs from a weather station. d. Remote Control. Keyboard button codes may be transmitted to a WM-101 proces- sor, thus permitting remote control. Also, the remote unit's display contents may be sent back to the control point for display. This feature enables a WM-101 at a base station to control the operation of another at a remote site. e. Real Time Differential /Translocation Positioning. By establishing a communi- cation link from a WM-101 at a known location to one or more units at unknown sites or on a moving platform, it will be possible to obtain real-time relative navigation or translocation surveying results. Ease of Use Satellite surveying equipment must be operated by a diverse range of personnel, from geodesy professors to part-time local help. The WM-101 has been designed with the flexibility to serve a wide range of applications yet is easy to use reliably by operators with minimal training. To illustrate the simplicity, only the following steps are required to perform a field measurement: 1. Set up antenna. This entails placing the antenna at the survey site (possibly on a tripod), measuring the offset from the antenna to the marker, and then attaching the antenna cable. 154 2. Set up processor unit. The processor unit is placed nearby, the antenna cable is connected, and the dust cover is removed to access the control panel. At the control panel the user applies power, inserts a tape cassette, and initializes the unit via prompted keyboard entries. 3. Collect data. The system runs automatically, collecting satellite data and recording it on the tape cassette. No user intervention is required, but the equip- ment and the survey status can be determined whenever desired by pressing a button. Completion of data collection can be based on a timed interval or on automatic evaluation of data quality. 4. Pack up equipment. When sufficient data have been collected, the user removes and labels the tape cassette, powers down the processor unit, disconnects the antenna cable, and packs the equipment. Achieving both operational simplicity and sophisticated functionality is made possible by the control panel shown in Figure 4. The display at the top provides three lines of 20 alphanumeric characters each. The "soft keys" located on either side of the display are used to select one of six options offered by the main pro- cessor. These keys also are used to designate which parameter being displayed should be changed. Below the display area are four groups of keys. The group on the right permits alphanumeric data entry. All other keys are called function keys. The group on the lower left is organized into three columns of three keys each. The first column permits control of basic system parameters such as mode of operation, datum shift parameters, or equipment option selection. The center column permits control of the tape transport and of the self -test function, and the AUX key is provided for functional expansion in the future. The third column provides information about the system, the satellites, or the position fix result. The key group at the upper left relates primarily to the display. For example, the information being displayed can be printed immediately. The INFO and HELP keys call up information either to explain a function or to remind the user of his survey mode. The UP and DOWN keys scroll the display when more than three lines of information is provided. The center three keys permit the system to be used by the least skilled personnel. A survey can be completed by using only these three plus the alphanumeric keys. The system switches from standby to operate when the START key is pressed, and the user is then led through a prompted sequence of date entry and selection options which initialize the unit for that survey location. Mission status can be determined whenever desired by pressing the center key. When the survey is over, the user presses the STOP key which terminates data collection, requests any final information, and then switches the unit to standby again. Basic survey parameters such as datum selection and definition of the information requested of the operator and the information provided to him when he presses the MISSION STATUS key are programmable by experienced personnel before the mission begins by using the MISSION CONFIGURATION key. For the experienced user, a sophisticated and extensive array of controls are at his command. This is made possible by the menu driven control concept. When a 155 function key is pressed, the display indicates up to six menu selections. Pressing the appropriate soft key gives access to the selected item, which in some cases can be another set of menus. Because clear mnemonics are used to designate each option, and because the HELP key can be used to explain any mnemonic, the keyboard is self-teaching. Therefore, the WM-101 combines clarity and simplicity of operation with access to a broad and sophisticated range of options. Although GPS is based on a World Geodetic System, most survey applications re- quire the use of a local datum and mapped coordinates in a system such as Universal Transverse Mercator (UTM). The WM-101 performs the necessary conversions automati- cally whenever the user inputs or displays a position. Initially, the user selects the desired conversion and specifies the necessary parameters. Thereafter, the conversions are performed automatically. ASSURANCE OF SUCCESS The MX- 1502 was not the first commercial Doppler surveying instrument, but has become the one most widely used. Its success would be easy to understand if it had provided substantially better accuracy or was far more portable than competitive equipment. In fact, however, these differences were marginal. We believe the primary advantage offered by the MX-1502 is its unparalleled assurance of success. The WM-101 has been designed to achieve the same standard. Design factors which optimize the probability of returning from a survey with good data contribute to assurance of success. Equally important, however, is the ability to tell the operator whether or not the mission will be successful. If a problem exists, an early warning permits corrective action to be taken in the field. Otherwise, having to re-occupy a site is always costly and aggravating. A major contribution to assurance of success, as mentioned above, is the number of satellites tracked. If a satellite can be seen at one site but not at the other, it cannot be used in the differential solution. Instruments which limit the number of satellites which can be usefully tracked increase the risk of not having enough intervisible satellites. The WM-101 minimizes this risk by tracking up to nine satellite signals at one time. The WM-101 also assures that data is recorded properly. As the tape is being written, it is also being read back and compared bit by bit with the intended messa- ge. If a single bit error is detected, the message is re-written up to three times to assure a perfect result. If errors persists, the operator is warned and given the opportunity to correct the problem before leaving the field site. Because it is so costly to re-occupy a site, the WM-101 is programmed to bring home error-free data. The on-site point positioning solution is extremely valuable in verifying that the equipment is working properly in the field. The operator can determine how many satellites are being tracked, the quality of each signal, and the quality of the point positioning result. By monitoring these indicators and having no error flags, the operator can be assured that the equipment is working properly, tracking a reasonable number of satellites, and providing an error-free recording of the necessary data. The operator can be sure the mission was a success when he leaves the site. 156 The WM-101 also is equipped with an extensive self-test capability. The main processor is in charge of this function and performs an "inside out" test sequence, beginning with itself. Sample computations are run, program memory check sums are computed, and all random access memory locations are tested. Self-test then expands outward to evaluate the antenna unit, all receiver channels, the tape recording function, the data display capability, and the input/output ports. Any error is reported to the operator for corrective action. The WM-101 is built to permit field repair by module replacemert. If the self- test function detecs an error, the faulty module is indicated. A successful self- test after replacing that module verfies that the equipment is ready to continue the survey task. The final point is not a characteristic of the WM-101 but of the support provided by the Wild Heerbrugg and Magnavox joint venture. Having an extensive network of sales and service agents assures that local training, spare parts, and maintenance will be readily available. Taken together, there are many reason why the WM-101 assures a sueccessful sur- vey. The equipment is designed to extract as much high quality information from the available satellite signals as possible. Information provided to the operator gives assurance that the equipment is working properly or indicates how to correct a problem. These characteristics plus a worldwide support network provide optimum assurance of success. POST-PROCESSING SOFTWARE To obtain a 3D vector between two WM-101 stations, the recorded satellite data needs to be combined and processed together in a computer. Although it is possible to program the resident computer of the WM-101 for this purpose (future feature), we foresee that there will be a continuing need to post-process the WM-101 data for geodetic applications. The main reasons are computation of geodetic networks, data editing, improved orbit information, tranformation of the results, and the combination of WM-101 results with terrestrial survey results. Consequently the GPS satellite surveying equipment, WM-101, includes the special post-processing software, PoPS, for comprehensive processing of the field data, on commercially available computer hardware. PoPS is designed to run on the following system consisting in its minimum configuration of: a. IBM PC XT or compatible computers, with 640kbyte RAM, 10Mbyte hard-disk, 360kbyte diskette (5.25"), 8087 co-processor, and DOS 2.0. b. MEMTEC 5450XL cassette terminal c. Printer for continuous tractor-feed paper of 8.5" minimum paper width. PoPS is a user-friendly, menu-driven, fully interactive software package for the determination of 3D positions from WM-101 measurements. Its theoretical background is clearly documented in the PoPS manual. Future features of PoPS will include the use of graphical displays and the required computations using L2 measurements. 157 At the core of PoPS is its data-management module which communicates with the f ol 1 owi ng components : Field preparation indicates the availability of satellites for any given time window and terrestrial position. The preliminary position is determined in WGS72 from known parameters of the datum and projection system. Data transfer permits easy, safe data transfer from the WM-101 tape cassette to the PoPS data-management module. Data pre-processing identifies pertinent orbital data, computes preliminary station coordinates, defines baselines, checks these baseline measurements, and performs single-point positioning. Computation solves geodetic network adjustments for up to ten stations. The unterlying principle is the computation of single differences of baseline measurements. Models for tropospheric and ionospheric propagation effects and clock behaviour are incorporated, taking the relevant deterministic and stochastic parameters into account. All results are given in WGS72 with comprehensive accuracy information. Transformation and results tranforms original results from WGS72 into any other known or user-defined datum and projection system. Over-determined similarity transformations between results may be performed. 158 500 Figure 1: Measurement Error (e) of Various Surveying Methods versus Distance (D) izv / Figure 2: The WM-101 GPS Satellite Surveying Equipment 159 QUARTER WAVELENGTH VOLUTE Figure 3: The WM-101 Antenna Pattern: 1575.42 MHz, RHC Polarization Voltage Plot lU .JL 3 ) POOP 3, IS 'G1]'EDI ■• fsn : f^r^ ' CZ3' yrof' /~1 CD e *ii mil # Q ©Q ©dEO S CIR f O * ' ^ W *" -^ ^ Figure 4: The WM-101 Main Control Panel 160 STATIC POINT POSITIONING WITH AN LI, C/A CODE GPS RECEIVER Alison K. Brown Mark. A. Sturza Litton Aero Products 6101 Condor Drive Moorpark, CA 93021 USA ABSTRACT The Global Positioning System (GPS) has a multitude of commercial navigation applications. It will be widely used in land, sea, air and space navigation. The Standard Positioning Service (SPS) has sufficient accuracy for most of these applications and by using enhancement techniques this accuracy can be significantly improved. For survey and geodetic applications, where the GPS receiver is stationary, position can be estimated from the GPS doppler shifts, the delta-ranges. These are measured to far greater precision in a GPS receiver than the pseudo-ranges. A least squares technique has been developed for optimally processing the delta-ranges, which are accumulated over the tracking interval to improve the position solution geometry. Since the delta-ranges can be determined to equal precision using either the Precise Positioning Service (PPS) or the SPS, this technique can be implemented using an Ll, C/A code GPS receiver. The positioning accuracy possible is dependent on the length of time that the delta-range measurements are accumulated. By tracking satellites for one hour, it is possible to determine absolute position from the accumulated delta-ranges to 16 m RSS, comparable accuracy to that achievable using the PPS. Since common GPS system errors cancel in a local area, relative position can be determined to 6 cm in the same time interval. Over a 100 km baseline this provides better than 1 ppm relative positioning accuracy, which is suitable for geodetic applications. 1 . INTRODUCTION GPS Description The NAVSTAR Global Positioning System (GPS) is a satellite-based radio-navigation system intended to provide highly accurate three dimensional position and velocity, and precise time on a continuous global basis. GPS has been under development by the Department of Defense (DoD) since the early 1970' s. When the system becomes fully operational in late 1988, it will consist of 18 satellites in six orbital planes inclined at 55 degrees. Each plane will contain three satellites spaced 120 degrees apart in 12-hour orbits. The relative phasing of the satellites from one orbital plane to the next is 40 degrees. In addition to the 18 operational satellites, there will be three active spares. Each GPS satellite will continuously transmit navigation signals at two carrier frequencies, Ll = 1575.42 MHz and L2 = 1227.6 MHz. The Ll signal will consist of the P-code ranging signal (10.23 MBPS) , the C/A-code ranging signal (1.023 MBPS) , in and 50 BPS data providing satellite ephemeris and clock bias information, signal will consist of either the P-code signal or the C/A-code signal. The L2 Navigation using GPS is accomplished by passive trilateration. The GPS user equipment measures the pseudo range to four satellites, computes the position of the four satellites using the received ephemeris data, and processes the pseudo range measurements and satellite positions to estimate three-dimensional user position and time. Two classes of the GPS service will be available: The Standard Positioning Service (SPS) and the Precise Positioning Service (PPS) . The SPS, utilizing the C/A-code signal, will be available to the general public. It will provide a horizontal position accuracy of 40 meters CEP (100 meters 2 dRMS) . The PPS, utilizing the P-code signal, will only be available to a limited number of non-DoD users in the interest of national security. It will provide a 3-D position accuracy of 16 meters SEP (Spherical Error Probable), which is equivalent to 18 m RSS. TRANSIT Surveying Since 1967, when it was first released for civil use, the TRANSIT satellite navigation system has been used for static point positioning. TRANSIT surveying has proven ideal in application where conventional survey techniques are too slow or costly. Difficult to reach locations or large areas without adequate control points are examples. Typical TRANSIT positioning accuracies are shown in Table 1. Several manufacturers have developed TRANSIT equipment specifically for the survey market place. The cost of a survey conducted using a satellite navigation system is directly related to the required time on site. From Table 1, the average time on site, for 10 meter la horizontal point position (~12 meters RSS) using TRANSIT is 10 hours. This paper shows that using GPS, only 1 hour on site is required to obtain 15 meters RSS point positioning accuracy and 6 cm RSS relative positioning accuracy. It is anticipated that GPS will significantly reduce the cost of satellite surveying as well as providing accuracies previously unobtainable. Table 1 TRANSIT doppler positioning accuracies (HOAR 82) Horizontal Position Accuracy la Doppler Positioning Technique Minimum Number of Passes Required Average Time to Completion >37m Single Pass Point Positioning 1 40 min >10m Point Positioning 15 10 hrs >lm Field or Real Time Translocation 4 (common to each station) 2 hr 40 min 162 2. GPS MEASUREMENT EQUATIONS Pseudo-Range and Delta-Range Measurements GPS receivers measure Pseudo-Range (PR) , the difference between the time of reception and time of transmission of the GPS signal, and Delta-Range (DR) , the difference in carrier phase over a fixed time interval, generally one second. The PRs and DRs are related to user^position error R , velocity error Vy and user clock and frequency offsets, S^ and AB^ through equations 2.1 - 2.5. , (R^ - R^) ,k _ — u —SI -U —SI 1 — 1 . — U —81 U /N If '^ If ^ It — 1 DR. = PR. - PR? ^ 111 PR^ = m^ - PR^ = l'^ . R^ + b'^ 1 1 1 — 1 — u u 1. LOS from user to ith satellite at time t, . — i k R Position of user. — u Velocity of user. R . Position of ith satellite, —si Ir PR. PR to ith satellite at time t, . i k DR. DR to ith satellite at time t, . i k B Users clock offset from GPS time. AB Change in user's clock offset over one sec. 2.1 2.2 2.3 2.4 D-fe^ = DR^ - Dr'^ = (llf - 1^1) . R^ * 1^ . V^ ^ AB^ 2.5 1 1 1—1—1 — u — 1 — u u 163 For static point positioning the user's velocity is known to be zero and equation 2.5 simplifies to DR, = (1, - 1^ ^) • R + AB*^ 2.6 1 —1 — 1 — u u The LOS vector to a GPS satellite does not change significantly over a one second interval, so to improve the geometry of the navigation solution it is advantageous to accumulate DRs over longer time intervals to form a new measurement variable. Accumulated Delta Ranges (ADRs) . Accumulated Delta-Range Measurements Since the DRs are formed from the difference between two phase measurements from the carrier tracking loops, accumulating DRs to form a new measurement does not increase the measurement error. DR =X^n +|;-n -|^ j 2.6 ADR TT. \ In In 2ir 2.7 The phase measurement error statistics are: E[*] = 164 Thus DR = , Var (dR } = 2ct^, DR'^DR = a. 2.8 ADR = ♦., Var (ADR ) = a. 2.9 u ([> Since adjacent DR measurements share a common phase measurement, the phase errors associated with these common measurements cancel out In the ADR measurement. The DRs have zero mean error but are correlated between adjacent time Intervals. Alternatively, the ADRs share a common bias error, the Initial carrier phase error, but apart from this bias all samples are uncorrelated. The measurement equation for the ADR measurement becomes ~ k k '^ k k ^k ^k ~0 ADR*^ = ADR*^ - ADR*^ = (1, - l") • R*^ + B*^ - b" 2.10 —1 —a — u u u As time Increases, the satellite geometry for estimating position error improves. Because of the independence between these measurements, it is possible to process an ADR every second from each satellite tracked. This allows position to be determined to far greater accuracy than by processing PR Measurements. 3. GPS ERROR SOURCES The major GPS error sources which affect the accuracy of the navigation solution are shown in Table 2. In each case their contribution to the ADR measurement error is estimated for the length of time, T, that measurements have been accumulated. Receiver Noise The receiver noise level is dependent on the carrier-to-noise-density ratio (C/Nq) of the GPS signal. The nominal C/Nq is 32 dB-Hz. The range equivalent phase noise on the ADR measurement can be modeled as white noise with measurement variance 0.972 mm la (Holmes 82). Receiver Clock The receiver clock is modeled as a high quality quartz oscillator with Alan Variance 5 x 10~12 at one second, increasing to 10"^^ at one hundred seconds. This can be statistically modeled by a range equivalent random walk in the clock offset from GPS time of 0.18 mm yilz and a white noise in clock offset of 0.67 mm la. Since the change in the user clock bias is estimated as part of the navigation solution, these errors do not affect the accuracy of the final position solution. Ionospheric Error The ionosphere affects the accuracy of the ADR measurements by altering the propagation time of the GPS signal. However, since the effect is proportional to frequency squared, it is possible to compensate this effect by measuring ADRs on 165 Table 2 Contribution of GPS error sources to ADR errors Contribution to ADR Error Source Model Error (la) Receiver Noise White Noise 0.972 mm la Ionospheric - Dual Frequency White Noise 2.983 mm la Compensation Tropospheric Range Error Markov T = 1 hour *0.8(1 - e"'^'''^)m Satellite Ephemeris Bias Along Track 0.8 m la *0.184 T mm Radial 6.3 m la Crosstrack 3.0 m la Satellite Clock Random Walk *3yT^mm *Not included in measurement noise model for translocation. both the Ll and L2 carrier frequencies (Russel 78) . If the C/A-code signal is not available on the L2 carrier signal, SPS users can implement dual frequency ADR ionospheric compensation by using codeless GPS techniques (MacDoran 84) . ADR = 2.5457 AD \ - 1.5457 AD \: 3.1 Differencing the ADRs in this manner affects their measurement accuracy. Since the receiver noise is proportional to wavelength, the measurement noise after ionospheric compensation becomes ^ADR = 6-^8 ^Ll -^ 3-^^ Ll 3.2 That is, the additive affect of the ionospheric error can be modeled as white noise with variance y 9. 4 2 O-^-^. For translocation, the ionospheric effect does not vary significantly over a local area. It is not necessary, therefore to provide dual frequency compensation for relative positioning, as the ionospheric error will cancel between stations. Tropospheric Effect The troposphere also introduces a propagation delay, which affects the ADR measurement. This affect is not dependent on frequency but can be adequately modeled (Hopf ield 69) . The residual error is approximately five percent of the total effect. This range error can be modeled by a markov process with variance 0.4 m and correlation time one hour. As for the ionospheric effect, the error in the tropospheric delay is common between stations in a local area. For translocation, therefore, the errors in the tropospheric delay will cancel between stations. 166 Satellite Ephemerls Error The satellite ephemeris error can be modeled as an along track, cross track and radial bias with la values as shown in Table 2 (Russel 78) . The effect of these errors on the ADRs increases with time as the position of the satellite changes with respect to the user. To improve the accuracy of the navigation solution, states should be included to allow these parameters to be estimated. However, in a simplified solution the error can be modeled as a random rate error of 0.184 mm/sec. It should be noted that this model is only valid when considering a single ADR measurement from each satellite. If multiple measurements are made during one satellite pass, the measurements are no longer independent. Because the satellites are orbiting at 20,183 km, the effect of the orbital errors will be common over a large local area. Over 100 km there is only 0.5% variation in the effect of the satellite position errors on the navigation solution. These errors will therefore cancel in relative positioning. Satellite Clock Error The predominant error in the cesium clocks, used on board the GPS satellites, is white noise in frequency; that is random walk in the satellite clock offset fr om GPS time. Typical white noise figures for a cesium clock are lO"-'-^ (sec/sec)/ JyLz. Since the same satellites are tracked at either station, in translocation, satellite clock errors are common between stations. In relative positioning, therefore, the satellite clock errors will cancel and can be ignored. 4. SATELLITE GEOMETRY Position Dilution of Precision The effect of the GPS satellite geometry on position accuracy is generally expressed as Position Dilution of Precision (PDOP) . From equation 2.10 the user's position error and clock bias drift can be directly measured from the ADRs to four GPS satellites. Formulating these four measurements in vector format gives the equation Z = ADR^ a5r^ = ADR^ ADR^ 4 ._ (4-lJ)^ 1 (1^-1°)^ 1 (1^-1?)^ 1 —4 —4 U 5° U = H X 4.1 The user's position and clock error can be solved using the least squares equation. X = H~^z 4.2 167 It should be noted that the observation matrix H is a function only of the satellite geometry. If the components of the measurement vector z^ are assumed to have equal and independent measurement variances, a^, then the state errors also obey the linear relationship of equation 4.2. T -1 T -T -12 E [XX ] = H E [zz ] H = (h'^H) a ^-3 Li T -1 The matrix (H H) is the Geometric Dilution of Precision (GDOP) Matrix. It can be used to derive the position and time variances from the ADR measurement error. The Position Dilution of Precision (PDOP) is the scale factor that should be applied to the measurement variance, due to the satellite geometry, to calculate the RSS user's position variance. Defining (H^H)?? to be the ith diagonal element of the GDOP matrix (rTh)"! ^^ PDOP =/y; (h'^H).I 4.4 - 'i=l From Equations 4.1 and 4.3 it is obvious that the RSS position error is given by: V2 2 2 a + a + a = PDOP * Or, 4.5 xu yu zu Z Satellite Selection Since there are generally more than four satellites visible in the sky at one time, minimizing PDOP can be used as a criterion for optimally selecting the best four satellites for the receiver to track. Figures 1 through 4 show PDOP calculated for different ADR time intervals, with the satellites selected using this stategy. As can be seen from the figures the PDOP is strongly dependent on the ADR time interval. As the time interval increases the satellite geometry improves and the PDOP decreases. Also as the time interval increases, more periods occur where the minimum PDOP achievable with the satellites visible throughout that period is significantly greater than the norm; that is, a satellite 'outage' occurs. GPS satellite 'outages' occur at various times of day and longitude, centered at latitudes 36° and 66° (Kruh 81). When an outage occurs, for about 10 minutes the PDOP associated with the PR measurement geometry approaches infinity, so that during this period position and user clock offset cannot be directly solved for. From Figures 1 through 4 the 'outages' associated with processing the ADRs are also centered around 36° of latitude. In Table 3 the average PDOP associated with 'normal' operation, that is not during a GPS 'outage', are catalogued for the various accumulation time intervals. Defining an 'outage' as the time interval when the PDOP is more than 50 percent above this 'normal' value, the percentage of time these 'outage' intervals occur is plotted in Figure 5. As the accumulation time interval increases, more and more frequently it becomes necessary to wait 168 J f * . ° . ! » ! » IL • ( OS CKO o.i 88«* i!IS : il;!: '■* "^'"■'=iili::::::!tii;i|;;i;iii|!H ° • ' !!!!ll!!l!Hiiijjj||i;i ;'e.99 ia.iSi ) "7^ 09 8'e.ea 3b. aa .80 M^ Fig. 1 PDOP for delta-ranges accumulated over 0.5 hour. 3 i O <5 « * , J ^J e g iiiil ni!l!!ll!llnnijji„„jj„jn,. "is i'0.£S 2'2.Ji ii.Za iZ.SQ /fl.iJ 33. JC ^.i^.SS Fig. 2 PDOP for delta-ranges accumulated over 1 hour, 169 • O • 8 * • o e §\s S * « e • » 9 a » • . illiniliill!! iiliiiilDliiiiisiii 88 I'a.es 2'0.eo a'a.eo S^aTaa ^a.aa SaTiJ TaTas s'e.sQ ^e.aa LfiTlfUOE CDE3) Fig. 3 PDOP for delta-ranges accumulated over 1.5 hour. 0(0-1 i 0. S 'I e '0 ^ (!) fl) » 8 o S i 9.0 j g « § 8 i § ■ •■lillll IhlMi^^^Stlss' lllllll"*"""'"a»eese«liBIIII||llll»l«! S s c c : je 10.23 2S.20 LftfnUDE COES 19. as oj.fij ?* . ao 'JG . mi Fig. 4 PDOP for delta-ranges accumulated over 2 hours. 170 before the 'optimum' satellite geometry associated with that particular time interval becomes available. With the one hour accumulation time interval, at 36 latitude outages occur ~75 percent of the time. This means, on the average, optimum satellite geometry will appear within 45 minutes. Positioning Accuracy The RSS position accuracy attainable through processing four ADR measurements can be calculated using the GPS Error Model in Table 2 and the PDOP, using Equation 4.5, Table 3 shows the RSS position accuracy attainable for DRs accumulated over 0.5 hour, 1 hour, 1.5 hour and 2 hour intervals. Increasing the accumulation interval from 0.5 to 1 hour drops the RSS position error by a half to 15 m, due to the decrease in PDOP. This is comparable point positioning accuracy to that achievable with the P code, but is available to C/A code users. Increasing the interval further to 2 hours, does improve the position accuracy but the PDOP is not significantly reduced. In addition as the time interval increases, so does the ADR measurement error, due mainly to the satellite ephemeris errors. Also as the interval increases, the 'outage' period grows as shown in Figure 5. Table 3 Point positioning and translocation accuracies with one set of GPS measurements Time Interval (Hr) 0.5 1.0 1.5 2.0 Average PDOP 74 20 10 6 Point Positioning Measurement Error (la) Point Positioning RSS Position Accuracy 0.419 m 31.0 m 0.774 m 15.5 m 1.109 m 11.1 m 1.435 m 8. "6 m Translocation Measurement Error (la) Translocation RSS Position Accuracy 0.31 cm 23 cm 0.31 cm 6.2 cm 0.31 cm 3.1 cm 0.31 cm 1.9 cm It should be noted that the numbers given in Table 3 cannot be reduced by the familiar factor ^iT, when multiple measurements are averaged. This is because in one satellite pass the effect of the satellite position errors acts as a bias and so is not independent from measurement to measurement. However, using a precise GPS ephemeris would significantly reduce this error source, as would using this measurement technique for translocation. In translocation, with two receivers tracking the same satellites over the same time interval and differencing to measure relative position, the satellite ephemeris errors and clock errors cancel. In Table 3 the RSS position accuracy possible for translocation is shown, where satellite ephemeris and clock errors are not included in the measurement error. By processing ADR measurements over one hour it is possible to determine relative position to 6.2 cm RSS. Over a 100 km baseline this is better than 1 ppm, geodetic survey accuracy. 171 TINT .5 HR TINT = 1.0 HR TINT = 1.5 HR TINT = 2.® HR i.ii {S.ii 215. S3 30.1315 413.301 ^0.33 50.00 LRTITUDE fDEG] 90.00 Fig. 5 Outage times for different accumulation time intervals. Comparing these point positioning and translocation results with those presently achievable using TRANSIT, as shown in Table 1, considerable time and accuracy improvements are possible using GPS with this simple measurement processing technique. In one hour, comparable point positioning accuracy is possible to that from using TRANSIT for 10 hours. Similarly, far superior translocation accuracy is achievable in half an hour with GPS than that possible in three hours with TRANSIT. These improvements are due in part to the improved clocks and ephemeris accuracy of the GPS satellites, but mainly to the solution geometry provided by the GPS satellite constellation. With TRANSIT only one satellite pass occurs approximately every 40 minutes, whereas with GPS it is possible to select and process four satellite passes simultaneously. Using a more complicated analysis technique it is possible to improve on the point positioning accuracy even further, measuring position to far greater precision than ever possible using TRANSIT (Brown 85) . 5. CONCLUSIONS It has been demonstrated that a GPS C/A code receiver processing Accumulated Delta Ranges (ADRs) can provide superior absolute and relative positioning accuracies to state of the art TRANSIT surveying (Hoar 82) . Using a simple least squares processing technique, absolute position can be determined to 15 m RSS within an hour, a significant improvement over SPS C/A-code accuracy. This technique can also be applied for translocation, where by storing the four ADRs from each satellite at two locations, relative accuracy can be determined to within 6 cm RSS in one hour. This opens up new applications for GPS in the civil surveying market. 172 REFERENCES Brown, A. K. , 1985. "Static Point Positioning Using the Global Positioning System," Ph.D. Thesis, UCLA. Hoar, C. J., 1982. "Satellite Surveying, Theory, Geodesy, Map Projections," Magnavox MX-TM-3346-81 No. 10058. Holmes, J. K., 1982. "Coherent Spread Spectrum Systems," Wiley Interscience. Hopfield, H. S., 1969. "Two Quartic Tropospheric Refractivity Profiles for Correcting Satellite Data," J. Geophys Res 74 No 1 4487-4499. Jorgensen, P. S., 1980. "Combined Pseudo Range and Doppler Positioning for the Stationary NAVSTAR User," CHl597-4/80/0000-0450$00. 75, IEEE. Kruh, P., 1981. "The NAVSTAR Global Positioning System Six-Plane 18 Satellite Constellation," NTC Record, New Orleans, Louisiana, Nov 1981, pp 9.3.1-8. MacDoran, P. S., 1984. "Codeless GPS Positioning Offers Sub Meter Accuracy," Sea Technology, Oct. Russel, S. S. and Schaibly, J. H. "Control Segment and User Performance," Global Positioning System, ION 0-936406-00-3. 173 THE MACR014ETER II™ UUAL-BA1>ID INTERFEROMETRIC SURVEYOR Jonathan W. Ladd and Charles Counselman III* Aero Service Division Western Geophysical Company of America 8100 Westpark Drive Houston, Texas 77063-6378 Sergei A. Gourevitch Steinbrecher Corporation 185 New Boston Street Woburn, Massachusetts 01801 ABSTRACT Geodetic surveying with GPS became possible over three years ago, with the introduction of the MACROMETER® Interferometric Surveyor. Since that time, C|V| MACROMETRY surveys have become the standard against which surveying with GPS signals is measured. Aero Service's newly developed MACROMETER II Surveyor offers superior accuracy with reduced observing time while retaining all the advantages of the earlier MACROMETER Surveyor, These advantages include millimeter-level accuracy for short baselines, and the ability to observe six satellites continuously and simultaneously. Operation is totally independent of the GPS codes, which are expected to become unavailable. The MACROMETER II Surveyor observes both the GPS "LI" AND "L2" signals, so ionospheric effects are insignificant . Field testing of the MACROMETER II Surveyor began in early January, 1985, and continues today. In this paper we report preliminary results from one set of these field tests which demonstrate that highly precise geodetic measurements, on the order on 1 part-per-million (1 ppm) , can be obtained in as little as 15 minutes observing time. INTRODUCTION The MACROMETER Interferometric Surveyor, introduced at the Third International Geodetic Sjnnposium on Satellite Doppler Positioning in Las Cruces (Counselman and Steinbrecher, 1982), is still the premier GPS surveying instrument. Other instruments have since been announced, but until the MACROMETER II system none has demonstrated the speed and accuracy of the original MACROMETER Model 1000 system, (Bock et al, 1984, 1985). Although the MACROMETER V-IOOO field unit is a single- band instrument (LI only), it can yield 1 ppm accuracy, given 3 to 5 hours of observing time. With the V-1000, a baseline vector can be determined with First Order (1:100,000) accuracy with as little as 30 minutes of observing time. In either case, the time required to process the observations to obtain the baseline *Also Professor of Planetary Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 MACROMETER II is a trademark, MACROMETER is a registered trademark, and MACROMETRY is a servicemark of Aero Service Division, Western Geophysical Company of America 175 determination is typically under 30 minutes. As far as we know, neither the observing time nor the processing time requirement of the MACROMETER Model 1000 System has been bettered by any other brand of GPS surveying instrument. Aero Service is pleased to introduce the MACROMETER II Interferometric Surveyor, a new dual-band system, which delivers high order geodetic accuracy in substantially less observing time. Aero has conducted an intensive research and development program in dual-frequency, codeless technology which has led to the production of a field-worthy MACROMETER II System, and the development of Aero's exclusive MACROMETER II Software Processing Package. The MACROMETER II Interferometric Surveyor retains all the advantages of the MACROMETER Model 1000 System including: 1. Complete independence from GPS codes, which may be subject to encryption; 2. Millimeter-level instrumental accuracy, which enables short baselines to be determined within a millimeter in all three coordinates; 3. The ability to track, continuously and simultaneously, the signals from up to six satellites (an advantage which will become even more important as the GPS constellation of satellites is expanded); 4. Fast data processing — normally under 30 minutes for a First-Order baseline determination. Field testing of MACROMETER II Interferometric Surveyors began in January, 1985. Here we present some test results. FIELD TESTS The first objective of the testing was to demonstrate that the dual-band MACROMETER II System can yield very high accuracy in a very short time. Such a demonstration is particularly important because there are so few GPS satellites available today. Since there are only a few hours each day during which a GPS surveyor can work, it is important to minimize the site occupation time. On January 25, 1985 we made four independent determinations of a 12.5-km line. Each determination used an observing span of only thirty minutes. Because all four observations were made on the same day, we did not have the advantage of optimum satellite geometry for all the spans. Instead, our schedule simulated a typical workday, in which a surveying party squeezes as many observations as possible into the limited time available. Between our successive observing spans there were interruptions of 10 to 15 minutes. All four spans were contained within the approximately 2.5-hour window during which four or more satellites were simultaneously visible (above 15 degrees elevation) in our test area in Massachusetts. The data from each 30-minute span were processed independently, that is without reference to any data from another span, by means of Aero Service's proprietary MACROMETER II software processing package. Precise orbital information was obtained from Aero's GPS tracking network, which provides ephemeris data for MACROMETRY surveys. 176 Each of the four baseline results was then compared with a reference of presumably superior accuracy. The reference value was obtained by averaging the results of two four-hour determinations, from two different days. These two MACROMETRY measurements, also dual-band, agreed with each other in all three baseline-vector components, within one centimeter, ~ for this baseline of 12.5 kilometers, this is less than 1 ppm. RESULTS In Figure 1 we show the results of the four 30-minute determinations. For the horizontal coordinates, every determination was within 1 ppm (12 millimeters) of the reference value. For the height, the worst determination was within 4 ppm (50 millimeters) . In order to show how a MACROMETKR V-1000 (single-band) instrument would have performed under the same conditions, we also processed the data from just the Li band, from each of these four observing spans. Figure 2 shows the LI only results together with the dual-band results. Note that the vertical scales have been halved in order to accommodate the wider scatter of the single-band results. The single-band results are obviously worse than the dual-band results. Still, (as MACROMETER V-1000 System users should be pleased to see) the single-band determinations, for all three coordinates and for every one of the 30-minute spans were within about 10 centimeters (1:125,000) of the reference. In order to show the operational capability of the new dual-band MACROMETER II System in an even shorter time-span, we divided the data from each of the four 30- minute spans into 15-minute halves. We processed the data from each of the eight half-spans independently (the number of observations used in each baseline determination was then half the usual number). The eight results are shown in Figure 3. In latitude and longitude, the RMS differences are 1.0 ppm and 0.7 ppm respectively. The RMS height difference is 2.1 ppm. These eight observations spanned the usable extent of the available 4-satellite window, including periods of less than optimal satellite geometry. Thus, the MACROMETER II System, over this span and with only one half the number of observations normally used in a MACR0I*1ETRY baseline determination, has produced measurements of a precision never before achieved in such a short timespan. REMARKS These preliminary results demonstrate a significant advance in the state-of-the- art of surveying. In further experiments with the MACROl-lETER II System, we are varying obseirving conditions and procedures in order to maximize the effectiveness of this unique system. REFERENCES Counselman III, C.C, and D.H. Steinbrecher, 1982; "The MACROMETER Compact Radio Interf erometry Terminal for Geodesy with GPS", Proceedings of the Third International Geodetic Symposium on Satellite Doppler Positioning, vol. 2. pp. 1165-1172. Bock, Y.J R.I. Abbot, C.C. Counselman, S.A. Gourevitch, R.W. King, and A.R. Paradls, 1984; "Geodetic Accuracy of the MACROMETER Model V-1000", Bulletin Geodesique, vol. 58, pp. 211-221. Bock, Y., R.I. Abbot, C.C. Counselman, S.A. Gourevitch, and R.W. King, 1985; "Establishment of Three-Dime nsional Geodetic Control by Interferometry with the Global Positioning System", Journal of Geophysical Research (Solid Earth), in press. 177 50 -50 Latitude (mm) JL 1 ppm n Longitude (mm) u _ — n -■■• • • * u n 1 1 50 -50 Height (mm) 10 11 12 (hrsUTCon 1/25/85) 13 Figure 1. Four independent determinotions of o 12.5-km boseline vector by MACROMETER IT" Interferometric Surveyors. Eoch determination was from observations spanning only 30 minutes. Plotted are differences with respect to the mean of two 4-hour determinations on 2/6 and 2/7/85. 178 Latitude (mm) 100 -100 100 -100 100 -100 .a: .''. : : :">■ . ■^ « * Dual* band" Longitude (mm) » » o' '?"•-. »i< Height (mm) 10 11 12 13 (hours UTC on 1/25/85) Figure 2. Comporlson of baseline delermlnallons obtained from LI -only and dual-band observations in four 30-minute periods on 1/25/85. Plotted are differences with respect to the mean of two 4-hour, dual-band determinations on 2/6 and 2/7/85. The baseline length was 12.5 km. Thus, full scale (100 mm) above corresponds to precision of 1:125,000. 179 50 -50 50 -50 Latitude (mm) 1 ppm Longitude (mm) •:::;•: »• '• — ♦' '•' 50 50 Height (mm) ^ ^ ^ •. ." . . . . — • •* ■ ■•• 1 - #■ • • • . . . . • ::::::::;::::::::":::•:::: :::::::! • « » 10 11 12 (hrs UTCon 1/25/85) 13 Figure 3. Eight independent determinations of 8 12.5-km baseline vector by MACROhETER H"^ Interferometric Surveyors. Eoch determinotion wos from observotions spanning only 15 minutes. Plotted are differences with respect to the mean of two 4-hour determinations on 2/6 and 2/7/85. 180 CODELESS SYSTEMS FOR POSITIONING WITH NAVSTAR-GPS by P.P. MacDoran, R.B. Miller, L.A. Buennagel and J.H. Whitcomb I STAC. Inc. 444 N. Altadena Drive, Suite 101 Pasadena, CA 91107 ABSTRACT. A codeless, NAVSTAR-GPS system has been developed for land surveying applications. Designed in consort with GEO/HYDRO, Inc., the system emphasizes field practicality and limited time on-site. GEO/HYDRO is the exclusive distributor of this survey instrument, designated GPS Land Surveyor, Model 1991 (TM). ISTAC development has begun on a low dynamic marine positioning sensor, (MPS-1). INTRODUCTION A new technology whose first commercial application is in land surveying is a civil use of the Department of Defense (DoD) NAVSTAR Global Positioning System, (GPS). This technology, named SERIES (Satellite Emission Range Inferred Earth Surveying), can do precision positioning with NAVSTAR-GPS signals with no know- ledge of their secret codes, i.e., it is codeless. Because of this capability, SERIES technology circumvents the potentially serious security problem posed by civilian NAVSTAR-GPS P-code correlating receivers as discussed by Booda (1984). SERIES was conceived and demonstrated at the California Institute of Technol- ogy, Jet Propulsion Laboratory (JPL), with funding from the National Aeronautics and Space Administration (NASA). The SERIES technology in its current config- uration of codeless pseudo-ranging was developed in 1980 (MacDoran, Spitzmesser and Buennagel, 1982), but its roots began in 1975 with a purely interferometric approach (MacDoran, 1979). The SERIES invention was originally intended for highly precise measurements of the earth's crust in a search for crustal deforma- tion patterns that could be used for tectonic studies and earthquake prediction, MacDoran discovered that signals from earth-orbiting satellites, especially the NAVSTAR satellites, could be used with no knowledge of the P or C/A codes, opening the door for use of the technique in a wide array of commercial and scientific applications. MacDoran has been granted the waiver of commercial rights to the invention by Caltech and NASA. The SERIES invention is a method and apparatus (equipment and processing software) that provides three-dimensional relative position — latitude, longitude, and height. ISTAC is an "equal opportunity radio signal consumer" because ISTAC will be able to use the radio illumination provided by satellite television transmissions or even the Soviet Union's global navigation satellite system (GLONASS) should the NAVSTAR satellites be unavailable for some unknown reason. However, the NAVSTAR satellites are clearly the radio illuminations of choice because of the excellent geometry and atomically stabilized radio-frequency transmissions. For a complete discussion of the NAVSTAR Global Positioning System, the reader is referred to Parkinson and Gilbert (1983). The first commercial application of the SERIES technology is the GPS Land Surveyor, Model 1991 available through GEO/HYDRO, Inc. of Rockville, Maryland. The Model 1991 has a current accuracy of 5 to 20 cm CEP (Circular Error Probable). 181 The antenna/receiver, atomically stabilized clock interface unit and digital data recorder are powered by self-contained batteries. Separate components weighing less than 30 pounds can be hand carried or back-packed to the job site. In addition to the land surveying application, ISTAC is developing a Marine Posi- tioning Sensor (MPS-1). The accuracy goal of the MPS-1 is 2 m CEP in a real-time dynamic mode out to distances of 500 km. One of the most advanced methods of exploration for hydrocarbon resources is known as 3D seismic surveying, a detail- ed discussion of positioning needs is given by Morgan (1983). In Morgan's paper, the possible benefits of using GPS are discussed. However, reliable access to the NAVSTAR Precise Positioning Service (PPS), allowing 15 m accuracy, continues to be a major inhibiting factor in making GPS a broadly used naviga- tional method. This paper will present the ISTAC-SERIES method and how wide civil use of the NAVSTAR-GPS is possible to levels of accuracy well beyond PPS and without dependence upon the DoD for NAVSTAR codes. Because of electronic countermeasures already devised, the ISTAC-SERIES technique is not useful in military environments. However, the ISTAC-SERIES methods are compatible with virtually every civil application. PRINCIPLE OF OPERATION Major advantages of the SERIES technology are the abilities to 1) use the NAVSTAR satellites without code knowledge (either C/A or P), 2) acquire data with no apriori knowledge of position and velocity of either the receivers or satel- lites, and 3) calibrate for effects of delays in the ionosphere. In addition, the option to buffer and dump data to another location greatly reduces the data acquisition receiver complexity and affords differential cancellation of the NAVSTAR signal biases for civilian applications in addition to attenuating the ephemeris error contribution to the baseline computation. The U.S. military's high accuracy mode for the GPS comes by way of the P-code channel and encrypted telemetry and achieves 15 meter accuracy in a single- receiver point positioning mode. This accuracy is limited primarily by orbital uncertainties. For the few meter accuracy requirements of the marine exploration industries, and especially geodetic land surveying this 15 meter accuracy is clearly inadequate and, as discussed by Morgan (1983), some form of differential operation is required to attenuate the uncertainty of the NAVSTAR satellite orbital positions. Differential operation of ISTAC-SERIES technology is no more cumbersome than differential operation of P-code correlating receivers. The obvious conclusion is that if differential operation is necessary for high pre- cision, then why not use the codeless technology? Although the SERIES-GPS technique is fundamentally a methodology for codeless pseudo ranging, the highest accuracy is obtained by operating pairs of receivers in a differential mode so as to cancel or attenuate certain error sources. For example, when the NAVSTAR-GPS is fully implemented with its 18 satellite constel- lation, the DoD may at its discretion incorporate into the transmitted signal structure what are known as methods of accuracy denial. Such denial will be achieved in several ways including altering the frequency and phase of the trans- mitted signals (dither) and changing the broadcast ephemeris message. Then only those receivers with the secret decoder will be able to acquire the P-code channel and know the real clock offsets and satellite orbital elements. However, by operating the receivers in a differential mode, it is possible to correct for these conditions (see Kalafus, Vilcans and Knable, 1983). A particular type of differential operation is preferred in the SERIES method which is insensitive to 182 the dither and allows the NAVSTAR orbits to be determined independent of DoD activity. The SERIES receivers are fundamentally codeless spectral compressors where the spread spectra modulations of several NAVSTAR satellites can be simultaneously received at L-band and compressed by seven orders of magnitude into audio or sub- audio bands. In the land surveyor, the sub-audio baseband output of the receiver is precisely clocked, digitally recorder and played back into a personal computer. A computer extracts the frequency and phase of each satellite in view. The data processing proceeds by a combination of Doppler positioning and phase ranging to the level of precision desired. The possibility of exploiting this high precision as accuracy remains substantially a problem of the calibration of the system for instrumental and atmospheric delay effects. Because C/A-code-only receivers may be easier to implement, it is natural to ask why we need both C/A and P codes to obtain the goal of 2 m CEP accuracy at 500 km or 5 to 30 cm at 50 km for land surveying? The answer is that, while at times differential C/A may approach that accuracy, error sources due to the lower intrinsic precision of C/A, planned manipulation of orbital ephemerides and timing parameters to protect and exercise protection capabilities of GPS, and lateral variations of ionospheric delays prevent commercial users from depending on differential C/A code alone for high accuracy. The C/A code has wavelengths of 293 m compared to the P-code wavelengths of 29.3 m; thus C/A has 10 times less precision than P. The DoD, for reasons of national security, plans to manipulate broadcast parameters (dither) to ensure that C/A-code systems have accuracies less than 100 m and that, if consistent with the national needs, to deny the entire GPS system. Deniability must be exercised and these exercises probably will not be widely announced to all possible users. Daytime single-receiver delays due to the ionosphere can typically be about 20-30 m in equivalent range. Differential operation will reduce this to a certain extent but likely will leave several meters of error contribution on time scales of seconds to minutes, especially when GDOP multiples of 3 to 10 are taken into account. The ionosphere is at times highly variable, both in a temporal and in a spatial sense (see for example Johanson, Buonsanto and Klobuchar, 1978). Although much is unknown about ionospheric behavior, calculations based on what is known lead to estimates of possible differential delays equivalent to several meters, especially at dawn and dusk and during magnetic storms. The conclusion is that, beyond about 100 km station separations, ionospheric calibration is necessary for 2 m CEP dynamic accuracy. The possibilities of taking a sufficiently large (several hours) data set in a static geodetic survey mode may allow the averaging out of some of the random components of the ionosphere but could leave several decimeters of system- atic error especially at high geographic latitudes. In order to calibrate ionospheric delays, we exploit the existence of the coherent dual L-band transmissions from the NAVSTAR to explicitly measure the total electron content of the ionosphere at the specific instant that the pseudo ranging is performed. In the conventional GPS mode, such an option is not readily available because the L2 channel normally contains only the P-code modu- lation to which there is no open access being planned. Thus, the motivation by some to have the C/A modulation also available on the L2 channel so that conven- tional civil GPS equipment can derive ionospheric calibration. The absence of a C/A code at L2 is, of course, intentional and is part of the NAVSTAR accuracy limitations upon non-DoD users with a single receiver. 183 Such a change in the NAVSTAR-GPS transmission implementation is, however, totally unnecessary since the SERIES-GPS technology makes use of the NAVSTAR signals without code knowledge. Thus, SERIES receivers exploit the dual LI- and L2-channel P-code modulations to extract the ionospheric delay from a single receiver along the line of sight to each of the satellites. This sub-system of a SERIES receiver is known as SLIC (Satellite L-band Ionospheric Calibration). Briefly, SLIC operates by using the fact that the P-code modulations in LI and L2 are nominally in-phase and coherent in the space vehicle at the time of transmis- sion. As these two wide band (20.46 MHz) signals pass through the ionosphere, the L2 channel experiences 1.65 times the delay effects that occur at LI. By measuring the phase shift of L2 relative to LI, it is possible to directly deduce the columnar electron content along the individual lines of sight. Actual results with the ISTAC-SERIES system using unsteered antennas have demonstrated multiple satellite simultaneous SLIC measurements with 5 degree or better differential P-code phase precision in 10 seconds. That precision corres- ponds to 0.4 TEC where 1 TEC unit corresponds to ten to the seventeenth electrons per square meter which is equivalent to 0.6 m of LI pseudo ranging. With less than 10 minutes of data acquisition, the ionosphere can be calibrated with a precision of 10 cm. The most complete accuracy assessments of the SLIC method have been performed at JPL by Royden, Miller and Buennagel (1984). In that analysis, using the original SERIES system with steered 1.5m antennas, agreement with Faraday Rotation ionospheric measurement methods has been demonstrated to 0.5 TEC or better with the Faraday Rotation accuracy estimated at 0.3 TEC. RESULTS Extensive testing on known baselines have revealed sensitivity to multipath contamination which has the greatest effects upon the local vertical parameter. The magnitude of the contamination is seen to be a few decimeters during 30 minutes of data acquisition. It was necessary to modify the microwave antennas to limit possible signal arrival directions. Tables 1. and 2. illustrate present performance given 30 minutes of data acquisition using broadcast ephemerides. The longest baseline measured was 53 km from Palos Verdes to Pasadena which demonstrated a 17 cm agreement with a GEO/HYDRO measurement using MACROMETER V- 1000' s. The ISTAC measurements achieve comparable baseline length measurement accuracy (3 parts per million) in 16% of time used by the GEO/HYDRO measurements. TABLE 1. ACCURACY DEMONSTRATION (Palos Verdes, ARIES 1 to ISTAC, Pasadena) X (m) Y (m) Z (m) length (m) ISTAC* 36861.685 8869.885 37778.258 53522.476 GEO/HYDRO** 36861.543 8869.593 37778.222 53522.304 (ISTAC-G/H) 0.142 0.292 0.036 0.172 GPS Land Surveyor, Model 1991 (TM), baseline length accuracy: 3.2 ppm * 30 minutes data acquisition 3/6/85, broadcast ephemeris ** 3 hours data acquisition 8/12/84, MACROMETER (TM) Model V-1000, Tl 21 24. 255 post-orbital computed ephemeris 184 TABLE 2. ACCURACY DEMONSTRATION Santa Paula, CA (Monument No. 7255 to Az Mk) Satellites (SV 6. 9. 11. 12. & 13) X (m) Y (m) Z (m) length (m) ISTAC NGS 100.152 100.287 -797.458 -797.380 -1117.422 -1117.426 1376.445 1376.413 (ISTAC - NGS) -0.135 -0.078 0.004 0.032 Diff. Local Coord. -0.083E -0.076N 0.108V Satellites (same as above + SV 4, shown as unhealthy) X (m) Y (m) Z (m) length (m) ISTAC NGS 100.158 100.287 -797.478 -797.380 -1117.400 -1117.426 1376.440 1376.413 (ISTAC - NGS) -0.129 -0.098 0.026 0.027 Diff. Local Coord. -0.064E -0.062N 0.137V Data Time Span: 30 minutes, 3/25/85. Ephemeris: Broadcast, 15 element set. Systematic errors probably multipath induced are limiting the system 30 minute inherent three-dimensional accuracy of 1 to 3 cm to 5 to 15 cm. Individual antenna calibrations appear to be possible but re-engineering of the microwave antenna is preferred. Figure 1. shows the experimentally derived instrument performance of the Model 1991. This figure relates to instrument accuracy which is independent of the baseline between the base and rover stations. The inherent accuracy is what is estimated from actual phase ranging measurements over various data time spans given no other error sources. The dashed line shows the current performance limit. Depending upon the baseline component measured, the accuracy will be in the region between the lower inherent accuracy line and dashed current line. For example, with 5 minutes of data acquisition the expected instrument accuracy is between 3 and 30 cm depending whether latitude, longitude or height is being specified. The height parameter is usually the least accurate parameter mea- sured. 185 Measured Instrument Performance (Independent of Baseline Length) 10 3 6 ' & 0.3 o i 0.1 < 0.03 O.OI T I 30min Current Inherent 10 100 1000 10,000 Data Time Span, sec Figure 1. MARINE POSITIONING SENSOR Based on the experience of developing land surveying technology a new dynamic navigation/positioning system is under development for the marine environment which is basically a real-time land surveyor: the Marine Positioning Sensor (MPS- 1). The MPS-1 is designed to be part of a high-accuracy navigation/positioning system that includes a data link to a several-hundred-kilometer-distant fixed reference base for differential operation as shown schematically in Figure 2. Monitoring of the position of a tail buoy is also possible with the system as shown. Allowable vessel velocities are up to 10 knots. For baselines up to 500 km, the MPS-1 will have accuracies of 2 m CEP (5 m 2 drms). For longer base- lines, the error is approximately linear with distance so that a 1,000 km base- line would have a 4 m CEP (10 m 2 drms) accuracy. Figure 3, shows the configuration of the dual-band antennas and receivers, the rubidium Clock Interface Units, and the microprocessor for the fixed reference station and marine vessel station. 186 SERIES RECEIVER TAIL BUOY HYDROPHONE GROUP Figure 2. REFERENCE STATION Dual- Band Antenna and Receiver Clock Interface Unit MARINE VESSEL STATION J L Communication Link 3-D Position to Ship Navigation System Figure 3. 187 EQUIPMENT DESCRIPTION The ISTAC-SERIES receivers are about the size of a book (20 x 25 x 5 centimeters) and consist of flat microstrip antennas tuned for 1575 MHz and 1227 MHz. The compact receiver configuration is achieved by the use of thick-film-on- ceramic technology. Located behind the antennas are low-noise (less than IdB N.F.), ambient-temperature amplifiers, a double conversion receiver, and a code- less spectral compression processor that operates without knowledge of the satel- lite orbits. The output of the receiver is an 80 Hz analog signal for each L band that contains all the positioning physics from the C/A and P-code modula- tions from all NAVSTAR satellites above the horizon. The audio bandpasses are digitally sampled using rubidium clocks and record- ed onto a data cassette. The cassettes are played back using a personal computer which performs spectral analysis to extract time dependent amplitude, phase and frequency for each NAVSTAR. The microcomputer then differences these values, removing any dither effects and attenuating satellite orbital errors by the ratio of the distance to the satellite divided by the separation between the receivers. Satellite ephemerides for the baseline vector estimation processing are provided in real time by extracting the broadcast ephemeris using a C/A code receiver. To operate either the land surveyor or the marine positioning in real-time requires a data link for transmission of reference station to or from the mobile stations. Requirements are for a to 200 Hz analog signal. Thus, any channel capable of voice grade communication would be adequate. For example, the link could be on current medium frequency (2 MHz) channels or via a satellite relay channel. APPLICATIONS OF THE MPS-1 Specific areas of application of the MPS-1 include precise positioning of seismic boats, buoys, pipe lay barges, inland waterway vessels, hydrographic survey vessels, offshore platform structure positioning and oilfield service boats. An unlimited number of multiple users can share the same reference sta- tion in a region. The present NAVSTAR constellation consists of eight prototype (Block I) space vehicles, all of which are useful to the ISTAC-SERIES system. Because of space- craft clock problems, the code correlating receivers have access to only five or six satellites. The constellation will be growing rapidly over the next few years. This year there will be a ninth NAVSTAR satellite available for position- ing. 24-hour 2-dimensional coverage in the world will be available in 1987. By 1988, a total of 18 operational Block II satellites and three on-orbit spares will make up the constellation. But, by that time, ISTAC-SERIES system users could potentially have a constellation of 29 satellite signal sources that could provide an even stronger geometry (more favorable GDOP) than would be available to users of conventional code correlating receivers. The reason for this greater availability is because as the NAVSTAR satellite on-board atomic clocks begin to malfunction, telemetry flags are placed in the broadcast message that inhibit conventional code correlating receivers from using these satellites. However, the ISTAC-SERIES differential methods find these satellites fully useful as long as these satellites continue to transmit, A separate ephemeris monitoring net- work would then be established to differentially derive the malfunctioning satel- lite ephemerides. 188 CONCLUSIONS ISTAC-SERIES technology presents no threat to national security since it re- quires no knowledge of the military codes, and electronic countermeasures against the ISTAC-SERIES methods are in place. The likelihood that civilian P-code receivers would be diverted by an enemy or terrorists into "smart" weapon systems is significant and must be of serious concern. P-code receivers, by their nature, possess high levels of electronic warfare resistance and autonomous operation. The benefits of independence from military operations that come from code! ess operation probably cannot be overstated when it comes to operating a for-profit business. The civilian geodetic land survey and marine exploration community has for some time been actively lobbying in Washington, D.C., to gain P-code select- ive-availability access. Our advice to the industrial community is to be careful of what you wish for, because you might get it! Commercial organizations with access to the P-code channel in the selective-availability mode will likely open themselves to dealing with high levels of security clearances, safeguards and operational expenditures that are uncharacteristic of current commercial opera- tions. In addition, the possession of such sensitive equipment will make their operations possible targets of international espionage. The advantages of the ISTAC-SERIES technology in the commercial environment are many: no new dedicated satellites need be launched to perform high accuracy civil positioning; data acquisition can begin without knowledge of satellite orbital positions and receiver location and velocity; a commercial enterprise at known locations can operate its own monitoring stations and compute its own NAVSTAR satellite orbits; the book-sized receiver equipment is portable and simplified since data processing can be performed at a distant location; the taxpayer investment in NAVSTAR-GPS (several billion dollars) for military appli- cations can now enhance civilian productivity in safety without modifications; and, especially important, no knowledge of military codes is needed or wanted. ACKNOWLEDGEMENTS The authors wish to thank Ron Hyatt and the staff at Trimble Navigation for assistance with the broadcast ephemerides acquisition; Tom Bandy, Assistant City Manager, Rancho Palos Verdes City Hall for hospitality in measurements at Palos Verdes, CA; Rowe Burgett and Robert Colbertson for data acquisition permission at Santa Paula, CA. REFERENCES 1. Booda, L.L.: "Civil Use of Navstar-GPS a Matter of Debate," Sea Technology (March 1984) 17-20. 2. MacDoran, P.F.,Spitzmesser, D.J. and Buennagel, L.A. : "SERIES: Satellite Emission Range Inferred Earth Surveying," Proceedings of the Third Interna- tional Symposium on Satellite Doppler Positioning , New Mexico State University (February 1982) 1 1 43-1 1 64. 3. MacDoran, P.F.: "Satellite Emission Radio Interferometric Earth Surveying, SERIES—GPS Geodetic System," Bulletin Geodesique (1979) Vol. 53, 117-138. 189 4. Parkinson, B.W. and Gilbert S.W. : "NAVSTAR: Global Positioning System — Ten Years Later," Proceedings of the IEEE (October 1983) Vol. 71, No. 10, 1177- 1186. 5. Morgan, J.G.: "The Challenge of Precisely Positioning a 3D Seismic Survey," Navigation (Fall 1983), Vol. 30, No. 3, 261-272. 6. Kalafus, R.M., Vi leans, J., and Knable, N. : "Differential Operations of NAVSTAR-GPS," Navigation (Fall 1983) Vol. 30, No. 3, 187-204. 7. Johanson, J.M. , Buonsanto, M.J. and Klobuchar, J. A.: "The Variability of Ionospheric Time Delay," Compilation of Papers Presented by the Space Physics Division at the Ionospheric Effects Symposium (lES 1978T t Air Force Geophysics Laboratory Report AFGL-TR-78~0080 (5 April 1978ril7-123. 8. Royden, H.N., Miller, R.B,, and Buennagel, L.A. : "Comparison of NAVSTAR Satel- lite L-band Ionospheric Calibrations with Faraday Rotation Measurements," Radio Science (May-June 1984) Vol. 19, No. 3, 798-804. 190 GEODETIC APPLICATIONS OF THE TEXAS INSTRUMENTS TI 4100 GPS NAVIGATOR Dennis J. Henson, E. Ann Collier, Kevin R. Schneider Texas Instruments Incorporated P.O. Box 405, Mail Station 3418 Lewisville, Texas 75067 ABSTRACT. When first conceived 12 years ago, the Global Positioning System (GPS) was designed to provide absolute, three-dimensional, real-time navigation with accuracy in the 10-meter range. When combined with state-of- the-art GPS receivers, GPS can provide precise relative position accuracies in the centimeter (and millimeter) range. This paper presents the receiver design and data of the TI 4100 GPS Navigator— a GPS receiver designed to optimally meet the demanding relative positioning accuracy requirements of the geodetic surveyor, in addition to the real-time needs of the standard navigation community. Two TI 4100 systems (standalone) collect all the data necessary for better than first-order, three- dimensional baseline determination. Standard off-the-shelf TI 4100 systems col- lect simultaneous raw observables of time-tagged code state and carrier phase (full cycles and fractions). Also provided by the TI 4100 are the real-time naviga- tion solution and the broadcast ephemeris required by postprocessing software to determine precise baselines. Preliminary postprocessing results using broadcast ephemeris are presented in this paper. The receiver subsystem of the TI 4100 is identical to the advanced geodetic receiver supplied by Texas Instruments under contract to the National Geodetic Survey (NOAA/NGS), the Defense Mapping Agency (DMA), the U.S. Geological Survey (USGS), and the Naval Surface Weapons Center (NSWC). These systems are planned for use during the 1980s and 1990s as the GPS standard for establishing geodetic control. GEODESY AND GPS When GPS was designed 12 years ago, it was perceived as an evolutionary improvement to the existing Navy Navigation Satellite (NAVSAT or Transit) system. The key mission of GPS is to provide a real-time, all- weather, worldwide continuous navigation service. Geodesists have discovered that applying interferometric techniques to GPS signals allows fast economical solutions to precise relative positioning problems that were previously cumbersome and expensive to solve. Several types of positioning problems, including point position- ing, relative baseline determination, six-degree-of-freedom attitude determination, artillery pointing through azi- muth determination, and transferring geodetic control to ocean bottom or moored sonobuoys can be solved using the highly accurate GPS carrier phase measurements. What factors limit the accuracy and usefulness of GPS? There are two broad types of limits: physical limits and Government policy limits. The physical limits result primarily from the effects of ionosphere and troposhere on measurement accuracy. For short baselines, it is reasonable to assume that the ionospheric error is the same at both ends of the survey baseline and, therefore, the error cancels out. For baselines longer than a few hundred kilometers, ionospheric effects become decorrelated. In this case, the geodesist interested in ultrahigh precision must measure the ionospheric delay. This is done using both GPS L-band frequencies as supported by the TI 4100. Figure 1 illustrates range and phase ionospheric measurements derived from a TI 4100 tracking GPS satellites. There are ionospheric models for users with only one L-band frequency; however, these are crude and inappropriate for geodetic accuracies. Tropospheric error, like ionospheric error, can sometimes be considered the same at both ends of the baseline and will cancel out. However, if there is a weather front between the ends of the baseline, or if the baseline is very long, then it becomes necessary to correct for the tropospheric error. Current tropospheric models rely on surface measurement of temperature, barometric pressure, and relative humidity. Recent experiments have investigated the use of water vapor radiometers for tropospheric error compensation. TI simulations indicate that uncompensated tropospheric errors can corrupt geodetic survey accuracy by as much as 1 to 6 meters, depending on the baseline length. 191 PSEUDORANGE IL.L,) • 1.54 lER PHASE (L,-L,l • 1.54 20 30 40 ELAPSED TIME (UINUTESI 4.0 3.0 2.0 1.0 -1.0 - -2.0 ■; -3 -4.0 : -5.0 ELAPSED TIME (MINUTES) SV/PRN9AND 11 Figure 1. Ionospheric Delay Measurements Figure 2. Double Difference Carrier Phase Error The other main factor in GPS accuracy and usefulness is the Governmental policy on GPS availability. In the interest of national security, civilian access to the Precise Positioning Service (PPS) may be prevented by encrypting the signal. In this case, U.S. Government agencies and their allies will use GPS receivers that are designed to receive encrypted signals. Non-Government users may be allowed access to the PPS on a "national interest" basis. If the Government chooses to allow access to PPS for all users and yet deny accuracy to real-time, non-Government users, then for short baselines, relative positioning will still be accurate. For longer baselines, a precise ephemeris should be obtained after data collection and used in the postprocessing. GPS DATA The GPS provides two fundamental observables: range derived from tracking the pseudorandom noise (PRN) codes and phase derived from tracking the doppler-shifted carrier. Real-time users of GPS obtain position information predominantly from the Coarse Acquisition (C/A) and Precision (P) codes which are biphase- modulated onto the GPS L-band carriers. They also obtain velocity information from the carrier doppler shift. The code-based method of determining position does not suffer from the lane-count (wavelength ambiguity) problem long associated with radio frequency (RF) navigation systems like Loran, Syledis, Omega, and "codeless" GPS receivers. Code tracking alone does not provide centimeter and millimeter accuracy, relative position determination. Geodetic accuracy requires carrier-phase interferometry. Geodesists, notably Fell (1980) and Remondi (1984) have proposed several different carrier phase observation schemes that are described here. For all these GPS observation schemes, it is assumed that all users who are cooperatively surveying will track the same satellites to obtain simultaneous doppler-shifted carrier phase at all observing sites. A carrier phase first-difference observable is created by taking phase data from one station and subtracting the simultaneous phase measurement from another station for the same space vehicle (SV). The first-difference observable eliminates common errors including SV clock, ionospheric, tropospheric, and ephemeris prediction errors. A second difference measurement can be obtained by subtracting the first difference observable for SV; from the first difference observable for SVj at a common reference time. In addition to removing the sateUite- dependent errors mentioned, this measurement form removes receiver clock errors, and common receiver chan- nel delays. Figure 2 shows typical carrier phase double-difference measurement errors computed from tracking orbiting GPS satellites. Goad (1984) suggests third-difference measurements for rapid survey work, computed by subtracting a second difference at time t from a second difference at time t + k. This measurement type offers the advantage that there is no wavelength ambiguity to be resolved, and this scheme can be used to quickly detect loss of coherent phase tracking. 192 Conceptually, these phase difference measurements are created from the raw-phase data recorded by GPS receivers, taking advantage of situations where common error terms are present at both survey stations, and a differencing operation can eliminate the common error and thereby improve baseline determination accuracy. DESIGN DESCRIPTION OF THE TI 4100 Texas Instruments has developed a flexible GPS receiver designed for most navigation and geodetic surveying applications. The TI 4100 NAVSTAR Navigator seen in Figure 3 provides the real-time user with accurate position, velocity, and time informa- tion. It also provides all GPS observables required for precise orbit determination and geodetic surveying. The receiver uses large-scale integration (LSI) custom GPS components and is a third-generation Texas Instruments GPS receiver. The receiver baseband design shows a maximum commitment to digital circuit and digital microprocessor components. One of the unique features of this advanced digital receiver is the ability for a single hardware channel to multiplex a number of GPS SV signals, returning to each SV within a few milliseconds, so that, in a sampled data sense, all the SV signals are tracked continuously as though multiple hardware receiver channels were present. Multiplexing eliminates interchannel bias on all measurements, which is, per- haps, the most remarkable performance feature of the multiplex receiver. The receiver can also concurrently multiplex between the Li and Lj signals of the same SV. Satellite multiplexing is a patented capability of Texas Instruments GPS receivers. See Ward (1980) for a detailed discussion of the multiplex concept, Maher (1984) for a comparison of GPS receiver design philosophies, and Henson (1984) for a description of TI 4100 design and real-time navigation test results. GEODETIC RECEIVER DESIGN CONSIDERATIONS Only receivers optimally designed to meet the most stringent tracking accuracy requirements are able to take full advantage of the geodetic potential provided by highly stable RF signals from GPS space vehicles. GPS receiver designers are often confronted with GPS mission requirements that force compromise when the opti- mum geodetic receiver is not the design goal. Important receiver design considerations specifically optimized for geodetic application within the TI 4100 include: Figure 3. TI 4100 Survey Setup Measurement types available to the user Phase measurement accuracy and ambiguity region Simultaneous measurements, number of SVs, and phase extrapolation errors Interchannel bias errors Oscillator instability Phase delay variation Antenna phase center variation Temperature sensitivity Jamming immunity Tracking integrity Reacquisition speed User friendliness and reliability. Subsequent paragraphs discuss each of these design considerations in more detail. It will be shown that multihardware-channel, sequential single-channel, and codeless receivers each have shortcomings when the design criterion is standalone geodetic operation. 193 MEASUREMENT TYPES AVAILABLE TO THE USER The following are the GPS observables available to the geodetic user from the TI 4100: • Li P-code state (pseudorange) • L2 P-code state (pseudorange) • Time rate of change of Lj P-code state (pseudorange rate) • Time rate of change of Lg P-code state Instantaneous Lj doppler frequency shift Instantaneous U doppler frequency shift Averaged line-of-sight SV acceleration Li C/A code state (pseudorange) Time rate of change of Li C/A code state (pseudorange rate) (pseudorange rate) • Lj (doppler induced) carrier phase (whole • Signal-to-noise measures and other data cycles and fractions) quality indicators. • L2 (doppler induced) carrier phase (whole cycle and fractions) The TI 4100 provides all these data simultaneously for four SVs in an output report available at 3-second intervals. Receivers designed only for dynamic application may not provide carrier phase data but instead pro- vide only a delta (pseudo) range derived by differencing two carrier phase values separated a little in time to obtain average velocity. Such a receiver would be inappropriate for geodetic applications. As a fiirther compro- mise, a sequential single-channel receiver can provide these data for only one SV at a time with the data from subsequent SVs typically separated by a few seconds of elapsed time. C/A-code-only receivers cannot provide the L2 range (or phase) observables required for ionospheric error compensation. Finally, "codeless" receivers provide no pseudorange information and therefore suffer the lane count problems. PHASE MEASUREMENT ACCURACY AND PHASE AMBIGUITY REGION Different GPS receivers track the doppler-shifted carrier signal in different manners. Two popular carrier tracking loop types are frequency-locked loops (FLLs) and phase-locked loops (PLLs). FLLs do not track the carrier phase coherently; instead, the loop tracking characteristics are determined from frequency-error-dependent calculations of the baseband signals. These loops can provide approximate doppler frequency shift estimates but do not provide high-precision carrier phase. FLL-only tracking may be appropriate for high dynamics, weak signal hold-on, or as a means of rapid signal acquisition for austere single channel sequential receivers, but FLLs fail to provide the intrinsic phase observables for the geodetic user. PLLs provide accurate carrier phase to the geodetic user. Advanced receiver designs (such as the TI 4100) use high-precision digitally controlled oscillators (DCs) to generate a local replica of the doppler shifted carrier signal. For high-accuracy geodetic applications, the word length of the DO input frequency control must contain sufficient bits so that the weight of the least significant bit (LSB) is negligible when compared to system thermal tracking noise. For the TI 4100, the frequency control word is 32 bits in length with an LSB weight of 103.56307 X 10"* Hz. This precise hardware control results in a negligible contribution to the phase error budget. For the TI 4100 multiplexing receiver, time sharing the carrier (or code) digital oscillators over multiple SVs requires precise initialization of the carrier (or code) phase at the start of each SV dwell period. The carrier phase preset word size is 32 bits with an LSB weight of 1/65,536 carrier cycle, introducing a negligible phase tracking error. The 48-bit length of the software phase accumulator value output to the TI 4100 user is sufficient to hold the entire phase accumulation of an SV pass. This feature provides the whole cycle and fractional carrier phase change over the complete pass of a satellite. The TI 4100 software must use this accumulator to preset the carrier DO at each SV dwell, thus providing continuous verification of the accuracy of the phase accumulator value. Any error in the phase accumulator will result in immediately detectable phase tracking disturbances. Continuous multichannel sets are not required to provide this hardware/software accumulator verification. The tracking bandwidth of the carrier PLL should be an important design consideration for geodetic receiver development. Receiver designers must choose the steady-state tracking bandwidth based on two major constraints. The loop bandwidth must be sufficiently wide to track the dynamic stress induced by the relative motion between the user and the SV being tracked. Wide bandwidths are required for high-dynamic applications and narrow bandwidths for stationary applications. Given the available signal power-to-noise density ratio, the tracking loop noise bandwidth must be lowered to meet the stringent root-mean-square (RMS) tracking error 194 requirements imposed by the geodetic user. The lower bound is determined by the maximum dynamic stress to be tracked and, for very narrow tracking bandwidths, by the instabihty of the receiver reference oscillator and synthesizing of internal receiver mixing frequencies. For the TI 4100, the minimum tracking bandwidth has been optimized for stationary survey user requirements consistent with the internal oven-controlled crystal oscillator stability of 1 X 10"" (1 second sample interval Allan two-sample standard deviation). The tracking loop is third order and has a noise bandwidth of 0.7 Hz. At the nominal carrier power-to-noise density ratio of 40 dB-Hz available for the current constellation of SVs, only about 2 degrees of RMS tracking jitter is produced. Biphase data-modulated L-band GPS signals are most often tracked by a Costas dual-channel tracking loop. A Costas loop provides the dual benefit of data demodulation and carrier phase PLL tracking. Costas loops inherently provide stable tracking points at each 1/2 cycle of carrier phase. Therefore, the Costas loop reports phase that is ambiguous to any 1/2 cycle. The TI 4100 is able to resolve the carrier phase to whole cycle ambiguities because it can continuously collect and demodulate SV navigation message data. Consider the impli- cation of this two-times improvement in ambiguity size on the three-dimensional geodetic solution space. A cubic relationship exists between the radius of the initial geodetic solution uncertainty sphere and the number (volume) of encompassed solutions. This means that about eight times (2^) more extraneous solutions must be carried along and eliminated during geodetic postprocessing than would be required by the whole cycle ambiguity of TI 4100 phase data. "Codeless" receivers that cannot track the code modulation or sequential receivers that cannot maintain continuous phase lock or continuously demodulate the navigation message data cannot resolve the phase ambiguity to whole cycles. Satellite ephemeris required for baseline determination is available in real time from code tracking receivers through the 50-bit-per-second data. Codeless receiver designs cannot demodulate the navigation message data, but instead must rely on third-party groups to provide the required SV ephemeris data, sometime after the initial survey data collection and, generally, for an extra fee. Each surveyor must consider the continuing expense of such a service in evaluating total system cost as well as the delay incurred in postprocessing the survey data. SIMULTANEOUS MEASUREMENTS, NUMBER OF SVs, AND PHASE EXTRAPOLATION ERRORS Geodetic postprocessing algorithms require simultaneous measurements from four SVs for all receivers at geographically disperse locations. The single, double, and triple difference algorithms depend on simultaneous measurement. When navigating in either stationary or low-dynamic modes, TI 4100 receivers around the world collect data simultaneously without any requirement for prior intersystem synchronization. Sequential single-channel receivers, on the other hand, at best produce simultaneous phase data for only a single SV. Phase extrapolation over several seconds to bring multiple SVs data into time synchronization is impractical because of the substantial phase extrapolation error incurred by the sequential single-channel receiver. This effectively prevents sequential single-channel receivers from being able to provide high-accuracy double or triple difference phase measurements. It has been estimated that a sequential single-channel receiver with a 1 -second satellite switching period would produce phase extrapolation errors of between 10 and 30 degrees for the three SVs that must be extrapolated to the coincident time of the fourth SV. INTERCHANNEL BIAS ERRORS Multiplexing and sequential single-channel receivers have no interchannel phase bias errors to corrupt a geodetic survey. Multichannel receivers produce phase delay differences for each hardware channel because of the different electrical paths encountered by each SV signal. Attempts are made to calibrate and compensate these multichannel receiver delays. However, the accuracy required by the geodetic user makes it extremely difficult to adequately compensate for these channel (SV) dependent errors. For example, a residual calibration error of only 5 degrees RMS at L-band (about 2.5 millimeters) amplified by 5 because of the geometry effects might yield a baseline determination error of 1.2 centimeters. For high-precision work, this error is probably intolerable. OSCILLATOR INSTABILITY GPS receivers have varying requirements for oscillator stability. Wide bandwidth PLLs associated with high-dynamic receiver designs can tolerate less stable oscillators than can the small-bandwidth PLLs associated with high-performance geodetic receivers. Inexpensive sequential receivers might be able to get by with 195 temperature-compensated crystal oscillators (TCXOs), but these oscillators would not meet the stability requirements of the geodetic user. The TI 4100 uses a voltage-controlled crystal oscillator contained in an oven. This is a high-quality crystal oscillator providing good short-term measurement stability. In addition, the TI 4100 provides a 5-MHz frequency input port and associated circuitry to enable the phase locking of the internal crystal to a high-performance atomic frequency standard. The use of atomic frequency standards allows geodetic surveyors and those interested in orbit determination to establish long-term oscillator stability from the external reference. TI 4100 receivers have operated connected to rubidium vapor, cesium beam, and hydrogen maser atomic frequency standards. PHASE DELAY VARIATION GPS receiver designers are often tempted to narrowband filter the received signal as much and as soon as possible in the downconversion process to reduce noise levels and improve jamming immunity. A postcorrelation narrowband filter before doppler stripping with frequency cutoff close to the expected doppler shift range will produce a nonlinear phase response in the filter output. This means that the effective time delay of the output signal relative to the filter input signal is not constant, but instead is a function of the doppler shift. This causes SV-dependent phase delays that cannot be tolerated by the high-precision geodetic user. The TI 4100 receiver has a wide-bandwidth channel capable of tracking 56 kHz of doppler shift. Stationary users receive, at the most, 9 kHz of doppler shift. Therefore, the TI 4100 design minimizes filter phase nonlinearities. ANTENNA PHASE CENTER VARIATION The apparent electrical phase center of a GPS antenna is the precise point of navigation. For relative navigation work, if the survey antenna phase center moves in a common manner with the other survey antennas in the network, no relative motion will be perceived, and no survey error introduced. If the motion is not common manner, then survey errors will result. For orbit determination applications, the absolute motion of the antenna phase center may be an important term in the error budget. The TI 4100 antennas are manufactured with a goal of building them as similar as possible. An azimuth alignment mark is placed on the assembly housing coincident with the beginning of the active element spiral. Relative survey users align all antennas in the network to a convenient direction (usually magnetic North) so that phase center motion will be common and cancel out as a first approximation. TEMPERATURE SENSITIVITY Temperature-induced phase errors may be of two types: common errors across all SVs tracked and errors that are satellite dependent. In the case of a multichannel receiver with different hardware paths, each channel is subject to individual response to temperature change, and SV-dependent phase errors are likely. The magnitude of these errors is difficult to predict and should be minimized with careful selection of temperature-insensitive components. A multiplexing receiver or a sequential single- channel receiver will probably produce no SV- dependent phase errors because of temperature change. Each advanced geodetic receiver version of the TI 4100 supplied to the Government is tested for phase stability over temperature. Observed phase changes because of temperature are common across all SVs tracked on both L-bands. Figure 4 is a typical example. For some Government applications where this apparent clock-like phase change over full temperature extremes is not negligible, a cubic » M u «" • '^'m-M !• ^ PHASE CHANGI CUBIC COMPENSATION POLYNOMIAL 10 20 30 40 TEMPERATURE CCI Figure 4. Phase Change Versus Temperature 196 compensation polynomial is used. Internal temperature provided by the receiver is the independent variable in the phase compensation function. Geodetic survey users employing double- or triple-difference phase processing algorithms will not see this phenomenon because receiver clock-like errors are not observable. Users working with absolute phase or first differences of phase require compensation of the TI 4100 data only if the receiver suffers an extreme temperature variation and a very high-quality atomic frequency standard is in use. ERROR BUDGET Table 1 presents a typical error budget for the TI 4100 carrier phase measurement when used as a double- difference phase for geodetic survey work. The double-difference plot of Figure 2 from orbiting GPS satellites verifies that this error budget is consistent with observations. Table 2 is a summary comparison of generic GPS receiver designs as they relate to geodetic requirements. TABLE 1. TI 4100 DOUBLE DIFFERENCE PHASE ERROR BUDGET Error Source Error (mm) Thermal noise (P-code) 3.0 L, Doppler-dependent error 0.0 Receiver oscillator instability 0.0 Software oscillator instability 0.0 Multipath 0.0 Ionospheric path error 8.2 Tropospheric path error 0.0 IF hardware 0.45 Hardware truncation 0.0 Software numerical resolution 0.0 Antenna phase center movement 1.0 Receiver hardware instability 0.50 RSS error (L, only) 3.2 RSS error including ionospheric correction 8.8 Comment Assumes four-SV MUX case at - 163 dBW Negligible with wideband filter Not observable for double difference Not observable for double difference Application-dependent 0.0 to 1 5.0 mm L/Lj phase correction (thermal noise) Not considered noise; correction source dependent (not a receiver error) Phase jitter 2.0 X 10-" cycles Carrier quantization 2.0 X 10"" cycles Noncommon mode variation RFM hardware instability Add multipath and tropospheric error based on application Add multipath and tropospheric error based on application TABLE 2. COMPARISON OF RECEIVER DESIGNS FOR GEODETIC APPLICATION Receiver Types TI4100 Four-Hardware Four-Hardware Sequential Sequential Four-Channel Channel Channel Single-Channel Single-Channel Codeless Characteristics Multiplex P-Code C/A Code Only L, P-Code C/A Code Receiver Continuous carrier phase lock Yes Yes Yes No No Yes One-cycle phase ambiguity Yes Yes Yes No No No (possible) (possible) (1/2 cycle) (1/2 cycle) (1/2 cycle) Negligible phase interchannel bias No phase extrapolation error Yes No No Yes Yes Yes Yes Yes Yes No No Yes Continuous navigation Yes Yes Yes No No No (not message collection possible) Crystal oscillator sufficient Yes Yes Yes Not likely Not likely No Real-time navigation fix Yes Yes Yes Yes Yes Yes (given initial fix) Measured ionosphere advance Yes Yes No No No Yes (new compensation option) Simultaneous double- Yes Yes Yes No No Yes difference phase collection P-code range L, Yes Yes No Yes No No U Yes Yes No No No No P-code carrier L, Yes Yes No Yes No Yes L, Yes Yes No No No Yes (new option) No C/AcodeL, Yes Yes Yes Yes Yes C/A carrier L, Yes Yes Yes Yes Yes Yes Standalone operation Yes Yes Yes Yes Yes No 197 OTHER RECEIVER DESIGN CONSIDERATIONS Other geodetic receiver design considerations, perhaps not as critical as those affecting measurement accuracy but important from an operational standpoint, include jamming immunity, tracking integrity, and reacquisition speed. Most geodetic receivers are not required to operate under the extensive jamming environments required of military GPS receivers. Receivers designed to operate in strong jamming environments may require additional hardware and rigorous testing in jamming environments, adding cost to the end user not appropriate for most geodetic applications. However, it is reasonable for geodetic receivers to operate undisturbed in the presence of unintentional jammers. Survey monuments are often located at airfields where radar and continuous wave (CW) systems of moderate power are likely to be in operation. Geodetic receivers should provide protection against jamming for these circumstances. In addition to the spread spectrum immunity, the TI 4100 has front-end limiting and an internal leakage signal spreading function to improve operation in the presence of unintentional jamming. Geodetic users of GPS many times require long periods of uninterrupted coherent carrier phase tracking. Receiver tracking integrity is extremely important to geodetic survey and orbit determination where high-quality coherent phase data are required. Many man-hours of testing and verification have been conducted with the TI 4100 to ensure that the system as built meets the long-term tracking integrity requirement of the geodesist. In addition, the TI 4100 provides direct-P (or direct-C/A) acquisition modes and a real-time navigation solution to support rapid recovery of final state tracking in the event of tracking disruption. Slow-rate, single-channel sequen- tial receivers cannot guarantee long-term phase lock because, at frequent intervals, these receivers are required to drop track on one SV and begin an acquisition process on the next SV in the sequence. RECEIVER EASE OF USE AND RELIABILITY Geodetic receivers must be reliable and easy to use before GPS will be widely accepted by the survey community. Field survey systems should be man-portable, lightweight, and compact in size. The system should operate reliably in human environments without modification. The system should be operated from readily available portable power sources. The GPS antenna should be easily mounted on a standard surveyor's tripod or optical plumb adapter. It is desirable that the antenna can be located remotely from the receiver assembly. Real- time performance monitoring is extremely important to ensure the surveyor that the survey is progressing as planned. Reliable self-test features should also be part of the configuration. The TI 4100 meets all these requirements. Flexibility and expansion to support new GPS requirements have been designed into the TI 4100. The system is available in either an all-PROM version or with RAM for the navigation processor memory and PROM for the receiver processor memory. RAM systems have the ability to load and execute application software developed by the Government survey community as well as the standard Texas Instruments supplied software. The receiver hardware and software can be upgraded to support selective availability for authorized users, should that be necessary. INDEPENDENT TESTING AND EVALUATION It is important that GPS receivers for survey applications undergo rigorous independent test and verification to ensure that the accuracy potentials of GPS are being met. Extensive multiyear independent testing of the advanced geodetic version of the TI 4100 has been conducted by the Applied Research Laboratories at the University of Texas at Austin (UT/ARL) in support of the Government user consortium. These extensive tests have analyzed the design criteria of the TI 4100 against exacting standards. In January 1984, these qualification tests were augmented by a rigorous field test program that exercised many TI 4100 geodetic receiver features. To study relative baseline determination accuracy, data were collected for several days at stations that are part of the NASA- Jet Propulsion Lab (JPL) crustal motion network. Double-difference phase measurements were used in a least-squares adjustment with data from subsequent days demonstrating repeatable results of 3.3 parts per million or better (Clynch 1984). In the spring of 1984, Geodetic Survey of Canada (GSC) conducted a TI 4100 Navigator data collection campaign to exercise GPS postproccessing software developed by GSC. Using a triple-differencing technique, 198 postproccessing software yielded a root-mean-square radial error of 7.8 centimeters for baselines with an average length of 37.6 kilometers. The polygon of baselines had an average closure error of 2. 1 parts per million (N. Beck, etal 1984). More recently, eight TI 4100s of both the Government configuration and the TI 4100 Navigator configuration were used in a cooperative test. The TI 4100s were dispersed across the country to allow various Government agencies (NASA-JPL, UT/ARL, NOAA-NGS, DMA, NSWC, and a university consortium) to explore the potential of using GPS for orbit determination, crustal motion, relative positioning, and the application of water vapor radiometry to determine the tropospheric delay. At Texas Instruments, several tests have been conducted to check the performance of the TI 4100 receiver operating as a geodetic survey instrument. The best-case accuracy was determined by observing satellites using two TI 4100 systems and only one antenna. This test is theoretically optimum because environmental and multipath errors will be identical for both receivers and cancel out in the postprocessing. The true baseline length is for this case. In two separate tests, the computed three-dimensional root-mean-square (RMS) errors from Texas Instruments postproccessing software were 0.4 and 0.9 millimeter. In May 1984, Texas Instruments conducted several tests at and around the University of Texas Advanced Research Laboratories Balcones Research Compound in Austin. The survey results are summarized in Table 3, Figure 5 shows a more recent triangle closure test conducted at the Texas Instruments Lewisville, Texas, facility in March 1985. The closure error is 7.6 millimeters with 7.1 millimeters of error in the up direction and a 2.7- millimeter horizontal error. Broadcast ephemeris was used and ionospheric and tropospheric errors were uncompensated. TABLE 3. TI 4100 SURVEY ERRORS Survey Name Reference Baseline Length (meters) Reference Survey Accuracy (meters) TI Computed Distance Error (meters) TI Computed Standard Deviation (meters) JMR— triangle BR0-BR4 BRO-TX HWY 27 619 8,875 0.003 0.003 0.018 -0.0052 0.0085 0.0030 0.0050 0.0050 0.0082 TEST POINT 8 TRIANGLE CLOSURE ERROR AX = +0.0022 METER AY = -0.0061 METER AZ = +0.0041 METER TEST POINT 8 HELD FIXED AT -652858.3006 -5314381.9903 3454436.0401 734.8195 A ALTITUDE RSS ERROR = 0.0076 METER 2.7MM HORIZONAL 7.1MM UP SOLVED FOR POSITION OF TEST POINT 3 FROM TEST POINT 8 -652849.5141 -5314501.3062 +3454251 .7745 = 9.815 SAVED FOR LAB POSITION ENDING -652247.5426 -5314662.9908 3454139.2331 TEST POINT 3 633.2602 ALTITUDE SOLVED FOR POSITION OF TEST POINT 3 FROM LAB -652849.5119 -5314501.3125 +3454251.7786 11.7572 POSITIONS IN WGS-72 REFERENCE FRAME ALL UNITS ARE IN METERS Figure 5. Triangle Closure Test 199 SUMMARY In summary, we have described how GPS can be used for geodesy. Several features of GPS receivers that exploit the complete capabilities of the system have been described, and particularly, how the TI 4100 was optimally designed to meet a broad spectrum of navigation and positioning requirements using the GPS multi- plexing technique patented by Texas Instruments. Several of the unique advantages of time-division-multiplexing for GPS were described. This receiver architecture can be upgraded to allow authorized Government users to receive all the power of GPS including the possibility of encrypted P-code tracking. At least three different groups using the TI 4100 have demonstrated relative positioning with accuracies in the range of a few parts per milUon for baselines of various lengths. These results confirm the expectation that GPS will enhance our knowledge in such diverse scientific areas as geodetic control, plate tectonics, atmospheric composition, and hydrographic survey. REFERENCES Beck, N., D. Delikaraoglou, K. Lochhead, D.J. McArthur, G. Lachapelle, 1984: "Preliminary Results of EHfferential GPS Positioning for Geodetic AppUcations," Position Location and Navigation Symposium 1984, IEEE '84 CH21 10-5. Qynch, J., A.J. Tucker, R.J. Anderle, M. Sims, B.K. Hermann, J.W. Rees, P.J. Fell, 1980: "Testing of a Field- Portable GPS Geodetic Receiver," Position Location and Navigation Symposium 1984, IEEE 84CH21 10-5. Fell, P. J., 1980: "Geodetic Positioning Using a Global Position System of Satellites," Report 299 of the Department of Geodetic Science, The Ohio State University, June. Goad, C, 1984: Private Communications. Henson, D.J., B.O. Montgomery, 1984: "TI 4100 NAVSTAR Navigator Test Results," presented at the Fortieth Annual Meeting of the Institute of Navigation, Cambridge, Massachussetts, 28 June. Maher, R.A., 1984:, "A Comparison of Multichannel, Sequential, and Multiplex GPS Receivers for Air Navigation," presented at the Institute of Navigation Technical Meeting, 1 7 January. Remondi, B.W., 1984: "Using the Global Positioning System (GPS) Phase Observable for Relative Geodesy: Modeling, Processing, and Results," Center for Space Research, The University of Texas at Austin, May. Ward, P.W., 1980: "An Advanced NAVSTAR GPS Multiplex Receiver," presented at Position Location and Navigation Symposium, 9 December. 200 PRECISE BASELINE DETERMINATION WITH A NEW CODELESS GPS RECEIVER James Collins Geo/Hydro, Inc. 2115 E, Jefferson Street Rockville, MD 20852 ABSTRACT. A GPS survey instrument has been developed for Geo/Hydro, Inc. employing the codeless SERIES receiver recently developed by ISTAC, Inc. The results of blind tests over a short and long baseline showed this new instrument to be highly practical for most geodetic survey applications. INTRODUCTION Geo/Hydro, Inc. has continuously performed GPS surveys since January 1983 when they introduced the Macrometer"^^ V-1000 instrument. Clients have ranged from national governments to small private firms. Based upon this experience in establishing over 2000 points for a wide range of applications we have come to the basic conclusion that: 1. The limited production using the V-1000 and the present constellation results in a per point price that is too high for most survey applications. 2. Portability of GPS survey equipment is essential for its use on a normal range of projects. 3. Use of GPS instruments in forest areas requires that the antenna be capable of being elevated above the tree cover. 4. Many clients prefer to have less accurate coordinates available immediately rather than wait several weeks for more accurate results. With these points in mind, we negotiated an agreement with ISTAC, Inc. to produce a portable GPS survey instrument that would provide the maximum accuracy in the shortest time using the broadcast ephemeris. This instrument, later tradenamed the GPS Land Surveyor^^ Model 1991, was fabricated this past winter and is presently in the process of final testing. GPS Land Surveyor"^^ Model 1991 The Model 1991 consists of three basic components: (1) The 201 28 X 28 X 6 cm 4 kg 66 X 36 X 22 cm 24 kg 46 X 36 X 15 cm 13 kg antenna/receiver (2) The signal processor/recorder, and (3) The clock/controller. The antenna/receiver is the SERIES receiver described in P.P. MacDoran's earlier paper. The output from this unit is fed into the signal processor unit where the analog signals are digitized, time-tagged, and recorded on magnetic cassette tapes. The fact that all LI band signals are recorded is a significant advantage to this method of operation. The third unit, the clock/controller, is contained in a briefcase sized case which can be easily transported between operating units. This feature is important for synchronizing individual unit clocks. The basic physical data for the GPS Land Surveyor*^^ Model 1991 are: Unit Size Weight Antenna/receiver Processor/recorder Clock/controller These dimensions and weights include the internal batteries that are needed for normal operations. In effect the entire system (including batteries) can be backpacked by two men to sites unreachable by vehicle. Unlike other GPS survey instruments, the Model 1991 does no processing or signal tracking during the data acquisition operation. The spectrum is simply digitally recorded for later processing. The disadvantage of this mode of operation is the lack of positive real-time feedback concerning the quality of the observations. The (preferred) advantage is that a power-hungry computer does not have to be transported and operated in the field. The Model 1991 provides sufficient indications that it is operating normally so the risk of having to reoccupy a point is minimal. Mode of Operation The GPS Land Surveyor^^ Model 1991 operates in a similar manner to the Macrometer"^*^ V-1000. Prior to beginning the day's observation, one of the (briefcase-sized) portable clocks is synchronized to Universal Time by means of a GOES satellite time receiver or other external source (i.e. Trimble Navigation Receiver). Following this, the clock (s) used by all other unit(s) are synchronized to the first portable clock. This entire process requires about ten minutes for four units. Each of the GPS units are next transported to the first (respective) station being occupied that day, the antenna/ receiver is plumbed over the station mark and connected to the processor/recorder by (up to 60 meters) coaxial cable. The start time and duration time of the observation are entered by means of function keys, and the equipment is ready for observations. The entire setup procedure requires between 5 and 10 minutes, 202 Like other GPS equipment , keeping precise timing among units is important. The portable clocks must be powered-up during the entire observation period or until their time is checked at the end of the day. The rubidium clock used in the Model 1991 unit can be shut off at the end of the day and warmed up again the next day in about 10 minutes. The rapid warm-up time of the rubidium means that this equipment can be used the same day that it is shipped to a site; unlike crystal clocks which require 24 hrs to stabilize. The major difference between the GPS Land Surveyor^^ and the Macrometer^** V-1000 is the fact that the Model 1991 does not require any preprogrammed satellite information (A-files) to operate. This feature provides a greater degree of flexibility in performing surveys since the Model 1991 can be set up and acquire data over any point and not just the points which have been preselected. Occasionally, our Macrometer teams have lost a day's work because the wrong satellite file was used or because an ephemeris file was not available. ACCURACY The design goal for the GPS Land Surveyor^** was 10 cm (rms) accuracy in all three coordinates after 30 minutes of (prime time) satellite observations. This instrumental error (exclusive of ionospheric error) was exceeded on a test over a 1.4 kilometer baseline established by the National Geodetic Survey in Santa Paula, California. The agreement between the NGS values and the Model 1991 results were: LAT LON HGT Diff. in local coord. +0.072ra -0.080m -0.113m These results agree well with other lines measured in the Pasadena area which are given by MacDoran. The Santa Paula test, however, is the only one I personally witnessed from data acquisition to final processing. The line measured was between the main station mark and the Azimuth mark. Both sites were clear of obstructions and provided nearly ideal GPS site conditions. Thirty minutes of data were observed during the period of best GDOP conditions. The broadcast ephemeris was used to process the observed data the day following the (midnight) observations. The other "blind" test that I can report is a line previously measured by our V-1000 survey teams between Palos Verdes (Aries 1) and a point on the roof of ISTAC's building. The coordinate difference between these two points were withheld from ISTAC until they provided best and final Model 1991 coordinates to Geo/Hydro. The following misclosures resulted: 203 LAT LON HGT Diff. in local coord. -0.215m -0.009m +0.245m ISTAC reported that their determination of the geodetic values on their building were accomplished with 30 minutes observation using the broadcast ephemeris. In contrast to this measurement the "true" value of the 53 km line was measured using a 3 hr Macrometer observation and a post-fitted ephemeris. The "uncertainties" given for this line by the V-1000 processing software are: LAT LON HGT Macrometer uncertainties 53 km line 0.029m 0.144m 0.055m Undoubtedly some of the error in the Model 1991 determination is due to the inaccuracy of the broadcast ephemeris. This line will be reprocessed in the near future when the post-fitted ephemeris becomes more readily available. PROCESSING All processing, for the GPS Land Surveyor^^ is performed on PC-compatible computers. Geo/Hydro is presently using a Compaq Portable and a Compaq DeskPro^^.The Portable has the advantage of being more easily transported while the DeskPro is a faster machine. The data processing consists of three steps: (1) acquiring ephemeris data from a Trimble GPS Receiver, (2) performing Fast Fourier Transformations of the observed GPS spectral data, and (3) computing space vectors from the (transformed) observations. The first step can be automated to the extent that the broadcast ephemeris can be acquired by the Compaq computer automatically. The ephemeris can then be transferred by floppy disk or by telephone modem to another computer. The second processing step presently requires the most time. The DeskPro requires twice the amount of time to process data than is required for observation. That is, it takes one hour to transform a one-half hour observation. This second step can also be automated to the extent that only a few minutes are required to start the transformation while the rest of the time the computer can be left unattended. For example, a team operating with four instruments observing four (15 minute) points per day would require 8 hours to transform the observed spectral data into frequency and phase "observables". More than one DeskPro might prove to be prudent for a four instrument survey team. 204 The final step of Model 1991 processing is to compute individual vectors from the transformed CA and P code phase data. This step requires about 30 minutes per line and is the step that requires the most operator interaction. There are several choices, for example, on how to treat clock corrections. The absence of "cycle slips" should speed up this processing technique considerably! PRODUCTION The results reported here were obtained during the best portion of the present satellite window. Observations made at other times will produce less accurate results. MacDoran in his paper will describe the trade-off between the length of observation and accuracy. In general terms typical survey accuracies can be obtained from observation periods of from five minutes and greater. The upper limit of diminishing returns has not been precisely determined; however, 30 minutes of data appears to be a good practical limit. The ability of the surveyor to choose the accuracy he desires and then design an observation scheme to meet his requirements should prove to be both practical and economical. In many cases surveyors do not require accuracies greater than 10-30 centimeters. In these cases the Model 1991 will prove to be most economical. SUMMARY The GPS Land Surveyor^^ Model 1991 appears to provide the solution to surveyors who require: portability, greater production at the expense of accuracy, a lightweight antenna that can be elevated above tree cover, and faster processing of results. This instrument is clearly not the most accurate GPS instrument in use today but its versatility will make it highly advantageous for projects requiring accuracies in the 10 to 30 centimeter range at low per point costs. Macrometer is a trademark of Aero Service GPS Land surveyor is a trademark of GPS Services, Inc. COMPAQ Portable and DeskPro are trademarks of COMPAQ Computer Corp. 205 NEW RESULTS ON THE ACCURACY OF THE C/A CODE GPS RECEIVERS Javad Ashjaee Trimble Navigation 1077 Independence Avenue Mountain View, CA 94043 ABSTRACT In this paper we introduce a new technique, which we call IC (Integrated Doppler, Carrier Phase, Code Phase) technique, for processing GPS-NAVSTAR signals for obtaining accuries for first- order survey and similar applications. This technique involves employment of integrated doppler, carrier phase, and code phase. Test results of this technique, implemented in TRIMBLE 4000S GPS SURVEYOR, are also provided. The initial differential accuracy obtained by the receiver, using integrated doppler, is better than 3, 5, and 2 centimeters in latitude, longitude, and altitude, respec t i ve 1 ey. The receiver also provides carrier phase measurements. Using the computed initial position along with carrier phase measurements, posi- tional accuracy of better than 1 centimeter can be achieved by post processing. The fact that the accuracy of the computed initial position is better than 5 centimeters eliminates the carrier cycle ambiguity problem and significantly reduces and simplifies the required post processing. The receiver is self- contained and does not require a highly stable external oscilla- tor. There is also no need for oscillator calibration and no need for bringing the receivers together for oscillator compari- son before or after the mission. The receiver provides online results as well as measured data for storage and post processing. The Model 4000S GPS SURVEYOR is a C/A code 4-channel GPS receiver. Our earlier reported results (Ashjaee 1984) on the accuracy in dynamic applications of he TRIMBLE 4000A GPS LOCATOR, a 4- channel C/A code GPS receiver, are also summarized in this paper. 207 I. INTRODUCTION To address the wide range of accuracy requirements of GPS users, TRIMBLE NAVIGAITON initiated research and development activities on two classes of C/A code GPS receivers - GPS LOCATOR and GPS SURVEYOR. The GPS LOCATOR (TRIMBLE 4000A), a 4-channel receiver, provides real-time position, velocity, and time information. The results obtained with 4000A have been reported earlier (Ashjaee 1984) and are also summarized in Section II of this paper. Two types of measurements can be made from each GPS-NAVSTAR satellites - code phase measurements from code tracking and carrier measurements from carrier tracking of the received signals. Carrier measurements, due to the finer resolution of carrier, can be used to provide very accurate position fixes in survey applications. TRIMBLE 4000S GPS SURVEYOR employs IC^ processing technique and provides initial differential position accuracies better than 3, 5 and 2 centimeters in latitude, longitude, and altitude, respectively. The accuracy then is further improved to better than 1 centimeter (see Section III) in three dimensions by rela- tively simple post processing of the provided carrier phase measurements, in conjunction with the initial computed position. This receiver also provides accurate measured carrier data and timing information for the users interested in processing data and computing position fixes using their own algorithms and processors. Section III shows the accuracy of TRIMBLE 4000-S GPS SURVEYOR. The features of this receiver are discussed in Section IV. II. RESULT SUMMARY OF TRIMBLE 4000-A GPS LOCATOR Figure 1 shows the plot of about 1500 position fixes while driving around the Bay of San Francisco. This figure shows the continuous signal reception and tracking in different electromag- netic environments. Reception interruption occured when driving under the overpasses, through the Waldo Tunnel, the lower deck of the Richmond Bridge, and close to the towers of the Golden Gate Bridge. The discontinuity in Figure 1, which is marked by '•*", is due to antenna cable being disconnected inadvertantly. Figure 2 shows the dynamic accuracy of TRIMBLE 4000A. The plots of position fixes while driving in the city of Palo Alto are shown in this figure. The absolute and relative accuracies of the fixes are better than 15 and 4 meters respectively. Figures 3(a), (b) and (c) show the scatter in latitude, longitude, and altitude components of velocity. The RMS noise in these components is on the order of .01 knots (5 mil limeters /second ) . 208 V +■ » £ o o CO w o X H IS O M ^ H Ci4 M to CZ4 O O CM O H H O W A4 H CM O M e V / I ^i2<' 5 ?) • « c CO X H z <^ O « M H O M CJ CO CO O H O ^ H PM CO o H (±4 209 LATITUDE COMPONENT OF VELOCITY -3 CM/SEC LONGITUDE COMPONENT OF VELOCITY - 3 CM/ SEC ALTITUDE COMPONENT OF VELOCITY FIGURE 3. PLOT OF SCATTER IN a) LATITUDE, b) LONGITUDE, AND c) ALTITUDE COMPONENTS OF VELOCITY. 210 The Model 4000A also provides timing information in the form of 1 pulse per second, which is synchronized to the GPS master clock with the accuracy of better than 100 nanoseconds. The receiver has the following three modes of operation: - 4 satellite mode, which provides 3 dimensional position and velocity, and time information. Requires no aiding. 3 satellites mode, which provides positions and velocity information in latitude and longitude and time information and requires altitude aiding. - 2 satellites mode, which provides positions and velocity information in latitude and longitude, and requires altitude aiding and stable oscillator. The performance degrades with the instability of the oscillator. III. ACCURACY OF TRIMBLE 4000S GPS SURVEYOR Carrier processing, due to finer resolution of the carrier signal (about 19 centimeter wavelength) and the ability to track to a small fraction of a cycle, can be used in survey applications to provide very accurate translocations. Several techniques have been reported in the literature for carrier processing of the GPS signal. The reported techniques suffer from the drawbacks of: a) a need for atomic clocks or very stable oscillators; b) calibration of the oscillators before and after the survey; c) extensive post procesing due to carrier cycle (nA ) ambiguity. These drawbacks reduce the applicability of these techniques due to high cost and to the length of time to survey a point. . . . . . The IC^ technique eliminates or significantly reduces the above drawbacks. This technique involves employment of integrated doppler, carrier phase, and code phase, in which the receiver computed position fixes provide initial results, and a more accurate result is obtained by relatively simple post processing. Figure 4 shows the scatter in integrated doppler measurements in the TRIMBLE 4000S. The figure shows that the accumulated error after 1.6 hours of phase integration is less than 1 centimeter. Figure 5 shows the result of the initial differential position fixes with the TRIMBLE 4000S SURVEYOR. In this figure, each point represents a differential position fix obtained every 6 minutes using doppler integration. The obtained differential accuracy of the initial position fixes are better than 3, 5, and 2 centimeters in latitude, longitude, and altitude components of position. The final order of magnitude vernier on translocation, 211 if required, is achieved by processing the time tagged carrier phase measurements of the two receivers (available via the RS232 port). Note that the carrier cycle ambiguity has been resolved and the post processing only involves simple position fix compu- tations using range-type measurements. It should be noted that the reported accuracy corresponds to the zero -baseline separation. The degradation of accuracy as a function of baseline and multipath follows the general rule and is not unique to 4000S SURVEYOR or IC^ technique. 10. min/marh 15 MM 10 i 5 \. -5 -10 -15 MM 1.6 HOURS WN: 273. Thu 5i 3. 38 UTC FIGURE 4. NOISE IN INTEGRATED DOPPLER MEASUREMENTS 212 S I I I I I I I > I I I I I I > I I I 1 LATITUDE LONGITUDE I I I >> I I I < I I I I I I I I > I < .« • SCALEi 1 CM/MARK CARRIER ONLY POSITION FIXES FIGURE 5. PLOT OF INITIAL DIFFERENTIAL POSITION FIXES USING INTEGRATED DOPPLER. IV. THE ADVANTAGES OF IC^ TECHNIQUE 1. NO NEED FOR HIGH QUALITY OSCILLATORS: An accurate time base plays an important role in achieving sub-centimeter position translocation. All of the accurate GPS surveyors available today require highly stable oscilla- tors and/or calibration before and after the mission. In 4000S, accurate timing is provided by using the GPS satellite clocks in a time transfer mode. This is achieved by continuously using the code phase measurements from 4 satellites. The timing accuracy is better than 20 nanose- conds in phase and 5 parts in 10 to the 12th in frequency, This exceeds the performance of most atomic standards in field operations. 213 2. RS232 OUTPUTS: Several measured and computed data are available via the RS232 port. These data include: Integrated carrier phase from each satellite. - Carrier phase from each satellite Time tags of signal transmission to the accuracy of better than 20 nanoseconds. Doppler measurements - Code phase measurements Estimates of position in cartesian and polar coordinates Frequency and phase offsets of the oscillator - NAV data including ephemerides, SV clock parameters, ionosphere, and GPS to UTC conversion parameters. 3. ONLINE RESULTS Although the measured and computed data can be stored in RS232 compatible storage media for post processing, the re- ceiver also provides online position results. Using the online computed position fixes eliminates the need for any post processing, except for subtracting the results obtained from the two receivers in two sites. The online computation eliminates the need for storage media. Post processing is necessary if accuracy better than 1 centimeter is required. NO NEED FOR LONG-TIME MEASUREMENTS: Using both integrated doppler and carrier phase reduces the amount of required data to achieve better than 1 centimeter accuracy. Typically, less than 10 minutes of data is suf f ic ient . REFERENCES 1. Ashjaee, J. M. and Helkey, R. J., 1984, "Precise Positioning Using a 4-Channel C/A Code GPS Receiver", Proceedings of IEEE PLANS °84, pp. 236 - 244, San Diego, CA, November 1984 214 EXPERIENCES WITH THE TI 4100 NAVSTAR NAVIGATOR AT THE UNIVERSITY OF HANNOVER Guenter Seeber Delf Egge *) Andreas Schuchardt Joachim Siebold Gerhard Wuebbena Institut fuer Erdmessung Sonderforschungsbereich 149 Nienburger Str. 6 3000 Hannover 1 Federal Republic of Germany ABSTRACT. The University of Hannover has taken delivery of a TI 4100 NAVSTAR Navigator in June 1984. This instru- ment was used for navigation and geodetic positioning in single station and differential mode. Within this paper software developments and experiences gained in various field projects are presented. Software developments pertain to utility packages for satellite alert computation, data acquisition, and preprocessing as well as positioning for stable and moving antenna setups. Field projects include ship positioning and geodetic positioning of known control stations. INTRODUCTION Precise positioning with satellite methods has been one main research topic at the Institut fuer Erdmessung (IFE) at the University of Hannover since 1975. In the first years, main emphasis was given to positioning with Transit Doppler equipment on land and at sea (Seeber et al. 1982). Much research work has been performed with respect to marine geodetic application within the "Special research center for geodetic and remote sensing techni- ques in costal areas and at sea" (SFB 149) (Seeber et al. 1980). About five years ago, first investigations were initiated with respect to potential applications of GPS in continental and marine positioning, which included extensive software simulations (e.g. Wuebbena 1983). On this basis it was possible to acquire a Texas Instruments TI 4100 NAVSTAR Navigator within the SFB 149, and to start operational GPS research immediately after delivery of the equipment (June 1984). Corresponding to the Transit-related research, the GPS-related work was performed in the following four areas: - development of TI 4100 data handling, - investigation of the TI 4100 user solution, - development of software packages for use of the TI 4100 raw data for static and dynamic positioning, - design and accomplishment of field measurement projects, if possible under controlled conditions. *) now with the University of Washington, Department of Civil Engineering, Seattle, Washington 98195 215 The objective was to develop a complete data line in order to perform special investigations under transparent conditions. Within this paper, basic concepts of this research work and first experiences with respect to the TI 4100 equipment are communicated. TI 4100 NAVSTAR NAVIGATOR The basic features of the Texas Instruments TI 4100 NAVSTAR Navigator are well documented (Ward 1982) and will not be discussed here. The selection of this particular receiver type was mainly due to the fact that at the time of order (early in 1983) this was the only equipment capable of providing the full geodetic capacity of GPS for static and dynamic applications. The TI 4100 computes a complete solution set including three-dimensional positions and velocities using the built-in navigation processor. In addition, a binary data output with different selectable record types is available through a RS 232 port. In the standard set-up these data are recorded on a rugged TI 4100 cassette unit, whereby 20 to 30 minutes worth of data can be stored on one cassette. Some versions of the TI 4100 also use the cassette unit for loading the binary operating program. Additional ports are available e.g. for connecting an external frequency standard. POSSIBILITIES OF DATA TRANSFER FOR POST PROCESSING Various ways of data transfer between the TI 4100 and a post processing computer have been realized as shown in Figure 1. Most efficient is the direct transfer to a mini or desk top computer. Some additional comments may help other TI 4100 users to go a similiar route. Common to all these transfers is the availability of proper connectors to prepare the appro- priate cable. VAX 750: The data output to the VAX 750 computer (VMS Operating System) is straight forward. Direct calls to the operating system are necessary. HP 1000 (E and M Series CPU): This connection is more complicated. A HP 12966 (BACI) card has to be available. Care has to be taken to assign the software driver DVFOO to this interface card. This software is available at INTREX,2570 EL Camino Real West, 4th floor. Mountain View, CA 94040-1314, USA for M/E/F Series Computers. Only this driver can handle the data input properly. A dedicated program with HP 1000 EXEC calls had to be developed for storing the data either on from disc or on magnetic tape. HP 216: This desktop computer proved to be most versatile. The built in RS 232 interface can be software adapted to the TI 4100 data stream. A HP program exploiting the background "TRANSFER" facility was used to store data on 3 1/2 inch floppy discs (270 KByte capacity). One disc can take approxi- mately the same amount of data as a TI 4100 cassette. From the HP 216 the transfer to the HP 1000 can be done very efficiently over the HP interfacfe bus (HP IB): It takes about four minutes for one full floppy disc. Using a special interwiring and a self-developed power supply, it has also been possible to connect the TI 4100 cassette unit to the HP 216 in order to read data from cassettes. 216 SOFTWARE DEVELOPMENTS Main software developments concern TI 4100 data handling and decoding, alert computation and satellite selection, static (geodetic) positioning solution, and navigation solution. The first step is the decoding of the binary data stream as it is out- put by the TI 4100. Various data types are available for the different application programs (see Figure 2). For planning and organization of observation campaigns the knowledge of constellation and visibility of the satellites is required. The alert software provides time-ordered elevations and azimuths, and selects the optimal configuration using the minimum PDOP criterion. Since the developments for geodetic positioning, based on carrier and code measurements are described in an independent paper (Wuebbena 1985), the following description is mainly focussed on the navigation software. In order to make use of the high potential of NAVSTAR GPS for marine positioning, the design goal was to develop fully transparent and modular software, capable to be extended for differential dynamic positioning and integration with other navigation sensors (e.g. inertial positioning systeirj). For positioning a single moving station an 8-state Kalman Filter is used as outlined below. The state propagation is modelled in discrete time as x(k+l) = A(k) x(k) + w(k) (1) where and x^(k) = [TTXXYYZZ]^ A(k) = 1 At 1 1 At 1 ; Q(k) = At At 3 2 At 2 At 2 [At 3 At ] 2 At 2 At 2 ^x 217 with X - state vector (receiver clock bias, antenna coordinates and respective time-derivatives) A - transition matrix w - system noise due to unmodelled accelerations Q - system noise covariance matrix cf'^, cf'^, 0* -2, 0* '2 _ variances of accelerations At - elapsed time between epochs (k) and (k+1). While the variance of clock aging can be predetermined by clock quality investigations, the variance of the antenna accelerations depends on the dynamics of a specific observation situation. Thus it has to be viewed criti cally on a case by case basis. The observations provided by the TI 4100 are pseudo-ranges and the Doppler-induced frequency shift of the carrier frequencies of up to four Space Vehicles (SVs). The latter can be regarded as an instantaneous measurement of the relative velocity between SV and receiver antennae, i.e. as pseudo-range-rate. Thus the observation equa- tions are where and \ = h(x^) + v^ (2) z, = [r^ ^1 ^2 "^2 "3 '^S ^4 ^4^ r. = r. 1 si + c (T . - T ) ^ SI u' (R . - R )(R . - R ) + c (T . - i) ^ SI u'^ SI u' ^ SI u' ; i = 1,...,4 r., r. h V -> -^ '^si' ?si "•^si' ^si ^' ?u ^u' ^u measured pseudo-range, pseudo-range-rate to SV i nonlinear measurement function measurement noise position and velocity of SV i in an ECEF coordinate system clock bias and clock bias rate (computed from navigation message of SV i) position and velocity of the receiving antenna] state 1 I u- J 1 I k- 4. \^ vector user clock bias and clock bias rate [ vacuum velocity of light 218 The above equations form the basis for an "Extended Kalman Filter" (e.g. Gelb 1974), operating in discrete time steps. A simple covariance model for the observation noise was adopted by assuming equal variances of range and range-rate measurements, respectively, and ignoring correlations. Table 1 shows measurement noise variances obtained empirically from TI 4100 data. It can be seen that the values depend on the antenna motion (static versus low dynamic). Before introduction to the Kalman Filter algorithm, the observations are corrected for relativistic and earth rotation effects as well as ionosphe- ric and tropospheric refraction. Some numerical results will be presented in the following chapter. GPS FIELD PROJECTS Several field tests were carried out in the second half of 1984. These are described below and some results will be discussed briefly. Throughout it can be stated that the TI 4100 NAVSTAR Navigator proved to be extremely reliable. Positioning at Sea In August 1984, GPS positioning was performed on the German research vessel "Polarstern" in artic regions up to 80 degrees North. Here extensive seismic and bathymetric surveys were made and GPS should supply precise positioning, if it is available. Usually the positioning is done by integra- tion of various sensors. The major components are the TRANSIT system and a Doppler sonar. In Figure 3 the track of this conventional navigation is plotted together with that of the TI4100 User solution. The superiority of GPS is obvious. During dead reckoning, a systematic error in the Doppler sonar (possibly on "watertrack") causes a position error reaching 1 km in this specific case. After update by a TRANSIT fix, the position again comes very close to that derived from GPS. The raw measurement data from that cruise were also processed with our navigation software. To prove the validity of the navigation software, the derived geocentric position coordinates were compared to that from th TI 4100 User Solution. In Figure 4 the two solutions are plotted together. The agreement is satisfying and it can be seen that our solution is somewhat smoother than the TI 4100 user solution. This is a result of different system noise parameters. In July 1984 we made a navigation experiment in the North-Western German offshore area. The goal was to test the real time navigation performance. The TI 4100 was installed on board the German sea surveying vessel "Norderney", which is operated by the Wasser-und Schiffahrtsamt Emden (WSA). The receiver operated without an external clock and data logging was done via a HP 1000 (M Series) computer directly on half-inch magnetic tape. In this offshore area the radio navigation system SYLEDIS is available, which gives continuous positions with an accuracy of a few meters in the 219 hyperbolic mode. The "Norderney" is equipped with a SYLEDIS receiver, thus reference positions are given and a comparison to GPS fixes can be performed. During two cruises we collected the TI 4100 data, while the SYLEDIS positions were supplied by the WSA. The processing was then done afterwards in the office where we concentrated on the TI4100 User Solution. The GPS positions are considered to be in the WGS 72 geodetic datum, whereas the SYLEDIS positions are given in a local datum. Therefore a datum shift has to be performed first of all. This is done by evaluating the medium difference of geocentric coordinate componenents of both data sets at identical epochs. This gives the datum shift parameters (aX,aY,aZ), which are sufficient for the investigated area of not more than 60 km^ ^ Only 4 - SV navigation data will be used for this evaluation. The computed datum shift parameters are reported in Table 2. The agreement with other data is quite good and in the range of the expected absolute accuracy of GPS, which is usually considered to be 15m. The residuals are shown in Figure 5. A noise of about 5 meters is obvious and drift effect can be seen. This drift is highly correlated with a dramatic increase of the PDOP value. Furthermore there are some peaks, expecially in the altitude residuals, which also translate to the horizontal position components. The reasons for this are still under investigation. A similar project was performed in December 1984. In cooperation with the Technical University of Delft (Netherlands) the TI 4100 was installed on board HR MS Tydeman of the dutch military hydrographical service. Cruises lead us through the dutch gas fields in the North-Sea, which are covered by the SYLEDIS system. There it was possible to fix SYLEDIS positions in the range mode. The geodetic datum is ED 50 and the accuracy of these reference positions, which were supplied by TU Delft, is in the level of 1 meter. Since the "Norderney" project and additional SV (PRN 12) was placed in its orbit and here we used an external rubidium frequency standard. For first investigations we chose the same processing technique for the compairson of GPS and SLYEDIS data as described above. The evaluated shift parameters are reported in Table 2. Reference values were found in Blanken- burgh (1978). The agreement again is sufficient. The residuals are plotted in Figure 6. A noise of a few meters can be seen again. The observation period can be separated into intervals, which are limited by peaks in the residual plot. These peaks are directly related to the instants when a SV drops out and a new one has to be acquired. For a moment, depending on acquisition time, the user solution operates with 3 SVs in time-bias-rate- hold mode if a precise frequency standard is attached. But the agreement between various configurations is excellent for horizontal position components and acceptable for the altitude, which is worst determined in all cases. An exception has to be made for the 2 SV navigation mode where the TI 4100 software holds the time-bias-rate and the altitude fixed (as can be seen very clearly from the plot). In this mode the data are no longer reasonable. 220 Geodetic Projects One main objective of research work in Hannover is the use of GPS for precise differential positioning in geodetic networks of short and medium inter station distances. To this purpose, further basic data sets using two TI 4100 receivers were created within two projects. The second receiver was provided by Texas Instruments Inc., Lewisville. Figure 7 shows the distribution of stations and interconnections during project NIENAC 84 (June..July). Corresponding to the satellite coverage one line could be observed each day with four satellites during approximately three hours. Figure 8 shows the observed lines within project HANNAC 85. The objective of this project is to investigate the potential of TI phase observations for use in geodetic surveying practice for short distances up to 10 km. NIENAC 84 was observed only with the internal clock. For HANNAC 85 two Rubidium oscillators could be used as external time base. Some of the lines in NIENAC 84 have been determined earlier through Transit Doppler and Macrometer observations so that comparisons will be possible. Also high accurate terrestrial coordinates (2- 3cm) are available. Thus a comprehensive GPS-data set is available to investigate the performance of instruments, techniques, and computer programs. The results will be published in the near future. REFERENCES Blankenburgh, J.C.,1978, Doppler - European Datum Transformation Parameters for the North Sea, Satellite Doppler Tracking and its Geodetic Applications, London, The Royal Society. Gelb, A. (Ed.), 1974, Applied Optimal Estimation. The MIT Press, Massachu- setts Institute of Technology, Cambridge, MA. Seeber,G., Egge,D., Hoyer,M., Schenke,H.W., Schmidt, K.H., 1982, Einsatzmoe- glichkeiten von Doppler-Satel 1 iten-messungen, Allgemeine Vermessungs- Nachrichten, 89, 373-388. Seeber,G., Egge,D., Schenke,H.W., 1980: Experiments in Satellite Doppler Control Positioning at Sea. Deutsche Geodaetische Kommission, Series B, No.252, 69-80. Ward, P. 1982, An Advanced NAVSTAR GPS Geodetic Receiver. Proceedings of the 3rd International Geodetic Symposium on Satellite Doppler Positioning, Las Cruces, New Mexico. Wuebbena, G., 1983, Simulation und Auswertung von Messdaten im Strecken- und Dopplermodus arbeitender NAVSTAR-GPS-Empfaenger zur absoluten und relativen geodaetischen Positionsbestimung, Thesis, Institut fuer Erdmessung Universitaet Hannover (not published). Wuebbena, G., 1985, Software Developments for Geodetic Positioning with GPS using TI 4100 Code and Carrier Measurements, First International Symposium on Precise Positioning with the Global Positioning System, Rockville Maryland. 221 ACKNOWLEDGEMENTS The reported work was only possible with the help and assistance of many individuals and institutions. Much of the programming and computing work has been performed by Arno Brueggemann, Sigrid Matthes, and Lutz Sauer. Logistic support during NIENAC 84 and HANNAC 85 was provided by Nieder- saechsisches Landesverwaltungsamt - Landesvermessung , Hannover. Shipborne experiments were made possible through - Wasser- und Schiffahrtsamt Nordwest, Emden, and - Alfred Wegener Institut fuer Polarforschung, Bremerhaven. Additional receivers were made available through Texas Instruments, Inc., Lewisville and Norges Sjoekartverk, Stavanger. This support is gratefully acknowledged. Table 1: Variance estimates of TI 4100 measurements Dynamic Mode Variance of P-Code range Variance of carrier range rate static low dynamic 0.7 m^ 2.7 m^ 1.4 (cm/s)2 61.0 (cm/s)^ Table 2: Datum shift parameters from various observation campaigns (reference values are from NIEDOC 81 doppler campaign and from Blankenburg (1978)) German datum - W6S 72 ED 50 - - WGS 72 Doppler GPS "Norderney" Doppler GPS "Tydeman" AX AY AZ 634m 16m 446m 63 6m 2m 459m 85m 106m 123m 92m 113m 125m VAX 750 T I 41 00 HP 1000 Tl 4100 CASSETTE HP 200 FLOPPY DISC Figure 1: Data lines with the TI 'tlOO 222 / TI tlOD \ V WW OUTA J DECODING SOFTWARE RCV (tASll©ENTS SVNAVfCSSAGE ^ St USER SOLUTION, GPS HJW*C OTHER If^JRmTION -p_ 1 >r \f GEODETIC WVIGATION TI IIOO USERSOUJTION OPS Al£«TS , ' COPARISON (IflSfRVATICN SOCOIE • Figure 2: GPS related software at Hannover TRAMS IT FIX MPt>ATH ■10 km IM 1 ■: i I I 1 ■,^ i i ° i 1 -•- t V ? ;? i f f Figure 3: Ship track from GPS ( ) and the integrated navigation using NNSS ( ) 223 . 11? IT. ■^V«/^S; -60f': 10 hici 12"15' Figure 5: Residuals of GPS, SYLEDIS as reference (Norderney) TIME 30 min Figure *» : Comparison of TI 'tlOO user solution ( ) and Hannover navigation software Figure 6: Residuals of GPS, SYLEDIS as reference (Tydeman) 224 PIlSUM MCSSOAtJ^p _Ju5^- ' ' // VtlB£B J '^T^ // ' ' 1 ^^^ / ^-\ / 2.5/ N / 5 / 2y/j^*^^ "^/^ 1 UHlHlttf^ ^/ Y |[I6 / /^""^•^ / }/ / ^^^^-^ / MiiHUHBEJC^;^ /^ ^^^^^^ §V^2 rigure 7: NIENAC l\ Network, Distances are in ka. Figure 8: HAKIIAC S5 NetMork, Distances are in k«. 225 Phase Center Variation in the Geodetic TI4100 GPS Receiver System's Conical Spiral Antenna Michael L. Sims U.S. Naval Surface Weapons Center Dahlgren, Virginia 22448 ABSTRACT The phase center tests were performed on two antennas. One antenna was a production unit, the other was a preproduction model. The preproduction model was built using the same fabrication techniques as the production antenna. Both antennas had the preamplifiers removed. The phase measurements were made on both antennas for LI (1575.42 mHz) and L2 (1227.6 mHz). The results show repeatable phase centers with acceptable variation over the 360 azimuth with measurements taken at least 10° above the horizon. DISCUSSION Test Objectives: The antenna test objectives were to determine the Ll and L2 phase centers, phase center variation with elevation and azimuth, and the repeatability between antennas. Set-Up: The Geodetic TI4100 Receiver System antenna's phase center was determined using NASA Goddard Space Flight Center's 70 ft., indoor antenna range. The chamber was temperature controlled and the test equipment was turned on 24 hours prior to the start of the tests. 227 Two antennas were evaluated, one a production run antenna (S/N105) , the other a preproduction model (S/N103). Both were right-hand, circular polarized, conical spiral antennas. Figure 1 is an artist's view of the antenna with the dome removed. The base of the antenna mount houses a preamplifier which was removed for the tests. The signal came from the antenna via a type N connector on the side of the preamplifier housing. Phase Center Determination: The following sequence describes how the phase center of the antenna under test (AUT) was determined with respect to the phase center of the radiating antenna. First, a probable phase center was selected. The AUT was then mounted on the range's rotating mount so the probable phase center was about three centimeters away from the AUT's point of rotation. Figure 2 is a relational drawing of the radiating (signal source) antenna to the AUT. The phase variation was recorded while the AUT was rotated >0°about convention. +/-90°about the eaxis. Figure 1 also gives the AUT's rotation The antenna was moved 90° in the (() direction and again rotated +/-90° about e while recording the^phase change. The operation was repeated for (^ equal to 180 and 270°. The AUT was moved 0.25 cm closer to the radiating source and the above repeated, with the exception of the first step. The phase centers were arrived at by analyzing the data produced curves for the best symmetrical maximums, with minimum phase shift difference between maximums, while providing the most coverage of the 0°Degrees of Phase Center Variation line. Figure 3 is the plotted L2 data for the preproduction antenna and is representative of the other frequency and antenna. The phase center for both antennas are 22.7cm for LI and 20.2cm for L2 as measured from the bottom of the preamplifier housing. Phase Center Variation Determination: Once the phase centers were determined for both antennas at both frequencies, the variation of their phase centers with respect to azimuth and elevation was investigated. The AUT was mounted with its phase center over the mount's rotation point. The AUT was rotated +/-90°in the 6 direction with respect to the signal source and phase measurements taken. The AUT was then rotated 30° in the (j) direction and the above repeated. Tables I to IV contain this data in a (j) vs e arrange- ment. Figures 4 to 7 are topographical displays of the data. Each antenna had a different - Opposition. The production antenna ' s (|> = Opposition was the blackline on the side of the preamplifier housing. This line was aligned with the base end of the LI antenna. The preproduction antenna did not have the black line. Its 4> = Opposition was chosen to be the center of the active type N connector. (The other type N connector receives a built in test signal that is fed directly to the input of the preamplifier.) This = position difference was not a problem in meeting the test objectives. From comparison of the topographical displays, the pre- production antenna's = reference is approximately 60 counterclockwise of the production antenna's <1) = reference. Tables V to VIII provide information on the phase center variation at points of interest. Figure 8 gives graphical meaning for the columns titled e maxl, Maxl, emin, Min, e max2r Max2, Min+80° and Min-80°from these tables. The columns titled -0.25+cm and -0.25-cm refer to the number of degrees in 6 that the signal source has to move towards the horizontal ^efore the phase center has changed by -0.25+/-cm from the 9 = phase amplitude; -0.25+cm refers to the right of e = and -0.25-cm is to the left of 9 =0. The Maximum Difference (Max. Diff.) columns are the maximum difference between signals that the antenna will exhibit for varioug . The largest Max. Dif|. for S/N103, LI, is 1.33cm at * = 330 ; L2 is 1.70cm at * = 240. ^ For S/N105, LI, the largest Max. Diff. is 1.20cm at** 210 ; L2 is 1.84cm at <() = 30°. The Span 0.25cm columns are the sum of the -0.25+cm and -0.25-cm values. The largest Span 0.25cm for S/N103, LI, is 155 at <\> = 240 ; L2 is 134° at 6 = 30 , 60 , and . 240 . For S/N105 LI, the largest Span 0.25cm is 153 at * = 120; L2 is 138r at (|> = 90 . CONCLUSION The Geodetic TI4100 GPS Receiver System's antenna is a satisfactory compromise between absolute and relative positioning. If the majority of applications were relative positioning, the user may wish to investigate a different antenna design. However, 229 selecting another antenna type because it shfiijld give better phase center stability should be avoided. Unless phase center test data are available and a controlled production technique is used to insure repeatability of the antenna's electrical characteristics, one would be better of£ staying with a known antenna. RECOGNITION A thank you goes to Ruth Darnell, U.S. Naval Surface Weapons Center, for technical assistance in preparing the paper. A special thanks goes to Billy Williams, NASA - Goddard, for running the tests and the initial data analysis. 230 o z < z O I— < z u LU O 231 c/) z < z z UJ z < ^F o CO Z o »— < < c .0 a> CN 3 O) v 232 233 o H & CO o § •H -P n3 •H a > o CO o CO o o oo o o OJ o o OJ o H C\J o o oo H o LA H O OJ H O O CO o oo H I o H I O CD LfN O On LA O I O UA 00 VD OJ o OJ a\ o oo o O OO o o H OJ O OJ OJ H O vo oooooooo I + + + + + + I o o vo oo o o H 00 o US H o 00 oo OJ OJ I o H 00 OJ o + O + O O + 00 OJ o + CO OJ o + H O I OO o o + oo OJ o + o o + o 00 o + VD O OJ o I OJ OJ o + o + 00 H OJ UA VD O OJ o + OJ 00 o + o OJ OJ o o I LTN o o + oo o + o + oo o + o I VD H OJ oo o + ON o o + OJ OJ o + oo OJ o + o OJ o + VD o o I o + o + ON OJ o + oo o + oo OJ o + OJ o VD ooooooooo I I + + + + + I I oo 00 00 o I ITN VD t- H o + oo o + OJ OJ o + o + oo 00 OJ H o + oo o o + VD o o + ON o + o 00 o + o + o I o I oo oo OJ o ON oo O OJ ooooooooo I I + + + + + + + O -=!- VD CO LTN VD O H H I o oo o I ITN o I 00 OJ OJ OJ VD o LTN o oo o o VD o H VD o ON o o I o + OJ H o + ON o + ON OJ o + 00 oo o + o OJ o + H H o I o o + o + oo H o + oo o o + o o + o o LTN o I o ITS o I oo UA oo VD LTN o I oooooooo + + + + + I I I o o o o o o + + + + + ooooooooo I I + + + I I I I o o oo H I o OJ H I o oo H I o o LfN -^ o o 00 0) o ON o o VD l/N OJ o LTN H oo H oo oo H OJ oo o VD o On OJ o OJ VD o OJ oo oo o + o + o + LTN 00 t— VD LIA OJ o OJ oo ^ o + OJ oo o + o H o I o o + o OJ o + LTN 00 o + J- OJ LTN o H O O O I I I I O O O O O + + + + + Lf^ LTN o I -=(■ ir\ o oo -d- VD o o o o o o o + + + I I I I o oo o OJ o 00 OJ H LfN OJ LfN oo O H o On o oo oo 00 oo H o o oo OJ ON oo H O OJ OJ CO 00 o o o I I I O VD OJ o o o o o o + + + + + o + o OJ VD OQ VD OJ OJ OJ o H o + 00 o o o + + OJ o + o o OJ H o LTN OJ oooooooo I I + + + + + + o o o + + + t~- -Id- o o o o I I I I H o o o o o + + I I I H I OOOOOOOOO ooooooooo Onoo ^-VD irN-=f OOOJ H + + + + + + + + + ooooooooo oooooooooo HOJ00-=riAVDt— OOON I I I I I I I I I 234 o en CO CM I en o CO H CO CO CM H o ir\ CO H H H H H OO CO OJ lA CVJ C3N opoooooo I + + + + + + I o + o o o o o + + + I I o o 00 ON a» vo H On H o CO t~ CO On OO ^ CO OJ H H O LTN H O O H ON 1-1 o CVJ I O O O O Q O C I I + + + + 4 o + o I O O O O O H + + + + I f CVJ I o o CVI o OJ I 00 vo c^ H CM ^ ^ CO ON CO 00 CVJ H o 00 o o H O IfN VD O rH O H o o I I o o o o o o + + + + + + o o o o o I I I + + o + o ir\ vo H O OJ I CM lA O H CO h a o •H •H ■P a o a; 01 a 0) I o o CM O H CM O O OO O O lA H O O CM O O CJn O O VO On OJ I CM I CM I CM I VO o CM I CM I -a- ^ H CO lA 00 CO H CO CO 00 H CO -=J- O CO O [— OO o o LA o CO o -Id- o C3N CO vo -=1- i-H o o I o + o + o + o + o + o + CO t- I— _:t CO CO ^ O 00 o -=r H lA 00 .:t 00 CM O O I o o I o I o I o « CO CO o o o + o o I H o I o o o o o o o I + + + + + + OnCJnH lACOCOHoO-^t HHlAOOJOOOOHO o o I I lA lA o o o I o I CO o H CO vo O H O H t— o o o o o o o I I + + + + + o o I I o o o o o + + + I I vo 00 O H O O -d- o CO [— CO ^:3- H OJ CM CM H O .=f CO ,:t OO O O O H CM CO CO o o o o o o o I + + + + + + o o o o I I + + o + CO CJn CM O CM H t- H ^ CM CM H ^ CO o o o o o ON CJN H CM O + CM O + VO CM O I o o o o o o o I + + + + + I o I o + VOHVOlAVO-^J-COOOlA OOCMHCMHOOO -:t CO O O O H CM OJ O + CO o + CO CO o + OS H O I H I H I H I o cp o p o o o I + + + + I I VO-=rO HVOIACOIAIA OOCOHHOOOO o o o I + + 00 lA lA O O H o + o + o + o + ON vo CM CO vo OO OO o CM H I I o p o o o o o I + + + I I I o o o I + + o + o + o + o + o I CVJ I LA CN OJ lA ^ C3N O H H I I I t>- vo 00 o CM I t- lA H CO O lA LA CO CM I O O VO CO H O OJ CO OO 00 CO o t— o I CO vo vo lA CO O CM I o o CO voHcocot-iA-=rco OPCOPOOOOO CM I I H t— OO P O H H t- ON lA On H On CO CO OJ O VO LA OJ P P p p o o I I + + + + OOPOOOOO I + + + + + I I VOOOCOOJ PIAIAPCO PHlAHHHHHP CM I VO ° ^ ? ? ? ? ? I I H I ?P O O O O O H T + + + I I I CM I CVJ CO OO vo lA l>- vo CM OJ H H t>- CO O CM I O CVJ CO t- OO H O OJ CVJ o o o + On H O + o + o + t— OO CO CO CO iH o + ITv O O + o I C^ C3N On H VO lA oooooooo I I + + + + + + OOCOVOHVOlA-a--;!- lA -:tVOHOHCO_^COH OOOOOOOOO • + + + + + + I I OJ _:3- O O 00 CM -^ CVJ CO H CO -* ^ 0\ 00 I I ooopopoo I + + ¥ + + OO 00 OO OO VO o CO CO H H -:j- lA OJ CO -=r CVJ o o o o + + + + CO ON -=f H OJ -* o o + + o I O O H I I I lA O OO 00 H H -:t CJN CO oooooooo I I I + + + + ■«% ONt— VOIACVJOnOOCJnCO IAVOHOCMCO_:J-COCVJ O O + + OJ VO O + O + O O O o o + + I I I H I OJ OJ CO CO _:!- OJ LA VO H lA On O O OJ VO lA O O I i o o + + o + o + o o + + OO o ^ -a- OJ lA -St -d- 00 OO H H H CVJ 00 CVJ O O + + o o o o + + + o + o I CO CM CM -:J- CO CO H VO O O O O I ON CO -It 00 o o p o o o p I + + + + + ^h o + o + o + o o + + o + o + o I o o I I H I OO t- -=j- J- -d- H OJ CO 0\ H OO CM CM CM O VO O O lA CM -d- O O CM CM O lA H t— H lA OJ ooooopoo I + + + + T + + On -^ t— 00 VO t- O H ON VO VO CO CM CO 00 OJ O + OO o o o o + + o + o o o o + + I I ON CM t— CM -d- ^ -d- CM lA O VO lA oooooooo I I + + + + + + OOOOOOOOO OOOOOOOOO CJnOO t-vp lAJ- COOJ H H -^ -=r -=r H CM t- [- CJN o CJN o H H "tri o CM CM CM H o o o H CM CM CM o LA oo H CO o • • • • • • • • • • • • • • • H CM H o o o O O O o d O O o o o H CM o PC4 OJ 1 1 + + + + + + + + + + + 1 (3 ON ir\ H 00 vo VO LTN H oo oo CO lA C3N ON oo lA OO VO o o H H -^ o H H H H o o o o H H H o lA CM o •H o • • • • • • • • • • • • • • • • • • +9 CO CM H O o o o O O o o o O o o o O H CM •H 1 H 1 + + + + + + + + + + 1 1 o\ OD lA t- -^ J- -::1- H 00 H lA CM vo oo 00 CM CO CM o H H ^ o H H H H o o o O H H H o lA H ON h o • • • • • • • • • • • • (U ir\ CM H C) o O O O O o o o d o o d d H H H ' 1 i + + + + + + + + + + + 1 ' 1 cn OD H H CO On OO -=t- -=f oo CO vo CM H H 00 OO VO 0) O on H J- o H H H H o o o o H CM CM o lA CM o (0 O • • • • • • • • • • • • • • • a CM CM H O (D O O O O o o o o O O o o H CM ^ H 1 1 1 1 + + + + + + + + + + 1 1 1 1 • CO CO o H OO VO OO VO \r\ H oo CM o\ On ^ CJN OO VO ^ O O 00 H -=r O CM CM CM H o o o o CM CM CM o ^ CM o CM H d O O d d d ,-* o o O O O o o H CM + + + + + + + + + + + + 1 1 en VO 00 CM OO c- ON tr- CJN t^ H H lA CM OO VO o t— O CM o o O CM -Id- o CM CM CM H o o o O CM 00 00 H J- CM - oo ON 0) u CO a) I, •H v\»^ •^=»^^'^'^ 238 r\] o CO v^^:^^ '^x^\^^v<:^ 239 --J O CO v\a'^> '^-:i^\^V\':^ 240 CM .-J O CO »"\ v<:> vvi- v\- :^- 241 > o > -a c E Q 0) o> _c '£ o 0) "o y IE a o 6 00 o Of < O lU >- => < o < 242 ■ h 6 e o I s as oa • > t g CO Q '°5 °a% m °o ft 1§ H 8 o 8 ft o 8 8 1 5 ■ i 8 ^- o ■ 8 8 1 eo 8 0\ M% •H rt r-» o o O i-» H 1-1 1-4 o o "g e 1 1 V >0 ITk V V % NO % f- ?5 O NO °OI NO V •^o 1 5 X s II 8 UN 8 8 1 8 8 1 UN 1 8 NO i ■? ? *? ? ? ? ■? ? ? ? Sm I e 09 Q o o o o\r-r-i/v«fvNO »- OOOOOOOOQOOO Q en .iC . - NO VO ^ NO NO NO NO m I H X OOOOOOOOO ^r-ONONO^ (Viirvo NO« *- 1-1 o p ^ tf\ iTN in .d' I I I I s g g NO .iSr WN ITN lA .» VN S o o o o o o * d d d d ~ o NO ^ CO c5 cJ - ^ « w « fO ., lA 00 NO g g S 5 g g g .» JT en II???????????? « "JoSh* ^CMA^^OkOOt- ':4 10 X O 00 CM (b ,. _ ^. -, . ro* o_ o_ o_ o o_ o_ o o_ o o o o o o o o o o o 243 Sot P« • (0 Q ^S •n • o o I I in rM E • O o + I O o GO I 00 + Z o oo oo oo o_o o 2i :::? o o 8 B cvi o\ o\ SSBSBSSaSS uuuuouuuuu 1-1 m cu 0\ 00 fn O O o o o o (r> ir\ \0 OOOOOOOO Ojroj-cvioooo ocvjvo t— \ovot— t— t— t— vovo ooooooq^oq_ooo h-t— [— r-vo t-t— t^t— r-vovo BBBBBBSSBBBS ouuuoouuuuuu t-HO\ir\OsO\O\H0JO\HH \0 IA.^VO t— t^VO-»-3'VD0OVO o o o o o I I I I I o o o o o o o I I I I I I I BBBBSBBaSBBB ouuuguuuuuua f_j..^vO0Ovovo ir\J-vo t— oo o o o o o I I I I I o o o o o o o I I I I I I I oa > SBBBBBBSBBSS uuuuuuoouuou 0\t-rHHmvOVDOrnvOrHO\ ? ? ? ? ?■ ? ? ? ? ? ? ? o o o o o o o_ o_ o o_ o_ o , mmHQiM^ mwQQOcg I I I I I I I I I I I I Ti B a B a a a a a s CI o CJ u u CI o o o o lA o oo o CM o if\ o oo m O 1-1 o O o H o o ? ? ? o 1 + ? ? ? Z o o o o o o o H o m m ^ -^ m -3- o H CM H X + 1 1 1 1 1 + + + o B a a a a a a § a a a a o u CI o u u o u o u o < m J- .* .» J- -* fO ^ -:» ^ « ? ? ? o + ? ? ? ? ? O + ? ? •-• ,. X o o o o o o O O o o O o i tE, a OS ^ ^ ^ ^ CM m ^ ^ }^ + + + + + + + + + + + + OOOOOOOOOOOO osQOCOOgo^o^ CM CM CM en m m \o 0\ S lA OO h 01 •P CI d ed o c O V ■p c 01 u « cd o rH CO > 0» ? Eh Z 1^ a, • CO Q X b. IS in CM E • o O I I in CM E • O o + o OO o_o ooo_oo_oo m jf ^ fncMHCMfn.3-pncMCM fncn < GEO 85017 PREAMP UT05 > UT06 UT03 , L_ /trequencyN ySTANDARPy Figure L ARL/UT Rooftop Test: 16 July 1984 246 The antennas were placed on mounts 32 cm above NGS first-order survey markers. The alignment of the antennas with respect to these marks was uncertain at the 3-mm level. MEASURED DATA ANALYSIS The receiver measurement accuracy was obtained by differencing two Uke sets of data. The numerical standard deviation of the differenced data was determined. Then, since the receiver measurement errors are independent, the receiver measurement accuracy is the differenced data standard deviation divided by the square root of two. On July 9, two receivers (UT03 and UT05) were connected to the same antenna and Rubidium clock (UT03 replacing UT06 in Figure 1). For this case though, one satellite (PRN-6) was on trackers 1 and 2 while a second satellite (PRN-8) was on trackers 3 and 4. This permitted differences to be taken between trackers and between receivers. Figure 2 presents a plot of the LI pseudorange difference between trackers within the same receiver for satellite PRN-6. Figure 3 presents a similar plot, only the differencing is between receivers. The receiver measurement accuracy standard deviations are similar to the above intertracker case. Over a number of trials, the receiver measurement accuracies are found to be in the range of 0.3 to 0.6 m. The pseudorange measurement accuracies due to receiver measurement error only are given in Table 1. Note, other effects (e.g., multipath and other propagation errors and local and satellite clock errors) are not included in these values. r3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 -? idbo 8000 aoDo wbo sdoo eooo todo RELRTIVE TIME (S) -3 1 -3 _"» 1 M ra -3 -^ I 1000 £000 3000 MObO GuOO 6000 700O RELRTIVE TIME (S) 1 H a dorfca .384 M data .378 M Figure 2. Single Intertracker Pseudorange Difference on Receiver UT03 for Satellite PRN-6 Figure 3. Single Interreceiver Pseudorange Difference (UT03-UT05) for Satellite PRN-6 247 Table 1. Receiver Only Measurement Accuracy Accuracy Measurement Pseudorange Doppler Phase (with drift and all other error removed) LI 30-60 cm 0.8-2.0 mm L2 20-65 cm 1.0-3.0 mm Similar plots of more accurately measured Doppler phase data were obtained. Figure 4 presents the LI phase difference between receivers for satellite PRN-6. Note that there is a significant drift between receiver measurements due to temperature changes in the receivers, which is common to all trackers and appears as a time bias drift. This is demonstrated by comparing the satellite PRN-6 differences (Figure 4) with those of satellite PRN-8 (Figure 5). Figure 6 presents the differences between Figures 4 and 5. Note the small values of these differences. The Doppler phase measurement accuracies due to receiver error only, with the drifts removed, are given in Table 1. 1 1 1 1 1 1 1 1 1 1 1 >>> 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 J 1 1 1 1 idbo edoo adbo Mobo gooo edoo todo RELRTIVE TIME (S) data .014 M 10 CM 10 CH RELRTIVE TIME tS) data .014 M Figure 4. Single Interreceiver Phase Difference (UT03-UT05) for Satellite PRN-6 Figure 5. Interreceiver Phase Difference (UT03-UT03) for Satellite PRN-8 248 I I I III I I III I I III 1 ' ' M ' I U i ' I i M rTT" lObO 8000 3CkX) wbo 6000 6000 Tubo RELRTIVE TIME (S) -f, 1 CH dota .002 M Figure 6. Difference Between Figures 4 and 5 The phase values in Table 1 are the measurement noise levels of the receiver. They specifically exclude the slowly varying temperature effect discussed above. This effect appears to be re- peatable within each receiver and to be modelable as a function of the measured internal temper- ature. The values of Table 1 also exclude propagation and clock errors. Twice the values given are the values to be expected in double-differenced data (i.e., phase measurements differenced between receivers and differenced again between satellites). RELATIVE POSITIONING The phase observations discussed above were used to obtain the baseline vector between the two antenna sites. Three baseline vectors are obtained from the three receivers illustrated in Figure 1: UT03-UT05, UT03-UT06, and UT05-UT06. Naturally, the last combination should result in a baseline with components that are zero, while the first two should be identical and agree with the given vector. Two frequency phase observations allow the ionospheric correction to be made. In this case, because the antennas are close together, this correction is not necessary. However, it is interest- ing to compare the noise of the corrected observations (LO) to the uncorrected (LI) phases. Both solutions appear in the tables. The receivers are time tag synchronized at the beginning of the observation period. It is important that the phase measurements be recorded at common times so that certain differencing techniques, which form phase differences between receivers, can be employed. In order to check that this occurred as planned, the pseudoranges and the broadcast ephemeris were used to compute the local receiver time biases with respect to GPS (Hermann 1981). The above receivers achieved synchronization to within 100 ns of each other. 249 There are four parameters that may be differenced to eliminate from the phase data error sources that originate in the instrument, the satelUtes, or the propagation path: time, frequency, satellite, and receiver. In general, it can be said that • Differencing phases in time eliminates the unknown phase (or range) bias. • Differencing in frequency (L1-L2) eliminates the propagation perturbation due to the ionosphere. • Differencing between satellites eliminates common receiver phase biases. • Differencing between receivers ehminates satellite phase biases and some ephemeris error. • Differencing a second time between any of the first differences ehminates a second parameter. In principal, one can difference four times and obtain observations free of all first-order effects (Remondi May 1984). Three different relative positioning procedures were appUed to the 16 July data set and are discussed below. Case A. Differencing in Time and Between Receivers Before describing this technique, the role of the pseudorange data in recovering the true local receiver time offset should be noted. The derived offsets are used to correct the local time tags. Even though the receivers may not have been synchronized perfectly in the field, this correction allows all data to be presented in a uniform time system. This computation is accomplished when the relevant data are transferred from the Standard Exchange Format (Scott 1983) to local data files. Segments of continuous phase data, nominally 12 min in length and sampled at 6-s intervals, are fit by a polynomial of fourth degree. The resulting polynomial is evaluated twice: 180 s after the beginning of the segment and 180 s before the end. Estimates of the data quality are obtained by computing the RMS of the residuals of fit. These are used as the weights for each segment in the batch least squares fit that follows. The phases from the polynomial are differenced over the included time span of 6 min and form the first phase difference. The second difference is formed by subtracting the phase difference of the identical interval obtained at the second site. The polynomial fit makes this method independent of the actual GPS time tag of the observations. The results in Table 2 were obtained from a batch least squares solution employing four independent nonconsecutive 12-min segments over an 84-min interval. Several 12-min segments were not used because one or more receivers failed to keep continuous phase track throughout the entire period of observations. The column headed "L" indicates whether the data are LI only (1) or ionospherically corrected LI (0). The column headed "PTS" indicates the number of 6-s observations used in the solution. The coordinates are presented as East, North, Height, and the baseUne length. 250 Table 2. Time and Receiver Differenced Solution Errors Solution Errors (m) for Coordinates RMS Receivers L 1 PTS 480 E -0.002 Ov E 0.001 067 H 0.004 a„ B 0005 0.228 Residual UT05-UT06 0.230 0.068 0002 UT03-UT05 1 480 -0.031 0.199 0.006 0.060 -0.015 0.060 -0.026 209 00045 UT03-UT06 1 480 -0.033 0.218 -0.013 0.071 -0.050 0.072 -0.033 0.230 0046 UT05-UT06 480 -0.024 0.024 -0.003 0.079 0.008 0.077 0.025 0.258 0.0008 Ur03-UT05 480 -0.183 0.248 -0.005 0.077 0.009 0077 -0.177 0.261 00157 UT03-UT06 480 -0.167 0.264 -0.012 0.086 -0.034 0.087 -0.163 0.279 0.0159 A general statement that can be deduced from Table 2 is that LI solutions are closer to the true baseline length than the LO solutions. The reason for this is clear from the RMS on the residuals of the fits. In the case where receivers do not share antennas, the RMS of the LO residuals is 3.5 times the LI value. In the case where receivers do share antennas (and have a common preamplifier), the factor is about four. The factor of three between LO and LI is about what one would expect if the LI and L2 phase measurements are independent and have about equal noise components. In practice, since L2 phase noise is a little larger than LI, the factor should be slightly larger than three. The corrected LI phase measurement noise equation is given below where aj and 02 are the standard deviations of the independent noises, expressed in length units: aj = 6.48 a] + 2.39 a] (1) It was expected that the ratio of 02'- Oi should be about 1.35 (Texas Instruments 1982). If this factor is used in Equation (1), then a = 3.29 a, (2) 01 Note that Table 1 empirically gives the 02'- 02 ratio as 1.25—1.50. For either LO or LI, the ratio of the RMS residuals between solutions of unshared antennas to shared antennas is nearly a factor of 20. This may be explained if the preamplifiers are the major noise source in this experiment. The loss of 3 dB of signal due to the spUtting of the cable to the two receivers may be causing some deterioration in the performance. If the re- ceivers share preamplifiers, the preamplifier noise will be correlated and disappear in the second differencing. When antennas are not shared. The preamplifier noise is independent and appears in the residuals. 251 Case B. Differencing in Time and Between Receivers and Between Satellites This procedure eliminates the receiver drift problem, since the drift is common to all satellite trackers in the same receivers. There are only three positional parameters that need to be determined. The LI only measurements were taken every 6 s and were differenced in time over an 18-s interval. The results of this procedure are given in Table 3. Table 3. Time, Receiver, and Satellite (Triple) Differenced Solution Errors Solution Errors (m) for Coordinates Receivers L PTS E o^ N Oj^ H a^^ UT05-UT06 1 955 -0.006 0.004 -0.002 0.023 -0.005 0.005 0.008 UT03-UT05 1 939 0.022 0.004 0.009 0.023 0.004 0.052 0.024 UT02-UT06 1 974 0.023 0.004 0.009 0.023 0.003 0.052 0.025 Receivers UT05 and UT06, which were connected to the same antenna, produced consistent relative positioning results with receiver UT03. Both produced baseline estimation error of about 0.025 m. The differencing of one satellite's data and partials with a second satellite's results in a significant improvement in the estimation accuracy. The standard deviations of the position estimates given in Tables 3 and 4 are based on a single tracker measurement error of 2 mm. Table 4. Receiver and Satellite Differenced Solution Errors Using Coherent Phase Measurements Solution Errors (m) for Coordinates Receivers L PTS E a^- N o^ H Ou B UT05-UT06 1 485 0.000 0.000 0.000 0.000 0.000 0.000 0.000 UT03-UT06 1 485 0.000 0.000 0.012 0.000 0.005 0.000 0.003 UT03-UT05 1 485 0.000 0.000 0.012 0.000 0.006 0.000 0.003 252 Case C. Differencing Between Receivers and Between Satellites Using Coherent Phase Data This procedure requires an initialization in order to determine the integer number of wave- lengths in the range differenced residuals. Here, the above triple range differencing procedure can be used as an initial estimate of position. The position is used to determine the residuals in range for differences between receivers and satellites, but not time. Since the correction partials do not change very much with time, the triple differenced partials are very small and sensitive to measurement noise. Determining the number of wavelengths in the residuals eliminates the need to difference in time. However, this may be difficult to do if the receivers are on different clocks and separated by large baselines. Although, for the given tests, the triple differ- enced position solutions were accurate enough to determine the residuals integer number of wavelengths, actual position values were used. The integer number of wavelengths was subtracted from the residuals and the relative positions were reestimated. The resulting solution errors are given in Table 4. Even with about half the amount of data as the triple difference pro- cedure, there is an improvement in the baseline accuracy to about 0.003 m. Due to an in- accurate antenna mount, this is within the accuracy of the measured antenna positions. CONCLUSION The fundamental noise levels in the phase and pseudorange measurement of the TI 4100 Geodetic receiver have been established. It has been found that the pseudorange noise con- tribution by the receiver is well below the noise inherent in the broadcast signal. The phase noise introduced by the receiver, exclusive of the frequency standard and systematic temper- ature effects, is very small and lies between 1 and 3 mm. It has been demonstrated that the receiver has a time-variable phase drift that appears to be correlated with its internal temperature. This variation is common to each tracker. The effect appears to be repeatable within a particular receiver as a function of measured internal temper- ature and to be modelable by a fixed third-order polynomial. The unmodeled drift settles to less than 2 cm/hr after 3 to 5 hr from turn-on. For relative positioning, this drift can be eliminated by differencing one satellite's data from another's. This explains why one of the double-difference methods examined in this paper does not perform as well as the other two. The time and receiver double difference (Case A) does not difference satellites (trackers) and, consequently, does not remove this drift component. The ability to remove the drift of the receiver by differencing is a significant advantage of the multiplexing receiver. Case C, the coherent phase method, which differences receivers and satellites, is very successful at determining the relative position on this short 25-m baseUne. The observing time of 48 min and 3 mm accuracy indicate that this method holds the most promise for the TI 4100 Geodetic Receiver. 253 REFERENCES 1. Duke, C. W., Jr. and Sims, M. L., 8 August 1984: 77 4100 VLSI Results, Letter to C. C. Goad, NOAA. 2. Griffin, C. R., 23 July 1984: Very Long Baseline Interferometry (VLSI) Field Test of the GPS Geodetic Receiver (GEOSTAR), ARL/UT TR-84-22, Austin, Texas. 3. Hermann, B. R., August 1981: Time Correction of Data From the NAVSTAR Geodetic Receiver System, NSWC TR 81-174, Dahlgren, Virginia. 4. Remondi, B. W., May 1984: Using the Global Positioning System (GPS) Phase Observable for Relative Geodesy: Modeling, Processing, and Results, Ph. D. Dissertation, The University of Texas, Austin, Texas. 5. Remondi, B. W., 8 August 1984: Evaluation of TI 4100 GPS Receivers — Preliminary Report, Letter to C. C. Goad, NOAA. 6. Sims, M. L., February 1982: "GPS Geodetic Receiver System," Proceedings of the Third Geodetic Symposium of Satellite Doppler Positioning, Las Cruces, New Mexico. 7. Scott, D. V. and Peters, J. G., 10 March 1983: A Standardized Exchange Format for NAVSTAR GPS Geodetic Data, Applied Research Laboratory, The University of Texas, Austin, Texas. 8. Texas Instruments, Inc., 23 December 1982: Design Analysis Report 111 for the Tl 4100 GEOSTAR Receiver, Lewisville, Texas. 9. Ward, P. W., February 1982: "An Advanced NAVSTAR GPS Geodetic Receiver," Proceed- ings of the Third Geodetic Symposium on Satellite Doppler Positioning, Las Cruces, New Mexico. 254 THREE-DIMENSIONAL GEODETIC CONTROL BY INTERFEROMETRY WITH GPS: PROCESSING OF GPS PHASE OBSERVABLES Y. Bock, R.I. Abbot, C.C. Counselman III, R.W. King Dept. Of Earth Atmospheric and Planetary Sciences Massachusetts Institute of Technology Cambridge, MA 02139 S.A. Gourevitch Steinbrecher Corporation 185 New Boston St. Woburn, MA 01801 ABSTRACT. Interf erometry with the NAVSTAR Global Positioning System (GPS) is the most efficient method of establishing three-dimensional geodetic control on local and regional scales. This is already true, even though the constellation of satellites is incomplete. We consider some theoretical and practical aspects of using differenced carriei — phase observations of the GPS satellites to establish three-dimensional control networks. We present simple and efficient algorithms for processing multi-station, multi-satellite observations. These algorithms have been used to establish three-dimensional control networks. Under widely varying conditions, we have obtained accuracies of 1 to 1.5 parts per million (ppm) in all three coordinates, or 1 to 3 cm for the coordinate differences between network stations separated by 10 to 20 km. When i ntef erometry is used also to determine the satellite orbits, we anticipate improvement of the accuracy of regional control networks to the level of 0.1 ppm. 255 INTRODUCTION GPS interferometry is a method by which three-dimensional relative-position vectors between observing stations can be estimated with respect to a world-wide, crust-fixed coordinate system. The processing of GPS observations and the accuracies obtained under widely varying conditions, not only for relative- positioning but also for single-point positioning and for GPS satellite orbit determination, have been described by Counselman et al. (1983), Bock et al. (1984), King et al. (1984), Bock et al. (1985), Abbot et al. (these proceedings), and Ladd et al. (these proceedings). We assume in this paper that the basic observable is a precise measurement of the difference beween the phase of the reconstructed carrier wave of the signal received from a GPS satellite, and the phase of a reference signal generated within the receiver at one site, at a series of epochs determined by the clock in the receiver. Me call this observable a one-way phase. (Such an observation can be made for the LI and/or L2 frequency band.) In practice, for a particular observing session, a number of receivers simultaneously observe several satellites over a time span ranging from several minutes to several hours. The simultaneity of observations is crucial since many sources of error tend to affect different observations equally at a given time, particularly instabilities in the receivers' and the satellites' oscillators, and errors in models of the satellite orbits and the propagation media. Differencing of the simultaneous observations at different stations cancels common-mode errors. Satellite- oscillator errors are virtually eliminated, and the residual errors of both atmospheric and orbital origin are approximately proportional to the distance between the stations, up to several tens of kilometers. Me call the resulting observables single-differences . Differencing again, between satellites that were observed simultaneously, results in an observable that is also free of receiver oscillator instability. The ability to observe several satellites simultaneously, and therefore to form doub le-diff erences , is what makes GPS so powerful for relative-position determination. This fact should not be forgotten in discussions of so-called "undifferenced" processing methods. In this paper, we consider some theoretical and practical problems in the use of multi-station, doubly-differenced phase, observations to establish three- dimensional geodetic control. Me present our solutions to these problems in the form of simple and efficient algorithms. A companion paper describes the application of these ideas to GPS satellite orbit determination (Abbot, et al., these proceedings). DATA PROCESSING ALGORITHMS Consider a typical GPS observing session in which M stations observe up to N satellites simultaneously. Satellites rise and set throughout the observation span. In addition, temporary obstructions of the satellite signals at one or more of the tracking sites may cause the number of one-way phase observations to differ from site to site. 256 Let us assume for a moment that there are no losses of data so that matching sets of observations are collected at the sites. From the one-way phases, at each epoch one can form M(M-l)/2 single-differences, but only M-1 are independent. The single-differences will sum to zero around any loop of stations, regardless of the nature of the observation errors; i.e., the closure is trivial. If each baseline were estimated independently, the baseline vectors would sum to zero around each closed figure. Differencing the one-way phases between stations introduces 50% correlations between the single-differences at an epoch, in the simple case of equal-variance uncorrelated errors at the individual sites. If these correlations are accounted for, any choice of M-1 single differences will yield identical baseline estimates. Mith this point in mind, consider the typical observing session where the observation sets differ from site to site. The following two-step algorithm will extract all the information from the raw observables and at the same time will take into account the correlations that appear as a result of differencing the one-way phases. The basic (linearized) observation equations for one-way phases can be expressed in familar matrix form by = AX+V+V (1) where (pis the observation vector containing the differences beween the observed phases and their a priori computed values, A is the design matrix containing the partial derivatives of the phases with respect to the parameters of interest, X is the parameter correction vector, V is the vector of the non-common-mode observation errors, and V is the vector of the common-mode observation errors. For the estimation model, we assume for the (normalized) non-common-mode observation errors that E{V} = E{VV'} = I <2> (3> where E denotes expectation and I is the identity matrix. The common-mode observation errors cancel in the subsequent differencing and can be neglected. The assumption, therefore, is that the non-common-mode errors of the one-way phases are statistically independent in space and time, with equal (and normalized) errors. The parameters of interest for three-dimensional control applications are discussed in the next section. Let us denote the one-way phase for station m and satellite n by(T)(m,n). At each epoch, M-1 uncorrelated and normalized single-differences can be computed for each of the N satellites by Dl(i,n) = M-1 0(i+l,n) > 0(m,n; m=l 257 1/2 (4) using a Gram-Schmidt orthogonal ization scheme. The index i in 01(i,n) denotes the single-difference series number. On the right-hand side of (4>, i points to the station number and is also used to compute the normalization factor. For example, for 4 stations observing simultaneously the signals from satellite 1, l\l/2 D1<1,1> = C-Cr)(l,l>J| — (5) <1,1> = C0<2,l>-(^(l,l>j{— j Dl(2,l> = C^<3,1)-— <(^< 1,1 >+<^<2,l )>]( — ) (6) 01(3,1) = C0(4,l) <^(l,l)+0<2,l)+0(3,l))3f--j . (7> It can be easily verified that under the assumptions (2-3), the observation errors of this set of single-differences are uncorrelated (and normalized). Suppose^ that at some epoch the view of station 1 to satellite 1 was obstructed so that(7)(l,l) was unavailable. Then only M-2=2 uncorrelated single-differences could be formed for satellite 1 from the one-way phases collected at the three remaining sites by 01(1,1) = CC/)(3,l)-C6(2,l)j(— I <8) (1,1) = C0(3,l)-(j6(2,l)j(— I (2,1) = C(^(4,l) (^(2,l)+(^(3,l))j(— -) 01(2,1) = C This simple scheme ensures that all one-way phase observations are used, except in the case when only one site is observing at an epoch. However, the one-way phases contain information on the absolute positions of the observing sites, as well. Therefore, if we include at each epoch the common-mode observable for each satellite <^(n)=— > (^(m,n M / I M ^ , (10) m=l 258 then the coordinates of each observing station can be estimated with respect to a global terrestrial reference frame. Of course, the relative positions of the sites will be more accurately estimated than the absolute positions (see Bock et al., 1984>. Note that the common-mode observable is orthogonal to the single- differences. For receivers with crystal oscillators, a between-satel I i tes observable (see below) is more valuable for point-positioning since any instabilites in the receivers' oscillators are eliminated. The one-way phase common-mode observable is valuable for more accurate frequency standards (e.g., cesium-beam) . For the most accurate baseline determination, a second difference is taken, between satellites. The above orthonormal ization scheme can be applied again. The double-differences are denoted by 02(i,J) where the index j denotes the double- difference series number. Me form for each series i (see (4)) of single-differences D2(i,j) = Dl(i,j+1) N-I -fl Dl(i,n) n=l (11) Thus, for M stations observing N satellites, there are (M-1)(N-1) orthonormal i zed double-differences that can be formed per epoch. This scheme is applied to all visible satellites, so that risings and settings of satellites are handled naturally (as obstructions are handled in the first orthonormal ization described above). Note that the order of orthonormal i zation could be reversed. That is, the satellite orthonormal ization could precede the station orthonormal ization. The latter order may be preferred for point-positioning with satellite-differenced observations. PARAMETER ESTIMATION The mathematical model relating the one-way phases to the geodetic parameters can be found elsewhere (e.g., Fell, 1980; Remondi, 1984). Here we point out that the partial derivatives used in a weighted least-squares fit of the orthonormal ized double-differences are manipulated in the same way as the observables in (4) and (11) (i.e., they are also orthonormal i zed as the normal equations are being filled). In three-dimensional network applications, for M stations observing a total of N satellites, we adjust as a minimum 3(M-1) station coordinates (3M if we are also point-positioning using one-way or satellite-differenced phases) and (M-1)(N-1) phase-bias parameters. The phase-bias parameters represent the ambiguities of the one-way phase observables. If the receiver clocks were not synchronized and we do not know the departure from synchronization a priori (e.g., from field measurements), then we solve for M-1 clock offset parameters as well. Rate and higher order clock terms cannot be determined well from the double-differences. They are better determined from the single-differences. 259 Theoretically, each of the double-difference phase-bias parameters has an integer value. in order to correct the one-way phases for cycle-slips (since the noise level is sufficiently low to detect the cycle-slips only in double-differences) and (2) in order to fix the phase-biases at their best-fitting values (since the biases are integers only after double-differencing). For an application of the approach outlined in this paper, see the paper by Bock et al. (1985), in which the analysis of a 35-station three-dimensional geodetic network is described. The results of that analysis indicate that three- dimensional geodetic control can be routinely obtained at the 1-2 ppm level under widely varying conditions. When interferometry is used also to determine the satellite orbits, we anticipate improvement of the accuracy of regional geodetic control to the level of 0.1 ppm. ACKNOWLEDGEMENT Research at N.I.T. has been supported by the U.S. Air Force Geophysics Laboratory (AF6L), Geodesy and Gravity Branch, under contract F19628-82-K-0002. 261 REFERENCES Abbot, R.I., Y. Bock, C.C. Counselman, R.M. King, S.A. Gourevitch and B. Rosen, 1985: Interf erometr ic Determinations of GPS Satellite Orbits, these proceedings. Bock, Y., R.I. Abbot, C.C. Counselman, S.A. Gourevitch, R.kl. King and A.R. Paradis, 1984: Geodetic Accuracy of the Macrometer Model V-1000, Bulletin Geodesique 58, 211-221. Bock, Y., R.I. Abbot, C.C. Counselman, S.A. Gourevitch and R.W. King, 1985: Establishment of Three-Dimensional Geodetic Control by Interf erometry with the Global Positioning System, Journal of Geophysical Research (Solid Earth) , in press. Counselman, C.C, R.I. Abbot, S.A. Gourevitch, R.M. King and A.R. Paradis, 1983: Centimeter-level Relative Positioning with GPS, Journal of Surveying Engineering . 109 . 81-89. Fell, P.J., 1980: Geodetic Positioning Using a Global System of Satellites, Dept. of Geodetic Science and Surveying Rep. 299, The Ohio State University, Columbus, Ohio. Gourevitch, S.A., 1984: The GPS Interf erometr ic Observable, M.I.T. internal memorandum. King, R.M., R.I. Abbot, C.C. Counsleman, S.A. Gourevitch, 6. J. Rosen and Y. Bock, 1984: Interf erometric Determination of GPS Satellite Orbits, EOS, Trans. AGU . 65 , 853. Ladd, J., C.C. Counselman and S.A. Gourevitch, 1985: The Macrometer II Dual-Band Interferometric Surveyor, these proceedings. Remondi, B.M., 1984: Using the Global Positioning System (GPS) Phase Observable for Relative Geodesy: Modeling, Processing, and Results, Report CSR-84-2, Center for Space Research, Univ. of Texas, Austin. Strange, W.E., 1984: The Accuracy of Global Positioning System for Strain Monitoring, EOS, Trans. AGU, 65, 854. 262 INTEGRATED MODELLING OF GPS-ORBITS AND MULTI-BASELINE COMPONENTS Giinter W. Hein and Bernd Eissfeller Institute of Astronomical and Physical Geodesy (lAPG) University FAF Munich Werner-Heisenberg-Weg 39 D-8014 Neubiberg, F.R. Germany ABSTRACT. The paper summarizes the main lines along the soft- ware developments at lAPG for the integrated determination of GPS orbits and multi-baseline components go. The simplified orbit model considers four disturbing accelerations: due to the earth's gravity field, due to solar radiation pressure, the attraction of sun and moon, and remaining accelerations due to unmodelled residual effects. The approach allows the combination of carrier phase observations in non-difference as well as all other differential modes and leads to an autono- mous solution independent of any orbit information. 1. INTRODUCTION The first results of differential carrier phase observations to the satellites of the Global Positioning System lead to the guess that relative geodesy will change their traditional positioning techniques and observation strategies drastically in the near future in favour of GPS measurements. This in spite of the fact, that GPS is not yet completely built up, and software developments are in just a starting stage. The software established up to now is dealing mainly with the determination of a single baseline using the phase observables in a single-, double- or triple-differ- ence mode (see e.g. Langley et al 1984, Remondi 1984). Atmospherical parameters for the tropospheric and ionospheric transmission delay of the signals are not in- cluded in the adjustments. The orbital precision requirements suggest that the given orbit data are not sufficient to derive high-precision results. On the other hand civilian user might strive the independence of any required orbital informa- tion. Methods for estimating such orbital biases have been already exploited in the processing of TRANSIT doppler data. However, those techniques are working in a purely geometrical manner shifting and rotating the orbit. Due to the high alti- tude of the GPS satellites it is more appropriate (and simple) to model or improve the orbit in a physical way. An example is the GPS orbit program presented by Beutler et al 1984. Our own software currently under development goes one step further. Following the philosophy of an integrated data processing and our own experiences in that field, called "integrated geodesy" (for the consideration of satellite geodesy in that context see Eissfeller and Hein 1984, Hein and Eissfeller 1985), we are in favour of an integrated determination of GPS-orbits and multi-baseline components which leads to an autonomous approach independent of any orbit information. This paper summarizes the main lines of theoretical background used in the pro- gramming. After reviewing the basic GPS observables and nonlinear observation equations the orbit model is discussed. Chapter 4 and 5 show the linearization and the adjustment procedure. Due to the limited space in these proceedings the reader 263 who is interested in details is referred to a forthcoming report of Hein and Eiss- feller 1985. Our own experiences with the adjustment of MACROMETER data in the German base triangulation net are summarized in (Landau 1985). 2. BASIC GPS OBSERVABLES AND OBSERVATION EQUATIONS Basic observable in a GPS receiver R^- is the instantaneous phase difference Ti(tR.) at time tp. , where <(>$.( ts.) is the transmitted phase signal of satellite Sj at time t^. , J J J and (^^. is the receiver reference phase, *R.(^R.) = 2^ ^R. ^R. . (2-3) V is the frequency of the signal, v = c/x . c is the wave velocity and x the wavelength. By p^-,- we denote the length of the wave path (range) between satel- lite j and receiver R^- (range). Ata^,- is the time delay of the wave propaga- tion due to atmospheric effects, m is an integer variable. Inserting (2-2) and (2-3) in (2-1), and replacing tR. by tR. = t + e.(t) (2-4) where ei(t) is a clock-error of the receiver, and approximating p-jj by Pij(\) = Pij(t)+P,.j(t).,(t) (2-5) we get the basic phase comparison ^.{t) = 2irm+|l[p.j(t) +Jij.(t) e.(t)] - 2Tr (V3+V.) [t + e.(t)] + 27r V3 Ata.j(t) (2-6) In order to derive relative geometric information (baseline vectors) from phase ob- servations of two receivers Ri , R2 to one identical satellite S,- we subtract the corresponding equations (2-6) and obtain the observation equation of the so- called single-difference method ^^^{t) = H;2(t) - H;i(t) (2-7a) 264 I^sd(^) = 2Tr (ni2-mi) +1^ [P2j(t)-Pij(t)] + 2tt (vi -V2) t + 2tt v<;[Ata .(t) -Ata .(t)] (2-7b) where the clock-error term ^ (t) is of the form ^e(t) = f^ [P2j(t) e2(t)-Pij(t) Ei(t)] + 27T V3[ei(t) -e2(t)] + 2iT [v^ ei(t) - v^ £2(^)1 • (2-7c) The double-difference method was introduced in order to compensate for receiver- dependent errors (e.g. clock-errors). The so-called double-difference observable is derived from two single differences (2-7) at epoch t using two different GPS satellites Sy. = (P,Q) "^d^^) = '^sd,Q(^) " '^sd,P where m. + 27T Vq [Ata2Q(t) -Ata^Q(t)] - 2tt vp [Ata^p(t) -Ata^p(t)] = m^p - mip+ m^p - m^p 2tt ^^Jt) = y^[P2Q(t) e2(t)-PiQ(t) e^(t)] + 2Tr (VQ-Vp) [e^{t) - e^{t)] (2-8a) (2-8b) (2-8c) (2-8d) If we assume that the transmitted signals of the two GPS satellites P,Q have (nearly) identical wavelength. 265 Xp = Xp = Xg (2-9) Vp = Vp = V3 then (2-8b,d) simplifies to ^If tp2Q(t)-P2p(t)^Plp(t)-PlQ(t)] + 2tt V3 [Ata2p(t)-Ata2p(t)+Atajp(t)-Ata^p(t)] + ^^Jt) (2-lOa) where the clock-error term i|; ^{t) drops nearly out, + [Pip(t)-p^p(t)] z,{t)} . (2-lOb) The triple-difference observable 4J t(ti,t2) is defined as the difference of two double differences (2-lOa) each belonging to a different epoch ti, t2 where the two satellites P,Q were observed. 1't(ti.t2) = ^l>^{t2) - n^^Cti) (2-lla) 'i'|.(ti,t2) = 27T (m^^ -m^^) 2tt + — [p2Q(t2) -P2q(^i) +P2p(^l) ■P2p(^2) + Pip(t2) -Pip(ti) +PiQ(ti) -p^Q(t2) + 27r V3 Ata2Q(t2) -Ata2Q(ti) +Ata2p(ti) -Ata2p(t2) + Ata^p(t2) -Ata^p(ti) +Ata^Q(ti) - Ata^Q(t2)] + 'J^e^t^^i'^^) (2-llb) where the clock-error term \i) ^.(ti,t2) has the form 'I^£.^t(tl,t2) = Y^ {[p2Q(t2) -P2p(t2)] E2(t2) + [Pip(t2) -PiQ(t2)] ei(t2) - [P2Q(^1)-P2P(^1)^ ^2(^1) - [Plp(ti)-PiQ(ti)] e^(ti)} (2-llc) 266 Referring to an inertia! system the range p and its time derivative p is given by PSR(t) = {[Xs(^)-XR(t)]^ [Xs(*)-2iR(t)l>°'' (2-12) 'SR (t) = [X3(t)-x^(t)]"^ [X3(t)-x^(t)]/p(t) (2-13) where x$ = [Xi,X2,X3]^ is the orbit of the satellite and xs its derivative with respect to time. The position of the receiver xr in the inertial system (in- stantaneous astronomical system at epoch to ) is related to its corresponding vec- tor yR = [yi,y2»y3]^ in the earth-fixed reference frame (ClO-system) by the transformation matrix R(t) . Thus, XR(t) = R(t) yp (2-14) where R(t) = N(to) P(to) P'^(t) N^(t) R3(-0(t)) S(t) . (2-15) The matrices in (2-15) are H,P^ due to nutation and precession, ^3 is the rotation matrix describing the rotation around the e3-axis (unit vector in the direction of the CIO), S(t) due to polar motion. e is the siderial time of Greenwich, and to is the initial epoch of the orbit integration. 3. ORBIT MODEL In order to get the final observation equations we have to determine the orbit _xs of the satellite in (2-12) and (2-13). Although the GPS satellites are in an altitude of more than 20 000 km, we can not assume, that their orbit is a perfect Kepler ellipse. Moreover, in this approach we will assume that the orbit is un- known and be determined simultaneously together with the multi -baseline components Ay . Thus, we include a simplified orbit integration considering only the relevant disturbing accelerations. These are: fi ... gravity acceleration of the earth's gravity field, £2 . . . acceleration due to solar radiation pressure, (3-1) £3 ... attraction of sun and moon, and J[^ ... remaining acceleration due to unmodelled effects (see e.g. Popinski 1984) . We are assuming further that air drag effects can be neglected. Due to the high altitude of the satellites £1 will be smooth, so that simple earth models can be considered. The basic vector differential equation of satellite motion (in rectangular coor- dinates) with respect to an inertial system is given by 267 a_ = 90+1 where lo - . GM 4 ^ = h li - i^i '^ ■' see (3-1) is " aCxg.x^.t) (3-2) where x^S ''S the acceleration vector, x^ the position vector and xs the veloc- ity vector of the satellite. After decomposing ai into the dominant acceleration £o (the radial symmetrical part of the earth's gravity field) and in a disturbing vector £ , (3-3) (3-4) (3-5) the solution of (3-2) with respect to gp leads to the Kepler ellipse described by the vector ui of six integration constants. Thus, X5 = X5(u,t) (3-6a) h " As(^,t) . (3-6b) Applying the method of variation of constants the entire problem (3-2) is solved by the expression t u(p,t) = Uo(to) + / Y(u(p,t),t) f(u(p,t),p,t) dt (3-7) to where 3u Y = — (see e.g. Eissfeller 1985; Eissfeller and Hein 1985). (3-8) ax iio(to) is the initial state vector at time t = to . The integral in (3-7) can be computed numerically. Inserting the results of (3-7) in (3-6) determines the posi- tion and the velocity vector xs» As °^ ^^^ satellite. For the necessary linearization procedure we decompose the dynamical parameters 2 (initial values of the Kepler elements, pole coordinates, siderial time, speri- cal harmonics of the earth's gravity potential, solar radiation pressure coeffi- cients, etc.) into p = pO + 6p (3-9) and find for the variation 6u of the Kepler elements 9u(p0,t) 6u(p0,t) = ^ 6£ . (3-10) It can be deduced from (3-7), that the Jacoby matrix 8£/3£ is a solution of the inhomogeneous matrix differential equation 268 3U 3Y 8Y f , 3f ^U 3f + Y + Y — - 3U 32 - 3p which in integral forms reads 3Y "3? (3-lla) 3u -3^ 3JJ0 t 3Y 3Y L -' 3f 3U 3Ui - 3U9 - f , . 3Y -^ f 3Uf; - 3£ dt + /Y dt+/Y tn ~ ^ii 9P tn - 3f dt (3-llb) Since 3]£/32 is on both sides of eq. (3-llb) the solution can be found only in an iterative (numerical) way using as starting value (3u/3£)o : = 3£o/3£ • Thus, the linear variation of the satellite position is given tlTen by 3X3(t) ^^s(t) = iU(^ ^i(t) 3X^(t) 3£(t) 3£(t) 3p and the variation of the receiver position by 6p (3-12) 6Xj^(t) = 3Xp(t) 5p + R(t) ^y^ (3-13) The Jacobi matrix 3XR(t)/3p consists only of the partial derivatives of the rota- tion matrix ^(t) with respect to earth rotation parameters in £ , all other par- tial derivatives are zero. Explicit forms of all partial derivatives can be found in Eissfeller and Hein (1985). For the final observation equations we still need to linearize the range (2-12). It yields ^P(t) = MtL6X3(t).Mfi^6x,(t) 3Xs(t) (3-14a) where 3p(t) ^ [Xs(t) - XR(t)] 3Xs(t) 3p(t) 3XR(t) P(t) = - 9p(t) 3XS (3-14b) (3-14c) Inserting (3-12) and (3-13) in (3-14a) considering (3-14b,c) we get the final ex- pression for 6p(t) 269 ^^<^' = SS) 3X5{t) 3u(t) 9XR(t) 3u(t) 8p 3p .MlLR(t) ^P-|^R(t)6y, (3-15) In a similar way the parameters a_ of the propagation-time delay Ata = Ata(a_,t) have to be linearized. 4. LINEAR OBSERVATION EQUATIONS FOR PHASE MEASUREMENTS For the basic phase comparison (2-6) we apply the following decomposition ^i(t) = ij^.(t) + &i,.{t) (4-la) TO where the approximate value i)^ is given by TO r^{t) = ztt m J. 2tt /. X -27T (vo+v.) t + 2^ v^Ata.(t) (4-lb) The upper index "°" denotes approximate values. Note in (4-2) and following deri- vations that the clock-error term is already of first order. For 6iJ;^(t) we get 2Tr 6il>.{t) = 2tt 6m + ^ 6p^-s(t) , 9Ata . cT\ Vc 6a • S da^ -1 2tt '0 o / J. ^ — p. 3 - 2. (V3 + V.) ■^it) (4-lc) Inserting 6p (3-15) in (4-lc) yields the final observation equation for phase measurements 6ii^.(t) = 2tt 6m + 2Tr ^Pis(^) Xs 6x5(t) 27T "^PiS^^^ — , , R(t) 6y. Xs 6X5 t -' ^1 3X3 (t) 3U^(t) 3X^. 3u(t) 3p 3p 6p ^ ^ 3Ata .^ + c-n Vc 6a. 9ai ~^ 2iT '0 — P.3-27T (V3+V.) ..(t) (4-ld) In the same manner one obtains the corresponding linear observation equations for single-differences (2-7), double- (2-8) and triple differences (2-10). In order to save space we write only the first down: 270 6^Sd(^) where lo 6e 2tt 6m + — '8p23(t) 3p^3(t) dX^{t) 9u(t) 3Xs(t) 3X5(t) 3u^(t) 3p 9p^3(t) 9Xi(t) 9P2s(t) 3X2(t) 3Xs(t) 3p 3pis(t) .21 + 2tt V 3Xs(t) " 3Ata2(t) R(t) 6y^ 3Xs(t) 3p 8P2s(t) 3d' 632- 3Xs(t) 3Ataj(t) 3ai 6p R(t) 6y2 6ai 4. "l" . -|^Pis(t)+2 A< TT V^ + 2tT Vj^ , 2tt )2c;(t) - 2lT Vq. - 27T V2 -T (4-2a) (4-2b) [Ei(t) , e2(t)] T 5. ADJUSTMENT PROCEDURE The linearized observation equations (4-ld) or (4-2a) form a linear system of type 1 = Al£ ■*" ^2:^ "*" -3- ■*■ -h- "^ - (5-1) where J_ is the vector of phase observables, £ the vector of unknown dynamical parameters, y the vector of unknown station coordinates in an earth-fixed refer- ence frame, a^ the vector of unknown atmospherical parameters, e_ the vector of unknown clock-errors and integer number of wavelength, and n is the vector of ob- servational noise. Ai j • • • » A^^ ai^e the appropiate design matrices. A solution of an overdetermined system (5-1) can be found by applying the usual least-squares norm. T p-i min (5-2) where C^^ is the variance-covariance matrix of the measurement noise, Depending on the different applications our software developments should solve the following items by (5-1): - Integrated modelling of GPS-orbits and multi-baseline components using the original carrier phase in a non-difference mode. This most general case is planned in order to be independent of any precise orbit information, where the orbit is determined e.g. by three or four re- ceivers at permanent occupied (fixed) stations. Thereby a priori information of the coordinates of those stations as well as of the orbit - if available - should be considered so that a Bayesian-type estimator can be applied. It is obvious that the number of unknown parameters in (5-2) requires a careful 271 rank-defect analysis of the special problem to be solved. Considering that GPS observations can determine absolute coordinates not better than 10 m, the results of the adjustment (5-1) have to be interpreted in the relative sense. - If information about the orbit (e.g. in the form of the parameters of a Kepler ellipse) is available, then the approach can be applied for orbit improvement using those information as initial state vector Uo(to) in (3-7), or passing directly over to (3-lla). - The general adjustment is able to combine all carrier phase observations in non-difference as well as all other differential modes as outlined in paragraph 2. Moreover, it is able to consider also differential pseudo- range and differential integrated Doppler measurements (for the observa- tion equations see Eissfeller and Hein, 1985). - The combined determination of orbit and baseline components leads to realistic error estimates, since possible orbit uncertainties can be con- sidered in the error propagation through the adjustment. REFERENCES Beutler, G., D.A. Davidson, R.B. Langley, R. Santerre, P. Vanicek, D.I. Wells, 1984: Some theoretical and practical aspects of geodetic positioning using carrier phase difference observations of GPS satellites. Department of Surveying Engineering, University of New Brunswick, Technical Report No. 109, Frederic- ton, N.B., Canada" Eissfeller, B., G.W. Hein, 1984: The observation equations of satellite techniques in the model of integrated geodesy. Proceedings of the International Sympo- sium on Space Techniques for Geodynamics, Sopron, Hungary, July 9 to 13, 19^4 , 119-129 Eissfeller, B., G.W. Hein, 1985: A contribution to 3d-operational geodesy. Part 4: The observation equations of satellite geodesy in the model of integrated geodesy. Report of the University FAF Munich , in print Eissfeller, B., 1985: Orbit improvement using local gravity field information and least-squares prediction. Manuscripta geodaetica 10, No. 2, in print Hein, G.W., B. Eissfeller, 1985: The basic observation equations of measurements to the Global Positioning System (GPS) including orbit modelling. In: Report of the University FAF Munich , in preparation Landau, H., 1985: Dreidimensionale Punktbestimmung im Deutschen Hauptdreiecksnetz mit Hilfe von GPS-Basislinienkomponenten. Internal Report of the Institute of Astronomical and Physical Geodesy, University FAF Munich Langley, R.B., G. Beutler, D. Delikaraoglou, B. Nickerson, R. Santerre, P. Vanicek, D.E. Wells, 1984: Studies in the application of the Global Positioning Sys- tem to differential positioning. Department of Surveying Engineering, Uni- versity of New Brunswick, Technical Report No. 108, Fredericton, N.B., Canada Popinski, W., 1984: The unmodelled effects in the motion of artificial satellites. Planetary Geodesy 19, 17-26, Polish Scientific Publishers, Warsaw-Lodz Remondi, B.W., 1984: Using the Global Positioning System (GPS) phase observable for relative geodesy: Modelling, processing, and results. Dissertation, The University of Texas at Austin 272 IMPROVED SECOND ORDER DESIGN OF THE GLOBAL POSITIONING SYSTEM * - EPHEMERIDES, CLOCKS AND ATMOSPHERIC INFLUENCES - E.W. Grafarend, W. Lindlohr Department of Geodetic Science Stuttgart University Keplerstr. 11 D - 7000 Stuttgart 1 Federal Republic of Germany A. Stomma Space Research Center Polish Academy of Sciences Ul. Ordona 21 01 - 237 Warszawa Poland ABSTRACT. In order to achieve a desired positioning accuracy with the Navstar Global Positioning System certain accuracy requirements of system components have to be fulfilled. Here the accuracy requirements of type prior information for the components (i) ephemerides, (ii) clock errors and (Hi) atmospheric refrac- tivity are analyzed in the case of interferometric time delay observations. As a function of stochastic prior information for ephemerides, clock errors and atmospheric influences the variance- covariance matrix for absolute and relative point positioning is computed leading to new insights into the strengths and the weak- nesses of the Global Positioning System. The simulation model is based on an extended GauB-Markov model which is equivalent to the generalized mixed linear model, the latter originating from a linearization of the observational equations with respect to a stochastic point of prior information. INTRODUCTION The establishment of a geodetic network design has been treated by numerous authors. A classification of the various order designs is given in full detail in the textbook of E. Grafarend et. al. (1979a). The second order design (SOD) deals with the problems of assigning proper weights or variance-covariances, respectively, to the observations which have been made within the network. If we introduce some additional information of type variance-covariance, we are talking of an improved SOD, This term has been employed e.g. by J. Bihhy and H. Toutenburg (1977) and B. Schaffrin (1984). Within our paper this concept will be implemented in a satellite geodetic netii?op/c,, consisting in a particular ground station configuration and four satellites of the Navstar Global Positioning System. The way in which we handle this problem is by the introduction of prior informa- tion. In general this additional information can be implemented by a vector k of the approximate values of the unknowns and their corresponding variance-covariances (5. Schaffrin 1983). Here we are only dealing with the variance-covariance matrix of stochastic prior information, i.e. k=0. In the following section we give a short descriptionof the simulation model of interferometric time delay observations as well as the underlying mathematical model, 273 which has to be interpreted as a generalized mixed linear one. Afterwards we de- scribe the variation of the three accuracy criteria mentioned above and undertake an analysis of the simulation results obtained. Finally we give a summary of the outcome of the simulation study and conclude with some recommendations resulting from our research. THE OBSERVATIONAL MODEL From the set of possible GPS measurements let us consider interferometric time delay observations ^ which are also known as differential ranges. These single difference observations S^^ := S^ - S^ = c(T^ - T^ ) (1) a. 3 3. a. ^ 3. o..' ^ ' between terrestrial points P and Pg and satellite points P^ are assumed to be measured, c denotes the velocity of signal propagation in vacuum. Once we neglect clock errors and atmospheric disturbances for a moment, the first problem is the establishment of a network configuration. As has been shown by A. Dermanis and E. Grafarend (1981), W. Paohelski (1983) and D. Delikaraoglou (1984) a minimum of g=5 ground stations have to simultaneously observe at least h=9 satellite points once we consider both the ground station positions and the satellite positions to be unknown and we are interested in avoiding any configuration defect {e. Grafarend and E. Livieratos 1978, E. Grafarend and K. Heinz 1978). Within the second order model we take clock errors into account. A common model for the observed time T is T^ = a^° + a^'(t-t^) ^ a^2{t-t^)= (2i1) where t is the conventional GPS time and t the synchronisation time instant, which has always been chosen in the middle of the simulation interval. apQ » a (e=a, 3 throughout the paper) are the time offsets of the terrestrial receiver and the satellite transmitter, respectively, while a , a^ and a 2 » ^ ai^e the corresponding drifts and drift rates. The minimum^ configuration ^ of a satellite geodetic network whose observational model contains clock errors has been established by D. Delikaraoglou (1984). The observational model of the ionospheric and tropospheric refration are the corresponding time delays eo ^Wopi = 9 (ts-P.E.hg) * K, (3) where according to E.H. Martin (1978) f denotes a function of carrier frequencies V , v„ , satellite elevation angle E and vertical electron content N of the ionosphere and according to H.S. Hop field (1969) and D.E. Wells (1974) g and h denote functions of surface temperature t , total air pressure p , partial pressure of water vapour e , elevation angle E and the approximative orthometric height h above the geoid. b , b and b are the refractivity biases of the ionosphere and of the dry ^ and ^ wet ^ troposphere, respectively. 274 THE GENERALIZED MIXED MODEL For the linearisation of the nonlinear observational equations S^^ = S(X ,Xq,X^) we refer to stoakasHc prior information x: = (x^,Xq,x^ } =(x^,y^,z^,XQ,yQ,ZQ,x'' ,y' .z"^) ~Cx ~p~ uOlOtppp of rectangular equatorial coordinates of terrestrial and satellite points, e.g. from former terrestrial surveys or broadcasted ephemerides ("^" in conjunction with latin letter x is related to prior information). The observational equations linearized at a stochastic point of prior information can be represented by V •=As'^ =S^ -S^ ^ • ^a.3 a. 3 a. 3 /s /\ II X«-X^ II - II x,-x^ II - ( II X -X^ II - II X -xY II ) "3 C3 C ~a ~ ~a ~ \ := (Ax^,....AZgf = (X^-x^,...,Z3-Z3)^ X2 := (Ax\Ay^,Az^)^ = (X^-x^Y^-^^Z^-^)^ ^1 •" ^^aO'^ar^a2'^30'^3l'^32'^ '^ '^ ^ ^2 •= (^o»^l'^2'V'^3r''32^^ y - u = A^x^ + A^x^ ^ B^Ci + \K^ = Ax -h B^ (4) (5i) (5ii) (5iii) (5iv) (6) where ||.|| denotes the "Euclidean 3d-distance" and u is the nx1 - vector of observation errors. The linear model (6) is a generalized mixed model containing the fixed effects E, and ^ and the random effects x and y. , The "2?est Zinear uniformly unbiased estimation" (BLUUE) of Z, yields the estimate ^ = L (y - Ak) L := [b'^(E + AE.A'^)"^B]"^b'^(E + AE.A^)"^ y X y ■■ X (7) containing the variance-covariance matrix E of the observations, the given varianoe-oovariance matrix Z^ of the stochastic prior informationy here of the terrestrial station coordinatis and of the broadcasted ephemerides. Finally the given vector k of stochastic prior information turns out to be the expectation of X . The "2?est inhomogeneously Zinear prediction" (inhom BLIP) identical to the "Z)est inhomogeneously Zinear weakly unbiased prediction" (inhom BLUP, "collocation"- solution) of the stochastic unknown vector reads X = K + E.(I , + NE.)"^aV^(I - BL) (y - Ak) X ml X y n N := aV^A (8) 275 Finally the dispersion error matrix of errors of x are calculated from E, and the matrix of mean prediction D(C) = D MPE(x) = D(x - x) = E^F (9) where the matrices equations system D and F are obtained from the solution of the normal I , + NZ- ml X a'V^b y ,-] 'y bV^b ml m2 (10) , I denote unit matrices of the order of the number of unknowns x , E, of ^ the number of observations, respectively. For more details we refer to B. Sohaffrin (1985a,b). ^-^and ^-2 SIMULATION RESULTS Figure 1 illustrates a real five ground station GPS test network in the center of Europe. The approximate cartesian equatorial coordinates of the stations (St. Mande, France; Grasse, France; Zimmerwald, Switzerland; Graz, Austria; Stuttgart, Federal Republic of Germany) have been taken from the EDOC - 2 network [c. Boucher 1981). The satellite orbits from the Navstar GPS satellites no. 5, 6, 8 and 9 have been taken into account. The orbit simulation used a J - perturbed Keplerian orbit with 15 degrees as cut-off elevation angle. Their ephemerides are taken from D. Davidson et. al. (1983) for the desired point of time. In Figure 2 a polar visibility plot for the central station Zimmerwald on January 30th, 1982 is given. JO .Yl ,Y2 The oscillator errors a'"^ , a'^^ and a''' within signal emitters have been set to zero, while for all ground station receivers standard deviations of ±10"^° sec, ±10-12 and ±^.]Q-ir .-1 sec"-' Tor a , a from R. Anderle (1982) and D. Davidson et.^ al. and £2 have been chosen throughout (1983). Description and Analysis of Solution Types First of all we were looking for the best kind of solution when removing the translational and the rotational datum defect by introducing stochastic prior information in the form of constraints either at the ground stations or in the satellite orbit. The following three types of constraints have been examined (the values for the orbit orientation and the first point in each pass are given in radial, tangential and normal direction, respectively): a) - ground stations - orbit orientation b) - ground free solution - first point per pass - orbit orientation 01X3) = o{y^) = o{z^) = a =0^=0 =0.12m r t n a = 5 m, a. = 10 m, a = 5 m r t n n 276 a = o^ = a =0.12m r t n c) - ground stations : o{x^) = o{y^) = o{z^) = a(x^) = a(y^) = 0(2^) = - orbit free solution (cf. E. Grafarend et. at. 1979b). In order to be able to compare the various solution types, two quantities have always been calculated. Both Q = [trace(n"^MPE(x))]^'^^ (Hi) and the spectral condition number c„ = X . /A (11ii) n nu-n max as quotient of the minimum and maximum eigenvalue of the mean prediction error matrix of the stochastic ground coordinates were used to deliver a judgement about the network in its entirety. The square root of the mean prediction error of the variance factor has been chosen to be 1m throughout the paper. The solution a) turned out to be the best one. The differences between solutions a) and b) in relative positions and in baseline length determinations are very small, a* and a. of solution a) are 19% and 30%, respectively, better, while in a. solution b) is 7% better; in baseline length the results are in average the same. But for absolute coordinates solution b) is much worse than a), since from interferometric observations it is only possible to obtain good relative positions and baseline lengths. The estimated standard deviations of the coordinate differences in the case of solution c) are in the range of 2 to 12 m, which proves this solution to be the worst one. Therefore throughout the following only vari- ations of type a) solutions are examined. Influence of Orbit Orientation Constraints As a basic value for the orbital orientation constraints we used 0.12 m in all three components. Here orbit orientation constraints denote errors of coordinate differences for successive points of the satellite pass. In order to see the influence of the orbit orientation constraints the basic value is multiplied by a factor of 10 and by a factor of 100, respectively, in all three componentes within different solutions. The influence is graphically illustrated in Figure 2a, by where the normalized trace of the mean prediction error matrix of the ground station coordinates and the logarithm to the base 10 of its condition number depending upon the number of satellite passes is plotted. The arithmetic mean value and the range of relative errors for different orbit orientation constraints are given in Table 1. As a result we can say that in general the solution with 0.12 m and 1.2 m orbital orientation constraints are capable to meet the requirements for first order accuracy both in baseline length and relative positioning. The solution using 12 m constraints satisfies first order accuracy only really for distances. At this point we have to keep in mind that within our simulations only four GPS satellites were used instead of the six now fully operational ones; a factor which has also decreased the accuracy in positioning up to this point of our research. Influence of Length of Simulation Interval In all of the solution presented so far, the simulation interval has been for the duration of half a minute. Now we double or quadruple, respectively, the simulation 277 the va ilues given the as as IS interval, where we equivalently have to double or quadruple, respectively, of the orbital orientation constraints. The results of the simulations are a function of the number of satellite passes in Figure 4. We can note that length of the simulation interval is of rather minor, secondary influence, also verified in Table 2. Influence of Clock Error Model Until now we have used as a model for the errors of the receiver oscillators , a second degree polynomial with standard deviations for the coefficients as given be- fore. What happens if we set these accuracies equal to zero, or in other words, if we have a set of perfectly running clocks? We employed the same conditions as before, but now neglecting the clock errors. A graphical representation again can be found in Figure 5 a,b . From the results of Table 3 we can see that the influence of the clock errors is very large, perhaps even the dominant effect. A little bit surpri- sing is the fact, that the condition number for 1.2 m and 12 m orbit orientation constraints is slightly better in the solutions with clock errors. There we must have more spheroidal, but even bigger error ellipsoids. Atmospheric refractivity The influence of refractivity is a mixture of the ionospheric constituent as well as of the dry and wet part of the troposphere. As in the case of clock errors the three atmospheric disturbances are modeled as purely additive terms. Therefore the effect of the atmosphere has a similar structure to that of the oscillator errors. This fact is impressively confirmed in Figure 6 where we have chosen for simplicity's sake ± 5cm as standard deviations of each of the three atmospheric components. Using this atmospheric model accuracies while setting the clock errors equal to zero, the effect of refractivity is approximately half the size of that of the oscillator model, as can be seen from a comparison of Figures 3a and 6. SUMMARY AND CONCLUSIONS As an example we have studied GPS-interferometric time delay observations. Within a combined terrestrial/satellite geodetic network some simulations from the field of improved second order design were carried out, which was equivalent to the intro- duction of stochastic prior information for the parameters to be determined. Vvior information was implemented either at the ground station coordinates or in the satellite orbit, where a combination of both has proven to be the most advantageous method. This fact, especially, holds in the case of relative positioning which is the most important one in geodynamical geodesy. Within our test network of a five station minimal ground configuration, the three main influences on the error budget, ephemerides, clocks and atmospheric disturbances have been examined. If the accuracy of the ephemerides of the GPS satellites is in a range which is comparable to Transit broadcasted ephemerides or even one or two orders of magnitude worse, the requirements for first order accu- racy in relative positioning can be fulfilled. The variation of the length of the simulation interval is of rather small influence. The usage of a realistic clock error model has proven to be the dominant influence factor, where we have to keep ^ in mind that the employment of no clock error model is a rather false assumption | from the electronical and mechanical point of view. Under the assumptions we have made, the influence of the atmospheric disturbances shows quite a similar structure but is only about half the size of that of the oscillator model. For a global ground station distribution in various climatic regions a three parameter atmospheric error 278 I model per station seems to be quite reasonable while for our European continental network an overparametrization could also be possible. After the statement and the analysis of the previous facts the question arises how to remove or to circumvent these problems. The method which we have implemented to combat them is not only by the use of differential GPS techniques for geodynami- cal purposes, but also by the introduction of proper stochastic prior information, which can provide a valuable contribution to modelling and processing GPS satellite observations. In addition to the above, the following factors should be implemented in the GPS satellite system configuration, i.e. a more accurate orbit determination, the em- ployment of more stabil receiver oscillators, the usage of dual -frequency receivers for the ionospheric correction and water vapour radiometer measurements for the reduction of the wet component of the tropospheric influence. Acknowledgement This research work was sponsored by Deutsche Forschungsgemeinschaft (German National Research Foundation) within Sonderforschungsbereich 228 "Hochgenaue Navigation" (High Precision Navigation). A. Stomma's stay was made possible through Deutscher Akademischer Austauschdienst (DAAD). This support is gratefully acknowledged. References Anderle, R.J., 1982: Doppler test results of experimental GPS receivers, NSWC TR 82-01, Dahlgren, VA. Bibby, J. and H. Toutenburg, 1977: Prediction and improved estimation in linear models, Chichester - New York - Brisbane - Toronto, Wiley. Boucher, C, P. Paquet and P. Wilson, 1981: Final report on the observations and computations carried out in the second European Doppler Observation Campaign (EDOC-2), DGK, Series B, No. 255, Frankfurt. Davidson, D., D. Delikaraoglou, R. Langley, B. Nickerson, P. Vanicek and D. Wells, 1983: Global Positioning System differential positioning simulations, Dept. Surv. Eng. Tech. Rep. No. 90, UNB, Fredericton. Delikaraoglou, D., 1984: Estimability analyses of the free networks of differential range observations to GPS-satellites, Proceedings Int. School of Geodesy, Erice, April 25 - May 10, (in preparation). Dermanis, A., E. Grafarend, 1981: Estimability analysis of geodetic, astrometric and geodynamical quantities in very long baseline interferometry, Geophys. J. R. astr. Soc, Vol. 64, 31-56. Grafarend, E. and E. Livieratos, 1978: Rank defect analysis of satellite geodetic networks I - Geometric and semi-dynamic mode -, Manuscripta geodaetica. Vol. 3, 107-134. Grafarend, E. and K. Heinz, 1978: Rank defect analysis of satellite geodetic net- works II - Dynamic mode -, Manuscripta geodaetica. Vol. 3, 135-156. Grafarend, E., H. Heister, R. Kelm, H. Kropff and B. Schaffrin, 1979a: Optimierung geodatischer MeSoperation, Karlsruhe, Wichmann. Grafarend, E., A. Kleusberg and B. Richter, 1979b: Free Doppler network adjustment. Proceedings Second Int. Geodetic Symposium on Satellite Doppler Positioning, 1053-1069, Austin, Jan. 22-26. 279 Hopfield, H.S., 1969: Two-quartic tropospheric refractivity profile for correcting satellite data, J. Geophys. Res., Vol. 74, No. 18, 4487-4499. Martin, E.H., 1978: GPS user equipment error models. Navigation, Vol. 25, No. 2, 201-210. Pachelski, W., 1983: Critical configurations of satellite networks. Artificial Satellites, Vol. 18, No. 1, 73-88. Schaffrin, B., 1983: Model choice and adjustment techniques in the presence of prior information, OSU-Rep. No. 351, Columbus. Schaffrin, B., 1984: Aspects of network design. Proceedings Int. School of Geodesy, Erice, April 25 - May 10 (in preparation). Schaffrin, B., 1985a: Models for deformation analysis considering prior information on the expected point movements, IV. FIG-Symposium on Deformation Measurements by Geodetic Methods, Katowice, June 10-16. Schaffrin, B., 1985b: Robust alternatives for network densification, lAG-Symposium on Geodetic Computations, Krakow, June 18-21. Wells, D.E., 1974: Doppler satellite control, Dept. Surv. Eng. Tech. Rep. No. 29, UNB, Fredericton. 280 Figure 1: Five ground station GPS test network configuration in Europe [1=St.Mand& (France, 2=Grasse(France), 3=Zimmerwald(Switzerland), 4=Graz(Austria), 5=Stuttgart( Federal Republic of Germany)]. Figure 2: Polar visibility plot for Navstar GPS satellites no. 5, 6, 8 and 9 for the central station Zimmerwald(Switzerland) on Jan. 30th, 1982. I 281 Fifun 3: a) Normal Ized trace Q of the nean prediction error ntr, 1 i r — 1 1 1 1. \ \ n \ \ 0.1 2\^ 1 — h^- — 12 16 t Ch] "C -1 0.12 _ -2 ig(c„J -3 / ^ ^.— —._.—— -3 // 1.2 -4 I / , JJ.^-- -4 -5 -5 -6 1 1 - -6 -7 -7 4 8 12 t 16 [h3 -^ bl ig(c„) -1 3 4 8 12 16 -1 ~ -2 / -2 -3 / 1.2 -3 / ^*^ ^•^' ^'^.^^ »^mW^ ' // -4 // 1 J . 12. r -4 -5 *^— ••— — [ -5 1 / i -6 // i -6 -7 / / 1 1 i 1 -7 -8 1 1 - 1 1 1 -8 -9 . -9 12 16 t Ch] Fifun 4: Q for various slwlatlon Interval lengths Cnln], Figurt 6: Q using an ataospheric error aodel (a*S cn in each of the three coaponents) for various orbit orientation constraints CaJ. Q Cm] 1.5 ) 4 8 12 16 ' ' 1.0 ii 1' i i '.1 ' ii i fl s V' n n ••'-I-:-. 1.5 1.0 0.5 '2 tCh] '« 0.0 Q Cm] i '\ 1 1 1 1 \ i V 1 \ 1 \ I '-K \ \ \ '..^12. ■\ \\ \ ^ ~ 0.1 2N^ 1^ 1 1 1 ■ 12 16 t Ch] 282 Table 1: Arithmetic mean different orhit values and ranges Ccm] of relative errors for orientation constraints Cm] . a^l0.12) a,/1.2) a,,(1.2) 0^^(0.12) 0^(1.2) 0^(0.12) mean 2.4 2.3 3.1 2.1 a^(0.12) a,y(1.2) - a,y(0.12) 0,^(1.2) - a,^(0.12) 0^(1.2) - 0(^(0.12) mean 22.2 22.8 24.3 21.4 range 9.3-37.8 10.8-37.8 8.2-46.9 7.5-38.7 ^ -Ax(12) -AX^1-^^ ".z"2' .,,(1.2) a,(1.2) mean 5.2 4.6 6.7 3.6 ^Ax(12) - -Ax(1-2) a,y(1.2) a,,(12) - o,,(1.2) %(12) - 0^,(1.2) mean 160.0 139.7 209.7 106.0 range 70.6-274.7 82.0-213.1 79.0-406.5 44.3-188.4 Table 2: Arithmetic mean values and ranges [cm] of relative errors for different simulation interval lengths [min]. -Ax(1) -AX^"-^^ o,,(0.i.) ".z(" .,,(0.5) 0^(1) 0^,(0.5) mean 1.2 1.2 1.2 1.2 a^(0.5) °.z(" - o,,(0.5) at,(1) - Ojj(0.5) mean 3.6 3.6 2.8 3.8 range 3.1-4.2 2.2-2.5 2.2-2.4 2.9-5.5 °Ay<2) -Az(2) 0^(2) 0,(1) mean 1.3 1.2 1.3 1.2 -Az(2) - -Az(1) a,(2) - a,(1) mean 4.2 4.7 3.8 4.9 range 3.6-5.0 3.6-7.0 2.9-5.5 3.6-7.1 283 Table 3: Comparison of solutions with and without a clock error model, (a) and (b) ^ respectively, for different orbit orientation constraints, ^ orbit orientation Cm] °iz(^> ajj(a) mean 0.12 3.9 3.4 2.3 4.0 1.2 2.4 2.3 1.3 3.2 12 1.8 2.4 1.3 3.4 ^ orbit orientation Cm] -Ax(^) - ai,(a) - mean 0.12 11.3 12.2 6.2 13.8 1.2 20.7 22.0 7.9 27.1 12 81.7 101.8 46.9 104.6 range 0.12 10.6-12.3 6,9-21.5 5.6-7.3 10.9-22.0 1.2 14.4-30.8 19.6-43.4 5.6-11.0 15.7-45.0 12 52.9-135.7 50.5-171.0 25.8-71.7 63.0-185.8 284 MAGNET-4100 GPS SURVEY PROGRAM PROCESSING TECHNIQUES AND TEST RESULTS Ron Hatch Magnavox Advanced Products and Systems Company 2829 Maricopa Street Torrance, California 90503 Ken Larson Geophysical Service Incorporated 7800 Banner Drive Dallas, Texas 75265 ABSTRACT. The MAGNET-4100 program was developed by Magnavox for Geophysical Service Incorporated (GSI) to process data collected using the Texas Instruments TI-4100 receivers. The program is designed to run on the Texas Instruments Professional Computer which, in the portable version, is employed by GSI in the field. High accuracy differential positions are computed simultaneously using the carrier phase measurements from as many as ten receivers. This paper describes briefly the unique computational techniques employed in the MAGNET-4100 program and then explores the accuracy which can be obtained as a function of time on site and receiver separation distance. INTRODUCTION The MAGNET-4100 GPS survey program was developed as the result of the synergistic objectives of Magnavox and GSI. Magnavox had developed a GPS survey program but had tested it only with simulated data. GSI had purchased a number of TI-4100 receivers, but no software was available to use the receivers effectively for precise geodetic survey applications. Magnavox had developed the basic capability of the MAGNET-4100 program in order to test some unique processing techniques which showed promise of being much more efficient and compact than any which had been described in the literature. GSI wanted a survey program which would reside in the TI PC computer and allow them to compute high accuracy results in the field as soon as the data was collected. The MAGNET-4100 program is the result. The unique processing techniques have proved effective and are fast and compact. The program has enabled GSI to routinely offer high accuracy results immediately after the data has been collected. 285 PROCESSING TECHNIQUES The original motivation for the development of the MAGNET-4100 program was the belief that the differencing and interferometric techniques being described and advocated in the literature were fundamentally inefficient and suboptimum. The GPS system is conceptually not much different than a "LORAN-in-the-sky" system. The LORAN technique most commonly used for navigation and positioning is to difference the measurements in order to remove the effect of the receiver clock. An equivalent technique could have been used in the GPS system by forming three differences to eliminate the clock and then solving the three hyperbolic surface equations for the three position coordinates. Seven years ago (Hatch, 1978) it was argued that differencing raw measurements should not be done but that the clock should be modeled and solved. The people developing the GPS navigation equations have recognized this principle. Almost universally the receiver clocks are a part of the navigation solution. But, where survey applications are concerned, we have turned back the clock. Most algorithms describe differencing and multiple differencing processes to eliminate the effects of the receiver and satellite clocks. The MAGNET-4100 does not form any differences. Instead, the phase noise in each satellite and receiver oscillator is explicitly determined as a part of the computation. This is the fundamental difference between our processing technique and that employed almost universally by others. It is also this characteristic which allows us to solve simultaneously for ten sites while storing all the measurements within the memory of a small portable computer. The measurements as stored have been preprocessed to compact them such that one measurement is obtained for each minute of data from each satellite at each site. Absolute Point Position The first step in the processing of data is to compute a point position solution for each site. The primary motivation for the point position solution is to determine the bias in each of the receiver clocks. Of course, the position itself is often of interest and serves as a check on the supplied position of the control site receiver. The time bias one obtains from the point solution is accurate to a few nanoseconds. This is actually far more accurate than is needed to adjust the measured receiver phase to a common time epoch. One microsecond time bias accuracy can be used to interpolate the carrier phase to better than 0.01 cycles. Using the code measurements of the receiver to solve for the receiver time bias avoids the necessity of bringing the receivers together to synchronize their clocks as is required by the "code-less" receivers. 286 The point position solution actually makes use of both the code and carrier measurements. The carrier measurements are used to smooth the code measurements using a process previously described (Hatch, 1982) . The error in both the position and clock bias values are dominated by the spacecraft clock and orbit errors. Thus, the relative positions out of the point solution computation will typically be significantly more accurate than the absolute position. Hyperbolic Solution The first stage of processing for relative positions is referred to herein as the "hyperbolic solution". It is the solution one obtains by straight forT^ard processing of integrated Doppler counts from each site. Specifically, the Doppler counts are not continuously integrated; but, when one ends, the next restarts at zero. This is the same result one gets by differencing with respect to time the continuously integrated Doppler measurements. These Doppler measurements give rise to equations of hyperbolic surfaces in space, hence the term "hyperbolic solution" . The phase noise of both the satellite and receiver clocks is explicitly solved for in this solution. This means that this solution is almost identical to the "triple difference solution" (Goad, 1983). Rather than solve for the phase noise of satellite and receiver. Goad eliminates them by double differ- encing. His third difference is the difference in time of the continuously integrated Doppler count. The motivation for the hyperbolic solution was the same as that of Goad. It provides a good initial solution which is not sensitive to receiver loss-of-lock. This solution can then be used to aid in filling any loss-of-lock. When the satellite and receiver clock phase noise has been explicitly obtained as part of the solution, the filling of the loss-of- lock becomes even easier. Doppler Pseudorange Solution We have labeled the second stage of the relative position computation the "Doppler pseudorange solution". The term "Doppler pseudorange" is used to avoid confusion with the code measurements which are normally referred to as pseudorange measurements. A continuously integrated Doppler count is the same as a range measurement with a bias error equal to the initial range at the time the Doppler measurement was commenced. The code pseudorange measurement typically used in GPS navigation algorithms is a range measurement biased by the receiver clock error. The advantage of the code pseudorange measurement is that the bias is the same no matter which satellite is being observed. Of course, for high accuracies the satellite clocks cannot be treated as perfect as they are for the code measurements . 287 There are actually a large number of methods of foirming Doppler pseudorange measurements. In a previous paper (Hatch, 1978) a method was described where, rather than biasing the continuously integrated Doppler count by the initial range, it was biased by the average range. Other techniques are described in the literature whereby the individual Doppler counts (differenced in time) are whitened (Bierman, 1977) or are weighted by a covariance matrix (Kirkham,1972) . All of these techniques are equivalent. The Doppler pseudorange solution can yield very accurate relative positions. Like the hyperbolic solution it explicitly solves for the satellite and receiver clock noise. It makes use of the previous hyperbolic solution to fill in any loss of lock. The operator can select several solution modes — refraction corrected, an LI and L2 average, LI only, L2 only, and even LI minus L2 . The average solution is typically the most accurate for short distances since it averages the phase measurement noise of the two channels. For longer separation distances between receivers, the difference in the ionospheric error at the two sites causes the average and single frequency solutions to be inferior to the refraction corrected solution. For short distances the Doppler pseudorange solution appears to be to within ten centimeters with a half hour of data from four satellites, and to within 20 or 30 centimeters for distances approaching 100 kilometers. In the first version of MAGNET-4100 the Doppler pseudorange solution was the final solution. GSI has recently published a paper (Stowell, 1985) describing MAGNET-4100 results from this first version of the program. In the new version a final stage of processing has been added. Resolved Lane Solution A final stage of processing is now included which yields differential positions accurate to the one centimeter level in as little as five minutes for short distances. The longer distances can take much longer to lane properly. The basic piece of additional information used in the "resolved lane solution" as compared to the Doppler pseudorange solution is the use of the initial fractional phase measured at the start of the first integrated Doppler measurement. The successful use of this additional piece of information depends, however, on knowing how many whole lanes (number of wavelengths) the satellite is from the receiver. Actually, if the number of whole lanes is in error by a small amount at the control site, it is enough that the error be the same at the remote site. The lane computation procedure depends upon the relative position of the site being accurate to within one-half wavelength in the direction of the satellite. Thus, the position accuracy out of the previous computation stage (Doppler pseudorange solution) is critical. 288 For short receiver separation distances the ionospheric error will be essentially identical at the two sites. This means that the measurement noise can be reduced by averaging the LI and L2 measurements. Thus a more accurate position is obtained out of the Doppler pseudorange solution. In addition, since the ionospheric range error aliases into the satellite clocks, the difference frequency (L1-L2) should also yield the same solution. Therefore, the difference in initial phase can be used to "wide lane" the fractional phase of the LI and L2 measurements. Since the wavelength of the difference frequency is much longer (86-centimeters) , it is much easier to achieve a successful resolved lane solution. For site separation distances greater than ten kilometers, the difference in ionospheric range error at the two sites is typically large enough that the average of the LI and L2 measurements should not be used. Instead, one should refraction correct the measurements. Unfortunately, the refraction process amplifies the phase noise rather than reducing it. This means that a longer data collection interval is needed to get the same accuracy out of the Doppler pseudorange solution. In addition, the ionosphere affects the difference frequency (L1-L2) differently than the LI which is affected differently than the L2 frequency. This means that the "wide lane" process becomes suspect. Thus, an even more accurate position out of the Doppler pseudorange solution is needed, which implies an even longer data collection interval to resolve the lane successfully. It should be noted that very little differential ionospheric error is sufficient to cause difficulty with the "wide lane" process. Even a few centimeters error creates problems. An example illustrates the danger. Assume a differential ionospheric error of 4.19 cm. or 0.2206 wavelengths of LI. Because the ionosphere affects L2 more severely, an error of 6.90 cm. or 0.2831 wavelengths of L2 would also be present. This is not a problem if the solution out of the previous stage is good to about five centimeters. However, if the "wide lane" process is used, one would compute the (L1-L2) wavelength and obtain -0.0625 wavelengths of the difference frequency which corresponds to an error of -5.38 cm. The "wide lane" process sets the lane of the LI and L2 fractional phase values to the value closest to the difference value. Unfortunately, subtracting one whole lane from the true value given above results in a value slightly closer to the difference value. Thus, the LI fractional phase would be set to -0.7794 wavelengths of LI or -14.81 cm. The L2 fractional phase would be set to -0.7169 wavelengths of L2 or -17.48 cm. The result is an incorrect lane resolution even if the input position were perfect. The best way to resolve the lane when the ionospheric errors are significant (if only we could modify the GPS system!) is to use a third frequency (Hatch, 1982) , 289 TEST RESULTS Three groups of data are described below. The first is a set of data from two receivers connected to the same antenna. The second group of data was collected using receivers separated by distances of less than a kilometer. The last group of data was collected by receivers located at points on the Transcontinental Traverse. GSI collected these data at their own expense specifically to test the MAGNET-4100 software. The data were collected between October of 1984 and February of 1985. Unfortunately, the TI-4100 receivers had not been modified to incorporate the new receiver software. This means that more frequent loss-of-lock occurred than was desirable. In addition, data were lost at each site simply because the tape recorder could not keep up with the data it received. Since different data were lost at each site, more phase noise appears in the compacted data. In spite of these problems, excellent results have been obtained. Two Receivers on the Same Antenna The limiting capabilities of both receiver and software can be tested by collecting data with two receivers connected to the same antenna. Though only 30 minutes of data were collected, it proved more than enough to analyze the performance which can be achieved under optimum conditions. Multipath clearly is not a problem when the receivers are connected to the same antenna because the errors are common and will alias into satellite clock phase noise. Ionospheric and tropospheric errors are also clearly identical and alias into the satellite clocks. The data received from one site started a bit later than at the other. Only 28 minutes of data were common at the two sites. In addition, one receiver had a faulty receiver oscillator which was 10 times noisier than the other. Finally, the last five minutes of data from satellite 6 had fractional phase errors of around one-third of a cycle on one of the receivers. In spite of these problems, the solution including all 28 minutes of data was excellent (see Table I) and essentially the same as for the first 23 minutes of data (see Table II) . It is apparent even from this one example that a systematic error source will often affect the Doppler pseudorange solution more severely than the hyperbolic solution. (Including the last five minutes of data caused the hyperbolic solution to get better and the Doppler pseudorange solution to become worse.) The 23 minutes of data were then split into two disjoint sets with 11 minutes of data each. The results are shown in Table III. Next, the data set was split into 22 contiguous data sets. Specifically, each data set contained two preprocessed compacted measurements of cumulative phase (continuously integrated Doppler) for each satellite/site combination. The end 290 I TABLE I Differential Position Error Using 28 Minutes of Data from the Same Antenna (Millimeters) Solution Type X Y Z Hyperbolic Doppler Pseudorange Resolved Lane Radial 18 -12 -18 28 9 -13 -19 25 -1 1 1 TABLE II Differential Position Error Using 23 Minutes of Data from the Same Antenna (Millimeters) Solution Type X Y Z Radial Hyperbolic Doppler Pseudorange Resolved Lane 25 -17 -30 43 1 -8 -12 15 -1 1 1 TABLE III Differential Position Error From Two Sets of 11 Minutes of Data from the Same Antenna (Millimeters) Solution Type Data Set X Y Z Radial Hyperbolic 1 30 -47 -47 73 II 2 67 3 -48 83 Doppler Pseudorange 1 -10 -26 -20 35 II 2 20 -3 -24 32 Resolved Lane 1 -1 3 -1 3 II 2 -1 1 1 measurement of one set was the initial measurement of the next. Differencing these two compacted measurements yields only one Doppler measurement, which is independent from one data set to the next. Since there is only one integrated Doppler measurement for each satellite/site combination, there is no difference between the hyperbolic and Doppler pseudorange solutions. The final resolved lane solutions are not independent since the end point phase of the continuously integrated Doppler is used in the solution. The 22 independent hyperbolic/Doppler pseudorange solutions are shown at the top of Table IV. The mean radial error of these solutions was 468 millimeters. The 22 resolved lane solutions (not independent) are shown at the bottom of Table IV. The mean radial error of these solutions (excluding the four with improper lane resolution) was 3.7 millimeters. 291 TABLE IV Differential Position Error Using Only Two Minutes of Data from the Same Antenna (Millimetrs) Solution Type Data set X Y Z Radial Hyperbolic/Doppler 1 14 198 -295 355 II 2 -210 52 68 227 II 3 483 -644 -184 826 n 4 -243 330 270 491 II 5 -285 1 120 309 II 6 630 -141 -90 652 II 7 -656 156 181 698 II 8 19 -445 142 468 II 9 -28 324 -213 389 II 10 16 422 26 423 II 11 551 -732 -305 965 II 12 -452 223 340 608 n 13 -18 168 11 169 II 14 216 155 -216 343 II 15 -3 -129 52 139 II 16 28 140 -8 143 II 17 75 156 -39 177 n 18 116 -621 72 636 II 19 -218 80 -123 262 II 20 -355 333 477 682 II 21 -134 -111 -423 457 II 22 834 -172 -244 886 Resolved Lane 1 -2 12 -4 13 II 2 -1 7 -4 8 II 3 1 1 II 4 -1 2 1 2 n 5 -2 4 -1 4 ti * 6 808 -47 411 907 II 7 -1 3 3 II 8 -3 1 1 3 II 9 -2 -1 1 3 n 10 -1 1 -1 2 M 4 f 11 1199 -1517 -310 1958 II 12 1 -5 3 6 II 13 -2 1 2 II 14 -1 2 -1 2 II 15 1 II 16 2 -1 2 II 17 4 -2 5 II 18 2 2 II 19 1 -4 3 5 " * 20 -1150 1346 434 1823 II 21 -1 1 -1 2 " * 22 732 1076 -818 1537 * Indicates improper lane resolution 292 The results tend to verify what was learned in the original simulations. First, the Doppler pseudorange solution tends to improve almost linearly with time (i.e. the error decreases inversely with time) . This can be explained as the combined effect of an increasing number of measurements (a square root of time effect) and an increasing baseline or satellite arc (also an aproximate square root of time effect) . In contrast, the resolved lane solution improves approximately as the square root of time, since it is not sensitive to the increasing baseline resulting from satellite motion. For many survey applications, the resolved lane solution is sufficiently accurate with even a few minutes of data. This means that time on site is determined only by how long it takes the Doppler pseudorange solution to reach an accuracy which can ensure a correct lane resolution. Short Baselines Compared to EDM Measurements The second group of data used to verify performance of the MAGNET-4100 survey program involved site separations between 12 and 720 meters. Good data was obtained on four baselines which had been measured directly by EDM equipment. Several other points were observed which were not intervisible. The results without the final resolved lane solution have already been reported (Stowell, 1985) . In this report the four baselines directly measured by EDM will be compared to the GPS measured baseline lengths. The baseline azimuth was not measured in a conventional fashion. Each baseline is considered separately below in order of increasing length. The shortest baseline was 12.762 meters as measured by the EDM. Twenty-five minutes of common data was obtained by the two receivers occupying the two sites. The MAGNET-4100 solution of the baseline length was 12.762 meters — identical with the EDM measurement. The data were then divided into five disjoint sets of five minutes of data in each. A five minute length was chosen because the common antenna data had not resolved the lane consistantly with only two minutes and because the data appeared to be somewhat noisier than the common antenna data. The results of these five sets of data are showm in Table V. TABLE V Range Difference at Twelve Meters (GPS-EDM) Using Five Minute Data Sets (Millimeters) Data Set Hyperbolic Doppler Pseudorange Resolved Lane _ — -24 -5 58 1 209 3 113 1 293 1 3 2 -9 3 62 4 217 5 57 The resolved lane results are very good. The Doppler pseudorange results are hardly to be preferred to the hyperbolic results. However, with only four Doppler intervals, this is not particularly significant. The next baseline was measured at 60.421 meters by the EDM. The two sites had 3 6 minutes of common data above 2 degrees elevation, but one set lost lock on one satellite in the middle of the interval. The resolved lane result was a GPS determined distance that was 16 millimeters long. Five sets of five minute data without loss-of-lock were processed. The resolved lane results were (GPS-EDM) : 21, 5, -89, 89, -41, and 8 millimeters. These errors are much larger than that observed on the twelve meter line. However, the largest errors are in the data sets bordered by the loss-of-lock and may simply reflect a receiver tracking problem. The third short baseline was measured at 579.945 meters by the EDM. Only 22 minutes of common data were obtained by the two receivers. The resolved lane solution obtained from the MAGNET-4100 program was 7 millimeters short. Four sets with five minutes of data each yielded the following results (GPS-EDM): 7, -6, -11, and -7 millimeters. These results are very good and are much more consistent than those for the sixty meter line. The last baseline was measured at 720.414 meters with the EDM. GPS data were collected for this baseline on two different days. On the first day 48 minutes of data above 20 degrees elevation was common to the two sites. However, there was a short loss-of-lock on one satellite at one site. The resolved lane solution resulted in a baseline determination that was 12 millimeters longer than the measured value. On the second day 46 minutes of common data were obtained which also had a short loss-of-lock on one satellite. The computed baseline with this data was 16 millimeters long. Five minute data sets without loss-of-lock were generated from both days data. The results were (GPS-EDM): 4, 9, 34, 10, -7, -48, 98, 55, and 8, millimeters from the first day and; 6, 0, -103, 88, 65, 25, -10, and millimeters from the second day. In this case the poorer results were not next to the loss-of-lock period and must reflect actual accuracies which can be expected with five minute data samples. The RMS error around the EDM measured distance is 48 millimeters. Data Collected at Transcontinental Traverse Stations In order to verify performance of the MAGNET-4100 program at longer baseline distances, data was collected at a number of Transcontinental Traverse (TCT) stations in Texas. Data from three baselines of approximately 6, 16, and 46 kilometers are presented below. The reference positions were supplied with a resolution of only three centimeters in latitude and longitude and one centimeter in height. The height of the stations is reported to be less accurate than the horizontal. 294 - six Kilometer Baseline - The six kilometer baseline had common GPS data above 2 degrees elevation for a little more than 3 minutes. A data set with 51 minutes of common data and with no loss-of-lock was formed — the data from the satellite which dropped below 20 degrees were simply edited. This data set was processed using refraction correction as well as using the average of LI and L2 . The answers differed by 8, 11, and 1 millimeter in X, Y, and Z respectively. Though this is hardly significant, it was decided to continue the processing using only the refraction corrected results. Using one of the TCT stations as the control station, the coordinates of the second station were compared to the refraction corrected resolved lane solution. The solution was 6 centimeters south, 1 centimeter west, and 25 centimeters below the actual coordinates. This "best" answer from GPS will be used to compare to three other answers. The first 3 minutes of data were used to compute an answer first. The change (new-best) in X, Y, and Z were 1, 23, and 3 milimeters respectively — latitude and longitude were almost unchanged; the height decreased by about 2 centimeters. Next, the 30 minute data span was split into two 15 minute groups. The change in the coordinates of the first 15 minute solution (new-best) was: 6, 10, and -8 millimeters in X, Y, and Z respectively. In the second 15 minutes the change was: -2, -29, and 13 millimeters. These results speak for themselves. - Sixteen Kilometer Baseline - The 16 kilometer baseline was similiar to the six kilometer baseline in that only about 40 minutes of data were obtained while all four satellites were above 20 degrees elevation. However, 92 minutes were processed with data from one satellite being edited when it dropped below 20 degrees. These data were processed both refraction corrected and averaged in order to assess the magnitude of the ionospheric refraction effect. The LI and L2 averaged solution differed from the refraction corrected answer by 14, 45, and 7 millimeters in X, Y, and Z respectively. While most of the difference shows up in height, the lane resolution becomes more difficult and the "wide lane" process starts to become suspect. The refraction corrected solution was 2 centimeters south, 6 centimeters east, and 40 centimeters below the actual coordinates of the remote TCT position. Like the six kilometer baseline, the first 3 minutes of data were used because this yielded a data set with all four satellites above the elevation limit for the entire data span. The X, Y, Z coordinates changed by 5, -81, and 5 295 millimeters respectively. Again, this is predominantly a height change. This 30 minute data set was split into two 15 minute data sets. However, reflecting the increased ionospheric distortion, the lane could not be resolved correctly in the first 15 minute data set. The second 15 minute data set did give a good solution which was 3, -56, and 7 millimeters different than the "best" solution in X, Y, and Z. - Forty-Six Kilometer Baseline - The last pair of TCT stations to be considered were approximately 46 kilometers apart. These data had problems similiar to the above — only a bit more than 30 minutes of data was available with all satellites above 20 degrees. To obtain our "best" GPS answer, 53 minutes of data were used with data from the satellite below 20 degrees being edited. In addition, a short loss-of-lock on one satellite occurred in the data span. As before, the effect of the ionosphere was assessed by comparing the averaged solution to the refraction corrected solution. The difference was -19, 97, and -36 millimeters. Clearly, with the ionosphere contributing errors approaching 10 centimeters, the "wide lane" process must be considered suspect. Nevertheless, both the "wide lane" and "narrow lane" process gave identical results for this "best" GPS solution. The GPS solution was 1 centimeter north, 8 centimeters east, and 12 centimeters below the actual TCT position. The Doppler pseudorange solution for this same data set is also very good and should be considered. If the ionosphere were slightly worse, then the lane could not be resolved properly; and one would be left with the Doppler pseudorange solution as the best answer. In this example, that solution is 1 centimeter north, 3 centimeters east, and 14 centimeters below the actual TCT position. This probably is a bit better than the typical agreement between the two solutions. However, with data spans approaching one hour in length, the importance of the initial fractional phase is not real large. Another way of viewing this phenomena is to note that the Doppler pseudorange which improved linearly in time has almost reached the same accuracy as the resolved lane solution which improved only as the square root of time. This means that, when the ionospheric effect becomes so large that the lane cannot be resolved, one can still get an almost equivalent accuracy by collecting an hour of data at each site. The first 30 minutes of data provided a resolved lane solution which was different from the "best" solution above by: 40, -30, and -36 millimeters in X, Y, and Z. This data set had a loss-of-lock on one satellite. No attempt was made to resolve the lane with shorter time intervals since the 30 minute interval lane resolution was clearly marginal. 296 In some cases there is more interest in determining the horizontal position than the vertical. At the longer distances this can be achieved with less data using a "mixed mode" solution. Specifically, the refraction corrected Doppler pseudorange solution is formed first. Its results are then used to resolve the lane of the LI minus L2 solution. This difference solution is adversely affected by the ionosphere but most of the error is in height. The advantage is that the difference solution is inherently a "wide lane" solution. SUMMARY Processing algorithms which appear to be unique to the MAGNET-4100 survey software have been described. They appear to offer significant advantages in compactness of code and processing speed. They have enabled GSI to offer near real time survey coordinates which are competitive with classical techniques in accuracy. Test results have been described which quantify the accuracy and show that most of the adverse ionospheric effects encountered with increasing separation distances can be overcome by simply increasing the time on site. As little as five minutes appears to be adequate at distances of less than one kilometer, though this probably should be doubled for safety considerations. When baselines reach the vicinity of 50 kilometers, the time on site needs to be increased to about one hour if results good to a few centimeters are desired. Many applications may need accuracies to only a few tens-of-centimeters or be concerned primarily about the horizontal position. When these conditions apply, the Doppler pseudorange or "mixed mode" solutions can be used with shorter time on site required. REFERENCES Bierman, G.J., 1977: Factorization Methods For Discrete Sequential Estimation, pp 47-50, New York, Academic Press. Goad, C.C. and B.W. Remondi, 1983: Initial Relative Positioning Results Using The Global Positioning System, IVIII General Assembly of the lUGG, Hamburg Germany. Hatch, R.R., 1978: Hyperbolic Positioning Per Se is Passe', PLANS-1978, IEEE publication 78CH1414-2, pp 51-58. Hatch, R.R., 1982: The Synergism of GPS Code and Carrier Measurements, Proceedings of the Third International Geodetic Symposium on Satellite Doppler Positioning, pp 1213-1229, Univ. of New Mexico, Las Cruces. Kirkham, B.P., 1972: An Improved Weighting Scheme For Satellite Doppler Observations, B. Sc. Thesis, University of New Brunswick, Fredrickton, N.B., Canada Stowell, J., 1985: Utilization of GPS, ASP-ACSM Convention, Washington D.C. 297 GPS INTERFEROMETRIC PHASE ALGORITHMS V Ashkenazi,L G Agrotis and J Yau Department of Civil Engineering University of Nottingham United Kingdom ABSTRACT. The Global Positioning System has been developed chiefly for instantaneous positioning and dynamic navigation. Geodetic relative positioning accuracies can only be obtained by making observations in (VLBI type) interferometric mode. Several receivers capable of ( inter ferome trie) phase measurements with the GPS carrier wavelength are now commercially available. The carrier wavelength is obtained from the received signal either by a •re-construction' process (which requires access to the C/A or P codes) or by a 'squaring process' (which destroys both the timing codes and the ephemeris message) . The program writer has several alternative strategies and corresponding algorithms at this disposal. These depend largely on the quality of the oscillator and other characteristics of the receiver, the geometry of the GPS satellite constellation (especially until 1988, when the full system becomes operational), and the duration of the common phase observations. A number of different algorithms, which have been proposed by different agencies, and their relative merits will be discussed in the paper. Results obtained by using software developed at Nottingham and elsewhere will also be included. 1 INTRODUCTION Recent field tests with GPS receivers have confirmed earlier predictions of very high geodetic positioning accuracies which can be achieved by using the Global Positioning System. In particular. Bock et al (1984) report that the Macrometer Model V-lOOO receivers are capable of single point positioning accuracies of the order 2 to 3 metres in each component, after only several hours of observation. In the most extensive series of geodetic field tests to date carried out by the US Federal Geodetic Control Committee (FGCC)/ Hothem and Fronczek (1983) achieved a level of relative positioning accuracy of several millimetres in all the three vector components, for baselines shorter than 1 km. Over medium baselines (up to 42 km in length) , the relative positioning accuracies averaged 2 ppm. This was repeated in later tests over much longer baselines, of up to several hundreds of km, and some as long as 2400 km (Bock et al, 1984) . Considering that the current model V-lOOO receiver operates only on the Ll carrier frequency, these results are clearly impressive. One should also mention that the V-lOOO requires an external empheris and is therefore incapable of real-time navigation. The US NGS has also carried out extensive field tests with two Macrometer V-lOOO receivers and report very high relative positioning accuracies, achieved by using different types of processing algorithms and corresponding software (Goad and Remondi, 1984) . The NGS is also participating in the development of the Texas Instrximents ' TI 4100 geodetic receivers. The stage is now set for the further proliferation of GPS receivers for geodetic positioning. Inevitably, these receivers will be capable of interferometric phase measurements (with one or both of the carrier frequencies) , a pre-requisite for high relative positioning accuracies. Opinions still differ on optimal 299 algorithms to be used in processing these interferometric measurements. The purpose of this paper is to list and mathematically define various possible interferometric algorithms and to show the relationship between these and non-interferometric processing techniques, such as ' pseudo-r anging ' and •continuous Doppler counts' used with Transit (NNSS) data. The paper is concluded by details of interferometric GPS software developed at Nottingham, given in §5. 2 PSEUDO-RANGE MEASUREMENTS Although this paper will largely concentrate on interferometric phase algorithms which alone lead to high accuracy positioning, it is important to begin with the basic GPS observational mode, namely pseudo-ranging . A GPS navigation receiver has to make at least 4 quasi-simultaneous pseudo-range measurements to 4 different satellites in order to obtain a real-time position. This can be achieved with either a receiver with 4 or more simultaneously receiving channels or one which can quickly seqpaence (multiplex ) a minimum of 4 satellites (see also §2.3). Pseudo-ranges are range measurements contaminated by clock biases. In general, a satellite clock is not in phase with GPS time, but a correction can be computed from the parameters in the satellite's navigation message and applied. This leaves the receiver's clock bias as an unknown, which is solved together with the 3 cartesian coordinates of the antenna position. 2.1 Pseudo-Range Model Equation The basic pseudo-range model equation consists of «,. = R. + cot + E. + E^ (1) X 1 o ion trop where i. : pseudo-range between satellite and receiver R. : corresponding true range a : receiver clock bias (relative to GPS time) o c : velocity of propagation of microwaves in vacuo E. : correction for ionospheric delay error ion E : correction for tropospheric delay error trop Jr r 2.2 Solution Method The 'observation equation' corresponding to the 'model equation' (1) is given by 3Jl. dZ. di. da iAc oil - AX + — - AY + — - AZ + — - Aa = (£° - i^) + V (2) dX dY dZ 3a o where AX,AY,AZ : least squares corrections to the provisional antenna coordinates V : least squares residual 300 Aa : least squares correction to the provisional value of the clock bias o a. : observed pseudo-range c : 'computed' pseudo-range /v ■ 1 which, in turn, is obtained from A^ = R*r + ca^ + E. + E^ ,,, 1 1 o ion trop (3) ^ = (X. - X)^ + (Y. - Y)^ + (Z. -Z)^h, and R where X./Y.,Z. : satellite coordinates, corresponding to the measured pseudo-range, derived from the elements of the navigation message X,Y,Z : provisional geocentric coordinates of the phase centre of the antenna c R. : computed range between receiver and satellite c a : computed (provisional) value of clock bias. The least squares solution of 4 or more observation equations of type (2) leads to the most probable (quasi-) instantaneous position of the antenna and the receiver clock bias, as well as a corresponding covariance matrix. Continuous pseudo-range measurements over several hours can also be used to obtain a much more accurate position of a stationary receiver. Model equation (1) and observation equation (2)still hold true, with the only change in data processing consisting of a sequential least squares procedure. Normal equations are formed separately for each set of simultaneous pseudo-range observations. As the clock bias correction, Aa©, applies only to one set of measurements, it is eliminated, leaving a 3 by 3 set of reduced normal equations. These are accumulated and solved at the end for the remaining set of common unknowns AX, AY, AZ. Back-substitution leads to the successive values of a , providing a useful indication of the receiver's clock drift. 2.3 Receiver Types Model equation (1) and the corresponding observation equation (2) above assiime a relatively inexpensive crystal oscillator in a receiver, which is capable of at least 4 pseudo-range measurements to 4 or more satellites simultaneously (or quasi-simultaneously) . Receivers, such as the TI 4100 , which can quickly multiplex between different satellites, belong to this category. However, pseudo-range measurements can also be made by receivers incorporating a highly stable atomic frequency standard, such as an STI 5010, and observing only one satellite for a period of time. The highly stable clock allows a more accurate modelling of the receiver's clock error, by adding 'drift and aging' terms. 301 The model equation now becomes a. = R. + ca + ca. (t. - t ) + ca_ (t . - t )^ 1 lolio 2io + E. + E^ ■ ^^^ ion trop where a : (linear) clock drift term a_ : (quadratic) aging term T. : local (receiver) time of observation i T : local time at start of observations o with a corresponding 'observation equation' incorporating the extra unknowns a and a . Moreover, in this case, one may by-pass the predicted satellite clock error parameters in the broadcast message, and model and solve for polynomial clock error parameters for each individual satellite pass. 3 PHASE OBSERVATIONS (DOPPLER COUNTS) 3.1 Carrier Frequency Measurements The two carrier frequencies of the GPS signal, Ll and l2, are respectively 154 and 120 times more accurate than the basic 10.23 MH frequency of the P code. A receiver can have access to the GPS carrier frequencies in one of two ways . In the so-called Tri-Agency approach, the receiver (eg TI 4100) generates the P or the C/A code which is then used to clear the incoming signal from that timing code, leaving the "reconstructed carrier" frequency. In the so-called "white noise" approach, the receiver (eg Macrometer) , a "squaring" process is used/ in which the received signal (strictly the 'beat frequency') is squared in order to get rid of the timing modulations . The resulting signal is then a pure carrier, but at twice the original frequency. In the process, one loses not only the pseudo-range measurements, but also the ephemeris message. 3 . 2 Carrier Phase Measurement The £>asic model equation corresponding to the 'beat frequency' phase reading can be obtained by substracting the phase of the received carrier signal (Ll or L2) from the phase of the signal generated by the receiver. The latter is obtained from (|)^(T) = <(), (T ) + 2TTf^(T-T ) (5) ^A A o A o where <|> (t) : receiver generated phase (in radians) >> (6) where (j) . (t ) : initial carrier phase reading f . : carrier frequency for satellite j range from station A to satellite j velocity of propagation of microwaves in vacuo phase errors due to ionospheric, tropospheric effects R. Aj 4* . 1^ xon trop Subtracting (6) from (5) , leads to the 'beat frequency' phase reading, one of the basic (Transit or) GPS observables. ^ (7) Phase readings ^, which are given in terms of radians, can be transformed to cycle readings N by dividing by 2ir. N .(t) = N^(t^) - N.(T^) + (f^ - f.) (T - t) Ad A030 A3 o + — R^.(i:) + N. + N c AD ion trop (8) A further multiplication by the carrier wavelength (9) turns equation (8) into a so-called 'biased range' equation c "aj'^' = f. N (T ) - N.(t ) A o DO + c A D + R„.(T) + X. AD D N. + N ion trop ] D J (T-T ) O 303 T- (10) Model equation (10) is identical to model equation (4) , subject to neglecting the 'aging' term in the latter and equating (clock bias) a (clock drift) a. N«<'f^> - N.(T ) A o J o ^A- ^3 . f . 3 (11) Equations (9) , (10) and (11) demonstrate that a least squares adjustment with 'biased range' observables is practically identical with an adjustment using 'pseudo- range' measurements (see also §3.3). Phase or cycle count readings can also be differenced and then used as observables. One can difference with respect to time. and obtain a Doppler Count, or with respect to two receivers at two different sites. \bj^'^ = %j^'^ -W^ ' (13) and obtain an interf erometric phase reading ( §5 ) . 3.3 'Doppler' and 'Biased Range ' Equations The full model equation corresponding to a Doppler count, as defined by equation (12) , is obtained by subtracting two appropriate model equations (8) . f . \j(^l'V = (^A-fj^ ^W -^ c N. (T., |_ ion 1 T_) + N (t 2 trop l'^2^] (14) By definition, a 'biased range' is an observed range obtained by adding a 'range difference', corresponding to an observed Doppler count, to the previous biased range, namely D (t ) = ^Aj^ 2' ^ >^^ ^t R .(T-) - R . A3 2 Ad i'v]' (15) 304 The observed 'range difference' is obtained from (14) as [w2^ - wi^Y [\on^^l''^2) -^ \rop(^l''^2)] iT ' (16) Simultaneous observations with both the Ll and L2 carrier frequencies enable the computation of the first order ionospheric errors N. , whereas measurements of temperature, pressure and relative humidity can be used to estimate tropospheric delay error N^ trop The 'biased range' observation equation is identical to that of a 'pseudo-range', and given by 1^ AX + |£: AY 4- 1^ AY + |£- Aa + |£ Aa = (p° - p^) + v (17) dX 3Y dZ da o da, 1 o 1 where p : biased range, p . (t„) A J ^ p : observed value, p . (t_) c : computed value, P^.(t^) The observed value is given by equation (15) and (16) , whereas the computed value is obtained from P^.(T„) = R^.(t„) + ca° + ca^(T^ - t ) (18) A] 2 A] 2 o 1 2 o Q where ^a*^^9^ ~ range computed from the provisional coordinates of the station and the satellite at t c ^ a =0 o c a =0 1 The initial 'observed biased range', P, ■ (t )/ can take any value, including the corresponding pseudo-range, 2, (t ) if available or, more conveniently, is set equal to zero. In the latter case, the resulting a includes both the clock bias and the initial biased range. For every new satellite pass and every time there is a loss of signal during the pass, p . (x ) is reset to zero and a new unknown a is introduced. A3 o o 305 f 4 INTERFEROMETRIC PHASE READINGS An interferometric measurement consists of the difference between two phase readings, each taken at a receiver on a different site, and corresponding to a signal which left a satellite at a given epoch t. The concept of an interferometric measurement originates from radio astronomy and YLBI (Very Long Baseline Interferometry) , where interferometric measurements are made on the same wave front/ from a distant radio source (eg a quasar) / arriving to two radio telescopes on two different sites. The observables are either a delay time (between the arrival of the wavefront to the first and the second telescope) or a phase delay. In the case of GPS, the observable is a phase delay or a phase difference. However, for computational reasons, the phase delay measurement relates not to a given satellite epoch t, but to a common local epoch t. 4.1 Single Phase Difference oOp \i <^' %i^'^ satellite j local time t stations A,B Single Phase Difference Fig 1 The model equation for an interferometric 'single phase difference' observable has already been defined by equation (13) as 306 Substituting for N (t) and N . (t) from (8), one obtains where N,«-(t) = a „. + (f„ - f^) (t- t ) AB3 AB] B A O + -3-|r .(T) - R, .(T)|+ N^ + N^ c B3 ^3 ^°^ trop a ABj [r3.(t) - R^.(x)] ^(T ) - N^(T ) DO DO (19) (20) and ABj *B-*A ^o'^ initial (at time t ) clock bias ( ' 2tt ambiguity ' ) difference of phase readings of the GPS carrier at stations A and B, at the same local epoch t frec[uency offset between the two receivers at A emd at B satellite oscillator frequency initial ( ' lock-on ' ) time , observation time . Apart from the initial clock bias , also known as the so-called ' 27t ambiguity ' , the 'single phase difference' observable is free from the satellite clock (frequency) error , f , . The corresponding model obseirvation equation can be obtained by differentiating the observable Nj. _ . with respect to the 8 unknown parameters , X , Y , Z (coordinates of receiver at A) , X , Y , Z (coordinates of receiver at B; , tne initial clock bias (or 2ir ambiguity) a . , and the frequency offset Af (= f - f- ) . The resulting system of observation and normal equations has a rank deficiency of order 3, which is allowed for by holding the coordinates of one of the two receivers as fixed and setting the corresponding unknowns to zero. 4.2 Double Phase Difference satellites j , k local time t stations A, B Double Phase Difference with '2 Satellites' Fig 2 307 A further refinement is obtained by differencing two 'single phase difference* observables made to two satellites j and k from one another. The resulting 'double phase difference' observable is then free from all clock (frequency) errors, in both local and satellite clocks. The corresponding model equation is obtained by subtracting two appropriate equations (19) for two satellites j and k from one another. ABjk^ ABjk ion trop '^[ %^^'^ -"fik'^' -'^j<^> ^''aj'^' ] (21) where ABjk ABk hBj and ABjk ABk AB3 The only unknowns in the corresponding observation equations are the two sets of receiver coordinates (one of which has to be held fixed when solving the normal equations) ,and the initial clock bias (or ambiguity) , a ABjk* 4.3 Double Difference with Time Double Phase Difference with 'Time' Fig 3 satellite j local times T^ , T. stations A, B 308 The differencing of the single phase difference can also be done 'with respect to time'. The resulting 'double difference with time' phase observable is no longer free from Af , the frequency offset between the two local clocks at A and at B, but there is no longer an unknown ambiguity bias. The model equation for this observable is obtained by differencing two single phase observables (19) , corresponding to two local epochs t and i from one another. AB AB N,t,-(T, ,T_) = Af^„(T„ - Tj + N. (T-,T_) + N^ lT,,T„) AB] 12 AB 2 1 ion 1 2 trop 1 2 ^Bj^V "V^V -\j^V ^Wi^ (22) where \bj^'^1'^2^ \bj^'^2> - \bj(^i) (23) and "ab' *b-*a The 'double difference with time' phase observable can be shown to equal to a Doppler count difference, corresponding to two local times t^ and t , taken by two receivers at stations A and B respectively. 4.4 Triple Phase Difference Phase differencing can proceed even further by taking the difference of any two double phase differences (^either (21) or (22) ^ . The resulting 'triple phase difference ' is defined as either or N (t .T ) = N (t ) - N (t ) ABjk^ 1' 2' ABJk^'2^ ABjk^ l' = ^ABk^^l'^2) -\bj(^1'V- (24) The only remaining unknowns are the station coordinates, but as a result the number of observations is reduced by about a factor of 4 compared with 'single phase difference ' observations . Theoretically speaking, the different types of processing models should lead to identical results, if the higher phase difference observables are introduced with appropriate a priori covariance matrices. However, in general, these are difficult to compute and the observables are treated as uncorrelated . An important drawback of the 'double difference with two satellites' and 'triple difference' models is that they are free from any receiver clock frequency errors. Clock behaviour is important and should be monitored, tipping the balance in favour of either the 'single phase difference' or the 'double phase difference with time' processing models. 'Triple phase difference' observations, which are devoid of any clock errors, exhibit a smoother behaviour and are therefore very suitable for filtering gross errors, before final processing takes place. 309 5 INTERFEROMETRIC SOFTWARE AT NOTTINGHAM The first two GPS data processing programs written at Nottingham University were with 'pseudo-range' and 'biased range' observables. They were tested by using data from an STI 50lO GPS receiver, which was supplied by the US Defense Mapping Agency (DMA) . The data was processed and the results published in 1984 (Ashkenazi and Agrotis, 1984) o Since then work has continued on developing inter ferome trie phase algorithms and corresponding software. The new programs are ready and testing is proceeding with data from a pair of TI 4100 receivers. Details of the software are given in §5.4. 5.1 'Differential Doppler' Model A slight re-arranging of terms in the 'double difference with time' phase observable defined by equation (22) leads to an interesting result. N (t .T ) = N (x ) - N (t ) ABj^ 1' 2' ABj^ 2^ ABj^ l' = N (t ) - N (t ) - N (t ) + N (t ) Bj^^2' Aj^ 2^ '^Bj^ l' Aj^ l' = N^.(T^,T2) -\A.^,T^) (25) Equation (25) defines a 'differential Doppler' observable, obtained by differencing the Doppler (beat) count between local epochs t-l and T2 at station A from the corresponding Doppler count at station B. Clearly, this is the same observable as that defined by equation (22) , but a lot easier to acquire from the data recorded by a GPS receiver, and easier to visualize for somebody accustomed to thinking in terms of Transit Doppler. The corresponding observation equation is given by ^ dX A 9N ^ ^ ^B ^^ 3Y, A A ^ dY 3Y^ ^^B 1^ dZ 3Z A A 9N ^„ 9N ,.^ o c. = (N - N ) + V (26) where N = ^ABj('^l''^2) Af = ^B-^A and N N ^BjC^rV f . %i '^2' N°.(T,,T,) - N*^^ - it^ A3 1 2 ion trop BD 1 A] 2 Aj ^■] (27) (28) 310 5.2 Corresponding Satellite Epochs Local and Satellite Epochs Fig 4 satellite j satellite times: ^Al' Si ^2' ^2 local times : ■^Al' '^A2 '^Bl' "^32 stations A, B In equation (28) above, W^ ' W^'' -""b .J * [w -"bJ * [ w^ -\ oT (29) where X^ . , Y^., Z^. satellite coordinates at local epoch t provisional coordinates of receiver at B However, satellite coordinates can only be computed . from the broadcast ephemeris or interpolated from the precise ephemeris, by using satellite and not local epochs. Referring to fig 4, ^Bl = '<^Bl' = T , - - R . (t J Bl c Bj 1 (30) As an approximation, the value of R . (t^ ) can be taken as the corresponding pseudo-range, A . (t ) ; but in general it is much better to treat equation (30) as an iterative operator and start the iteration by setting the initial value of R_ . (t- ) to zero. BD 1 311 ^.3 Correcting for Local Clock Errors The continuous Doppler count (CDC) observables measured and listed by a GPS receiver assvime that the receiver's clock has no drift and that therefore the counts are made repeatedly for constant local time intervals. In practice, this is not the case, and the local times listed against the CDC's have to be corrected by the appropriate clock errors. In the case of a TI 4100 receiver, this can be done by carrying out repeatedly a independent point solution using pseudo-ranges and determining, in the process, the successive values of local clock bias with respect to GPS time. These a values are then subtracted from the corresponding local time epochs. 5.4 Software Details The Nottingham 'double phase difference with time' or 'differential Doppler' program is made up of 3 routines. The first, PREPARE, reads in pseudo-range and CDC measurements and checks for poor signal strength and missing count readings. The second routine, FILTER, reads in the pre-processed data from PREPARE, and outputs continuous Doppler count (CDC) readings at two stations corresponding to the same local epochs. However, before doing this , the two local clocks are synchronized with GPS time, as explained in §5.3, and the Doppler counts corrected to correspond to identical local times. The last routine, UNITY (University of Nottingham Inter ferome try) , is the main program, based on a least squares solution of 'differential Doppler'. The TI 4100 outputs CDC's at 3-sec intervals. However, for computational and other reasons, 30-sec intervals are considered more suitable. Each observation involves two stations and one satellite, and leads to an observation equation with 7 unknowns, ie the 3 cartesian coordinates of each of the two receivers and the frequency offset between their two oscillators. Additional simultaneous observations to other satellites, from the same two stations, do not introduce new unknowns. In particular, observations to 4 satellites, between two common local epochs, result in a system of 4 observation equations with 7 unknowns. The resulting 7 normal equations can then be reduced to a 6 by 6 set of reduced normals, by eliminating the frequency offset unknown. A 'cumulative least squares' procedure follows, with the final set of 6 by 6 equations solved by holding one of the two stations as fixed (ie by setting the corresponding unknowns to zero) . Back-substitution allows recovery of the successive frequency offset unknowns. ACKNOWLEDGEMENTS Research on GPS navigation and precise positioning at Nottingham University is supported by industrial research contracts, notably by British Petroleum, and a benefaction frcmMagna vox Advanced Products and Systems Company. The two research students directly involved in GPS research were individually sponsored by Nottingham University post-graduate studentships. The authors of this paper are grateful to several geodesists for fruitful discussions and exchange of information. In particular, they wish to acknowledge the help received from Dr R Wood and Dr A H Dodson from Nottingham University, Dr A T Sinclair from the Royal Greenwich Observatory, Dr C C Goad from the US National Geodetic Survey, Dr R J Anderle from the US NSWC, Mr M M Macomber from the US DMA, Mr R Hatch from the Magnavox Company, and Dr D Delikaraoglou from the Geodetic Survey of Canada . 312 REFERENCES Agrotis, L G 1984: ' Detexminatlon of Satellite orbits and the Global Positioning System'. PhD thesis, Nottingham University. Ashkenazi, V and Diederich/P 1985: 'Positioning by Second Generation Satellites: GPS and NAVSAT', The Hyrographic Journal, No 35, January 1985. Ashkenazi, V 1985: 'Positioning by GPS and NAVSAT: Will it be the End of Geodetic Networks?', Proc Survey and Mapping 85, Reading. Ashkenazi, V and Yau, J 1985: 'The Global Positioning System and Geophysical Applications', Proc EUG III, Strasbourg. Ashkenazi, V and Agrotis, L G1984: 'Satellite Positioning Systems and Geodetic Applications', Proc VIII UK Geophysical Assembly, Newcastle-upon-Tyne. Bock, Y, Abbott, R I, Counselman, C C, Gourevitch, S A, King, R W and Paradis, A R 1984: 'Geodetic Accuracy of the Macrometer Model V-IOOO', Bull G^od, No 58. Goad, C C and Remondi, B W 1984: 'Initial Relative Positioning Results using the Global Positioning System', Bull G€od, No 58. Hothem, L D and Fronczek, C J 1983: 'Report on Test and Demonstration of Macrometer Model V-lOCX) Interferometric Surveyor*, FGCC Report IS-83-2, NGS, NOAA, Washington DC. 313 ON THE ELIMINATION OF BIASES IN PROCESSING DIFFERENTIAL GPS OBSERVATIONS P. VanlSek A. Kleusberg R.B. Langley R. Santerre D.E. Wells Department of Surveying Engineering University of New Brunswick P.O. Box 4400 Fredericton, New Brunswick, Canada E3B 5A3 ABSTRACT An ideal processor of GPS differential observations should have the capability to eliminate as much as possible the effect on estimated positions of different biases — e.g., those originating in orbital ephemerides, clocks, and atmospheric delays — and of phase ambiguities. These effects can be eliminated either Implicitly (as was implemented, for instance, in the GEODOP Transit data processing program) or explicitly, after the biases themselves have been estimated. In this paper, we show the relative merits of both these approaches and experimental results using different update intervals. Other attributes of an ideal processor of GPS differential observations are also discussed. INTRODUCTION The Department of Surveying Engineering at the University of New Brunswick (UNB) has been involved in designing GPS positioning software for the past five years. During this time, our thinking has evolved resulting in the differential positioning software package presented here. This latest version of our software was implimented on an HP 1000 minicomputer. This paper focusses on the bias modelling aspects of our software. Other aspects of our experience are described in other papers appearing in these Proceedings [Kleusberg et al., 1985; Wells et al., 1985; Beutler et al., 1985; Moreau et al., 1985]. However, to put the bias modelling in perspective, we also outline what we think an ideal software package should do and what it is that our software does at present . We have also decided to concentrate on the explanation of the problems and concepts involved as well as presentations of numerical results rather than the mathematical formulation. We have discussed the mathematical and physical basis of our software elsewhere [Van^Hek et al., 1985]. THE IDEAL PROCESSOR The basic GPS observations, be they. code pseudoranges or carrier phase, are biased ranges . The challenge in processing GPS data is in how best to handle the biases in order to extract the true ranges. The biases originate from a small number of sources : 315 - Imperfect clocks in both satellites and receivers; - Ionospheric and tropospheric delays; - cycle ambiguities, in the case of carrier phase observations; - orbit errors. We introduce the concept of observing "session": it is the time span over which GPS signals are received continuously and simultaneously by both receivers. It is also that part of an observing campaign characterized by a unique set of biases . Several approaches can be taken to deal with these biases. If a bias has a stable, well understood structure, it can be estimated together with the station coordinates as nuisance parameters (cycle ambiguities, tropospheric delay scaling, orbit biases). In some cases, additional observations can be used, either to directly measure the bias (ionospheric delay), or to derive a model for the bias (tropospheric delay). Finally, if a bias is perfectly linearly correlated across different data sets, it can be eliminated by differencing the data sets (clock biases). This last approach warrants further discussion. The double differencing technique (differencing across satellites, to eliminate receiver clock biases, and across receivers, to eliminate satellite clock biases) works well. However, it introduces some mathematical correlations in the data. If r receivers continuously and simultaneously track s satellites, then there are r(r-l)' s(s-l)/4 possible double difference data series which can be formed, only (r-l)*(s-l) of which will be independent. Even with the present baseline-by-baseline observing techniques, it is not always simple to decide how best to form the double differences. It is worth while considering whether alternatives to double differencing can be devised, which will be as effective in handling clock biases. In particular, can the nuisance parameter approach be taken? If we have phase measurements from s satellites at r receivers (i.e., r*s time series (t)), to foirm the "traditional" single differences we subtract the time series between pairs of stations (eliminating the influence of satellite clock errors) . This reduces the number of time series from r*s to (r-l)s. If, instead, we were to introduce as nuisance parameters s time series of satellite clock bias parameters, one such time series for each satellite clock, the effect should be similar. More specifically, consider the (simplified) observation equation: ^i^V = '^^^V " ^i' ■*" ^^t^^'^k^ "^ ^^^i^ V ' i "*■■*■ i where pr(t ) is the observed range from receiver i at R. to satellite j at r-" at time t, ; c is the speed of light, and where At represents the satellite clock error, and AT- the receiver clock error. In the differencing approach, we .difference two such equations from different stations i, in which case the At (t.) term (which is independent of i) disappears. In the .nuisance parameter estimation approach, we solve for independent values of At (ti^) for each t, , using observations from all stations i. (Note, if we were to explicitly eliminate the nuisance parameters from the normal equations, we would, in effect, return to the differencing approach.) The advantage of the nuisance parameter approach is that we can then work with "raw" phase 316 measurements, and not have the complicated bookkeeping and correlation problems involved in processing differenced observations. Similarly for double differences — instead of differencing between satellites, and (in the "traditonal" method) reducing the number of observational time series from (r-l)s to (r-l)(s-l) (eliminating the influence of the receiver pair differential clock errors) — we could introduce instead r time series of receiver clock bias parameters. We lose nothing from the degrees of freedom point of view. In the differencing approach we reduce the same number of observation time series as we add in the nuisance parameter estimation. And our flexibility is vastly improved. For example, merely by fiddling with the a priori weights on these nuisance parameter time series we can enforce the equivalent of single difference or double difference (and "partial" differencing) very easily. Also, by introducing some kind of serial correlation function (i.e., smoothing the nuisance parameter time series), we can effectively vary our model for these clocks from something that is considered completely uncorrelated (an independent nuisance parameter for each satellite and each receiver at each time epoch) to something having strong serial correlation over lengthy periods (equivalent to using a model with only a few nuisance parameters such as a truncated power series in time) . This would mean that one algorithm, with options on the nuisance parameter weighting and serial correlation, would effectively duplicate the phase, single, and double difference algorithms. This approach would make it imperative to process all the 'observations from one epoch in one step. It would, however, place no limitations on which of the many possible observing strategies was used, the selection of which could then be made on other grounds (logistics, cost, time, etc.). DIPOP PHILOSOPHY Our present program package, the Differential Positioning P^rogram (DIPOP) package is the result of several years of development. It stems from the following basic ideas : (i) It should be capable of processing data collected by any GPS receiver through a system of tailored preprocesors . (So far only Macrometer" V-IOOO and TI 4100 preprocessors exist in the DIPOP.) (ii) Observations (carrier phase time series) could be processed in any desired mode: biased ranges, single differences, double differences, triple differences. (iii) Cleaning up of observations (pre-estimation of range biases — ambiguities, elimination of cycle slips, elimination of bad observations, reduction of number of observations if necessary), preparation of pseudo-observations (various differences) and evaluation of satellite positions (see, e.g., Beutler et al.[l984]) should be done within the preprocessors. (iv) The main processor should process pseudo-observations in a sequential manner within each session [Langley et al . , 1984] as well as session by session. At present, the step of the sequential process is variable from one epoch up. 317 (v) Positioning, rather than position differences, must be estimated. This is made possible by employing the weight matrix of the initial estimates of positions, called P -matrix (see, e.g., Vani^ek and Krakiwsky [1982]). Proper employment of a P -matrix can also take care of the crudest form of orbital biases, the common translational bias of all orbits with respect to the coordinate system in which the initial positions of unknown stations are given. (vi) The main processor must be designed to estimate (and eliminate the effect of) the whole family of biases: the ambiguities, clock biases, orbital biases, tropospheric and ionospheric delay biases. (At the moment only ambiguity and clock bias estimation have been fully implemented.) Biases can be estimated at any step of the sequential filter. The most up-to-date estimates of biases are used continuously to eliminate the effects on observations. Biases are estimated only within individual sessions [Vanf^ek et al . , 1985]. (vii) Full variance-covariance information about the estimated positions and biases must be available. (viii) A comprehensive output, including optional plots of position determination histories, residuals and biases, should be available. (At present this is the role of the postprocessing program.) COMPARISON OF BIAS ELIMINATION MODES It is clear that the biases can be evaluated/updated either at each epoch, at desired intermittent times, or only at the end of each observing session. For the time the biases have been updated, it is immaterial what mode has been used up until that instant; the results are — at that instant — identical. One strategy — elimination for each satellite pass--is similar to the strategy used in the Doppler observation processing program GEODOP [Kouba and Boal , 1976]. The other extreme strategy — elimination at the completion of processing of unknowns — is equivalent to a batch mode adjustment. The most compelling argument for the bias to be evaluated as often as possible is to keep the resulting positions determined by the sequential filter as accurate as possible at all times . The most compelling argument for the bias to be evaluated as seldom as possible is to keep the computer time (consumption) low. To illustrate this point, let us quote a study done by our undergraduate students in SE4231 (Special Studies in Adjustment): For a configuration consisting of 3 satellite receivers and 4 satellites, 1 hour session sampling at a rate of 1 observation per minute (resulting in 720 "observed" double differences), the following statistics hold. The bias elimination and bias evaluation/ elimination approaches require about 3.4 x 10 operations each. Evaluation at every second epoch results in a reduction of 41% in the number of operations, every fifth epoch gives a reduction of 65%, and every tenth epoch a reduction of 74%. Clearly, if the study of evolution in time of position parameters is of interest, we may wish to either evaluate the biases at each epoch or go for some intermittent solution, as we have done in the cases discussed in the next section. 318 EXPERIMENTAL RESULTS In this section, we describe some results obtained by range bias and clock bias modelling using data (carrier phase series) collected by Macrometer™ and TI 4100 instruments in two different locations in Canada (Ottawa and Quebec City) for short (550 m) and long (66 km) baselines processed in a "baseline mode." The "network mode" results require more extensive analysis which would be inappropriate for a paper of this length. On Figure 1 we show changes in the length of a 548.58 m long baseline observed during the Quebec City Macrometer™ 1984 campaign [Moreau et al . , 1985]. Double differences of carrier phase recorded by the V-1000 receivers during one 3-hour 20-minute long session were processed in a baseline processing mode using three different approaches to range bias (ambiguity) elimination. In the first approach, the range biases were solved for in the preprocessing stage, using the values obtained from an earlier processing run rounded off to the nearest integers and all double differences corrected accordingly. No further estimation for these biases was carried out during the main processing. The second approach consisted of solving for range biases during the main processing at every 10th epoch. So estimated values we rounded off to nearest integers and held fixed for the next 9 epochs . It can be seen from the plots that the final solutions from both these approaches are identical (548.5845 m) and depart from the invar-taped "ground truth" (548.5834 m) by 1 . 1 mm, i.e., by 2 ppm. Clearly these two approaches give identical position results every 10th epoch. The Macrometer™ results presented here do not take into account the mathematical correlations between the double difference observations and therefore differ from the values presented in the paper by Moreau et al [1985]. In the third approach, we solved for range biases during the main processing at every epoch. These estimates, however, were not rounded off; they were used as real values in correcting "observed" double differences. The final solution for the baseline length (548.5815 m) departs from the ground truth by -1.9 mm, i.e., by -3.5 ppm, and from the two integer-bias-solutions by -3.0 mm, i.e., by -5.5 ppm. It is interesting to note, however, that during the course of measurements, the difference between this and the integer-bias approaches reaches up to 12.5 mm (epoch 41), i.e., to 22.8 ppm, clearly an unacceptable difference. In Figure 2 we have displayed results from another experiment. This time we have taken the longest baseline (66,268.70 m) observed during the 1983 Ottawa Macrometer™ campaign [Beutler et al . , 1984]. The recorded double differences from three 5-hour long sessions were processed again in the baseline mode using three different techniques. For the sake of simplicity, results are displayed again in terms of baseline length variations. The first technique solves for ambiguity and clock biases at every 20th observing epoch as well as every time a new satellite rises above local horizon and uses these biases to evaluate baseline coordinate differences for all the intermediate epochs. We arbitrarily perturbed the "ground truth" coordinates of both points by about 3 metres and specified again the P matrix for both points accordingly. This we call the "floating points solution." 319 Significant perturbations of the order of 10 ppm occur at the very beginning of the plot (around epochs 20 and 40). At epochs 60 and 160 perturbations of the order of 1 ppm perturb an otherwise relatively smooth curve. These glitches are associated with some changes in the satellite configuration as shown on the plot . The second technique seeks the solution by eliminating both ambiguity and clock biases at each epoch. The final solution as well as all the interim solutions at 20th epochs are identical, with the final length being 66,268.827 m. The result differs from the fixed point solution presented by Kleusberg et al . [1985]. Between the evaluation epochs the two solutions vary but no more than expected from the character of the curve as discussed above in the context of the first technique. The third technique was essentially the same as the first except that clock bias was not sought. The character of the curve is similar to the first curve except that the departures from the mean are less pronounced. The final line length is 35 mm shorter (corresponding to a difference of -0.5 ppm) compared to the first two techniques, the latter being closer to the ground truth. None of the three techniques shows any discontinuity between sessions. Figure 3 shows the last experiment we wish to report on here. The experiment focusses on the question of what effect does weighting of initial positions have on relative positioning. We have taken again the longest (66 km) baseline of the Ottawa network and double differences collected by a couple of TI 4100 receivers [Kleusberg et al., 1985]. Then we have estimated the baseline components (A(t), AX, Ah) using two different solutions: first we specified the initial coordinates of both points to have the values obtained from GSC adjustment of terrestrial and Doppler data [McArthur, 1985]. We then declared the position of the first point to be known exactly rendering the diagonal elements of that part of P matrix which belongs to the first point very large. The part corresponding to the second point was chosen so that it represented one sigma uncertainties in coordinates of the second point equal to 1 m. This is what we call "fixed point solution." The second approach solves for the relative positions assuming both points to be equally badly known (the floating point solution). Again we perturbed the "ground truth" coordinates at both points by about 3 metres and specified again the P matrix for both points accordingly. In this case, both points are forced to wander away from their initial positions to a certain degree to assume positions that are the most compatible with the observations. One may think of this solution as acknowledging that there may be a several metre translative bias in the given ground coordinates compared to the coordinate system in which the GPS satellite positions are given. This is probably a realistic assumption. However, other sources of error may contribute to the observed translation. The comparison of the two sets of results is interesting. There seems to be a definite bias involved in the comparison of the two coordinate systems used. The differences "floating points minus fixed point solutions" given in local geodetic coordinate systems of the end point are 5(t) = -85 mm, « o c CO a 9 u w 500 400 300 200 100 -100 -200 -300 -400 -500 ^ 5 r i s e s II. M M M M (^ III/ '^ #4riseftV "/ #9rjse s ■ - ! 'V\ A ' / / ' #5rl8e8>:..^/'^'^ t A -V W '^ t. ^J;X ^— — H > J I i_L I/) 9) #=5sets 80 100 120 Epoch number 140 160 / ^1 100 80 60 40 20 --20 -40 H-60 -80 -100 110 I Number of visible satollites FIGURE 2. Change in the length of a 66 km long baseline implied by partial solutions. (1) solution for clock and range biases determined at every 20th epoch. (2) solution for clock and range biases determined at each epoch. (3) -- solution without clock biases • epoch of bias update for solution (1). special event, xxxx no solution in this interval due to lack of observations. Note change of scale at epoch 40. Discrepancies are, for each solution, with respect to tne tmal length of the solution. 323 I I I I I (luuj) Aouedajosip q^Buai M C ti ■H C ■P -H 3 o rH O. w < o ^ s-« <+-i Ti 0) T3 -H -0 r Q) M fl) 1— CO C x M- fO u ' iz: CO c nj o x; CO -H (J (U iJ •H 3 O rH . C O ro CO CO o- M cu r O O (U O CO X H -H •r^ P4 Q UH 324 MODELING THE GPS CARRIER PHASE FOR GEODETIC APPLICATIONS Benjamin W. Remondl National Geodetic Survey Charting and Geodetic Services National Ocean Services, NOAA Rockvllle, MD 20852 ABSTRACT. This paper deals with GPS L-band signals after the various modulations have been removed (leaving Doppler-shif ted carrier signals). The carrier phase quantity and the measure- ment of this quantity are described. Then a physical model for the carrier measurement is developed. Advantages and dis- advantages of defining new observables as linear combinations of the raw measurements are considered. Attention is given to employing simple and descriptive notation so that the model is easy to understand and to program. Computational aspects, with regard to processing these data, are included. INTRODUCTION Each GPS satellite transmits unique navigational positioning and identifi- cation information centered on two L-band frequencies L^ (1575.42 mHz) and L_ (1227.6 mHz). The L^ carrier signal is modulated with a precision code, known as the precise positioning service (PPS) code, and a coarse acquisition code, known as the standard positioning service (SPS) code. On the other hand, the L„ carrier signal is modulated with just the PPS code. These codes are pseudo-ran- dom noise codes: the PPS code has a chipping rate of 10.23 mHz and a repeat per- iod of 37 weeks; the SPS code has a chipping rate of 1.023 raHz and a repeat per- iod of 1 ms (Spilker 1978). Both signals, L^ and L_ , are also modulated by a 50 bit per second (bps) message which includes, primarily, satellite orbit and timing Information. The PPS and SPS codes are used for identifying the GPS satellites and, along with the 50 bps message, for satellite to receiver transit-time ranging and the synchronization of code receivers to GPS time. The PPS code is complex and difficult to acquire; a receiver may therefore first acquire the simpler SPS code and switch to the PPS code via the "handover word" in the 50 bps message (Van Dierendonck et al. 1978); if the a priori receiver location and orbital infor- ation are of high quality, immediate PPS acquisition is possible. Thus, these L-band carriers are modulated by codes and message information. Receivers with knowledge of these codes have a number of advantages such as: (1) high signal noise suppression; (2) rapid and easy receiver clock synchroniz- ation to within 10 to 100 ns; (3) availability of GPS broadcast ephemeris data for real-time applications; (4) real-time availability of transit-time ranges for instantaneous point positioning to 10-30 m as well as several hour point positioning at the 1-m level; (5) acquisition without a priori almanac preparation. Measuring the carrier phase can be readily accomplished once the modulation is removed from the carrier. Code receivers use correlation methods to generate a modulation-free replica of the satellite carrier. Some receivers which do not possess knowledge of these codes strip the code and message from the signal (e.g., by squaring the signal); others can operate In spite of the phase discontinuities 325 caused by the codes and the message data. (For example, the number of zero-cross- ings of a pure sinusoid will not change when subjected to random 180" phase rever- sals.) Some non-code GPS receivers, therefore, successfully treat the L-band signals, after signal processing, as signals having twice the nominal carrier freq- ency, and thus half the wavelength. Although code receivers have some tremendous advantages from the point of view of real-time activities and simplicity (especially in the presence of dithering — intentionally perturbing the carrier), non-code receivers are very useful as well, especially for relative positioning. Even real-time time interval transfer and real-time relative positioning can be accomplished with non-code receivers. In fact, it is possible to determine, in real time, the relative motion (trajectory) of one non-code GPS receiver with respect to another non-code receiver to the centi- meter level (Remondi 1985). In the following sections, carrier phase will be described, modeled and analyzed in terms of performing point positioning and relative positioning, although the emphasis will be decidedly on the latter. The discussion will begin with a des- cription of carrier phase and the measurement of carrier phase. Then a model of the raw measurement will be developed with no consideration given to the prop- agation delays. Some practical least-squares considerations will be included. Advantages and disadvantages of forming various linear combinations of the raw measurements will be discussed. Emphasis will be placed on those combinations which have thus far proven to be most practical. Because loss of lock and cycle slips have proven to be nui- sances, an approach to overcoming these problems automatically will be sketched. A SIMPLIFIED DESCRIPTION OF CARRIER PHASE The GPS satellite L. and L„ carriers are, nominally, at 1575.42 mHz and 1227.6 mHz, respectively. Let f be the nominal frequency of one of these car- riers. The phase of the carrier signal will now be described. Figure 1 depicts the received carrier signal as a function of time. L-HAND CARRIER S -.bL—i I L d, -I 10 IS 20 SB 30 30 40 TIUH (IN QUARTER CYCLES) Figure 1. — Received L-band carrier signal. By the fractional phase of this carrier, F(t), is meant the point in the cyclic oscillation at time t. For example, at t*l the phase is 0.25 cycles (or 90°). One can plot the fractional phase as shown in figure 2. If one describes phase as a monotonic function, <|>(t), based on the number of cycles which have been re- ceived since an initial time t , the corresponding phase plot would be as de- picted in figure 3. In this idealization the phase is shown as a linear function of time. The phase history of the received GPS carrier, however, would not be truly linear due to the Doppler effect (as well as numerous secondary effects such as oscillator drift, refraction effects, relativity, etc.). Consider the depiction in figure 4. A GPS 326 F(t) FRACTIONAL PHASE 10 IS 20 20 30 TIUS (IN QUARTER CTCLSS) 30 40 Figure 2. — Fractional phase of the L-band carrier. (t ). A GPS receiver will receive this phase event at a time t 1 S 1 H according to its own time reckoning. In actuality, the receiver will be wrong and the true receipt time will be t +fit (where 6t represents how much the K R R receiver's clock lags GPS ephemeris time). This is a crucial realization; this truth applies to the receipt of all phase events. CONCEPTUAL DESCRIPTION OF THE CARRIER PHASE MEASUREMENT PROCESS One could count signal peaks or zero crossings as they were received, but the count would be meaningless unless it were made over a fixed time interval. This implies the receiver must have a stable oscillator. One could time tag occasional zero crossings; this too requires a stable receiver clock. Since a receiver clock (oscillator) is Indispensable, why not measure the phase of the incoming signal with respect to the phase of the nominal GPS carrier signal generated by the re- ceiver oscillator? Thus it makes sense to measure ^ ~ ^t)' This is the approach used by the MACROMETER™ (Counselman and Gourevitch 1981; Counselman and Steinbrecher 1982) and the TI-4100 (Ward 1982). It is not the only approach, however. The SERIES approach (MacDoran et al. 1982; MacDoran et al. 1984a; MacDoran et al. 1984b) takes advantage of the fact that there is a rich spectrum emanating from GPS satelites. SERIES exploits the fact that there is a known phase relationship among the numerous frequencies (e.g., L^ , L„ , PPS code, SPS code, L^ - L_ , etc.) and converts phase measurements, at many frequencies, to (biased) range measure- ments. SERIES uses the low frequency signals for ambiguity resolution, and the high frequency signals for range measurement precision. Other approaches are possible (e.g., Interferometry) . In this paper only the approach of measuring carrier phase relative to the phase of a GPS receiver's local oscillator will be considered in detail. Consider the simplified depiction of a GPS receiver shown in figure 5. Suppose It can track five GPS satellites simultaneously. We shall assume that there are no interchannel biases, or that one channel is used for all satellites in MACROMETER™ is a trademark of Aero Services Division, Western Geophysical Com- pany of America, 8100 Westpark Drive, Houston, Texas 77063. 328 a multiplexing mode. Visualize the carriers of these GPS satellites passing through the receiver in the upper five panes while the receiver's own carrier (which is passing through the lower pane) performs two functions: First, the receiver time will be based on the number of cycles which pass the cross hair; w Ant. Receiver Oscillator GPS Receiver crosshair \ '\/\A/\/\/W\ ^VW AAAAAA/NAAA VWWWNAAA/ crosshair / /\AAAAA>V\A Figure 5. — Conceptual depiction of a five-channel GPS receiver. Second, when the number of cycles that passes the cross hair corresponds to a prescheduled measurement time, say t , the five cross hair differences ()> ~ ♦«> X S K. j=l,...,5, will be measured (e.g., within ±0.01 cycles) and recorded. Let us realize, from the start, that although the receiver "believes" the time to be t in terms of GPS ephemeris time, the actual measurement time is t.+6t,, where St, is unknown (but very real). Let us designate the transmission time associated i i with t.+6t, by tz, . (Since all the satellite phases are measured at the same time, the transmission times must be satellite dependent.) It is not essential that our relative phase measurements be taken simultaneously; however, it is convenient if that is so. Should they be taken at slightly different receiver times (within the stability period of the satellite oscillator), this could be dealt with satis- factorily. There may be a discrepancy between the receiver "realized" time t and the actual observation time. A constant discrepancy common to all channels Random interchannel would be indistinguishable from St, and would be harmless, discrepancy differences at the few picosecond (ps) level would be consistent with phase measurements at the ±0.01 cycle level. Large systematic variations (e.g., 100 ps/hr) are avoidable with careful design. It will be assumed here, without loss of generality, that the relative phase measurements are taken simultaneously. In summary, if m (i) is our measurement, having time tag t , the measurement-model relationship might be assumed to be: m^(i) « ^(t^(i)) - V^i^^^i^ ^ ^^^^^ * ^^^^^ ' ^2^ So long as carrier tracking is maintained, only one integer unknown (per receiver, per satellite, for all times) appears in the model. DEVELOPING THE MODEL Ignoring such factors as propagation delays, relativity, etc., the transmission time of the carrier phase [event] can be modeled as t^(i) - t^ + «t^ - T^(t^+«t^), (3) where x (t.+4t ) is the actual signal transit time from the j-th GPS transmitter to the GPS receiver. f^(t,+6t ) can be represented as 1(1) where x^(i) a T^(t^+6t^) - ip^Ft^ + 6t^ - \l>Ht^ + 6t^ - ^P^(----))] . (4) c is the speed of light, and p is an instantaneous geometric slant range. Notice >f J, that, in eq. 4, p^ is a function of all that follows it. These are not to be interpreted as multiplications, x (i) is a series expansion of p /c about t + is about t«t . , the scheduled receipt time, and not the actual receipt time, t, has the unique prop- erty that it is common to all receivers scheduled to take measurements at epoch t . . Thus t. and ^ (t.) are, both, receiver independent. Suppose there are n satellites, n receivers and measurements are scheduled to be made at t «t,+(i-l)*At, where i»l,*-*,n and At is the selected epoch inter- val. Suppose, for simplicity, all n satellites are "visible" over the scheduled period and there are no losses of lock. In such a case there would be n -n-'n- •^ ^ s R E measurements 330 where M represents the receiver and where the symbol 6 t. represents receiver n 1 M's clock error at t , ; it is not a product of quantities. The quantity p.. defined 1 M *>y B»j(i) ^ f ^*«t. - 4>n(t +dt.) is effectively independent of satellite since ■;M AsMl-iRi i f-* s f +Af"^ where Af is, typically, on the order of a few Hz and 6„t. s s s s Ml. varies from microseconds to milliseconds — depending on receiver type. For a specific example, suppose n ""B, n =»3 and n =100; there would be 1800 measurements. Assuming perfect orbits, no medium delays, etc., there would be 927 unknowns in the 1800 equations: 600 ^, 300 « t . , 18 N^d), and 9 S R Ml M 4 4 coordinate unknowns (the receivers' coordinates are included in the -f •x~,(i) s M term). See Goad (1985) for an excellent treatment of processing this observable. This somewhat simplified discussion does not bring out that in the "real world" singularities must be addressed. Briefly, there is Insufficient geometry to 1 M determine, precisely, all the 6 t, and the <}> -(|> . This singular situation can Ml s K be rectified by establishing references. Thus we can express 6..t. as fi„t.-6„t. Mi M i M 1 + 6„t, and solve for n_ of the 6„t, and (n„-l)'n_ of the 6„t .-6-.t- . It would Ml R Ml t, R MlMl be seen that the 6„t. would be determined at the microsecond level whereas the M 1 4-^t,-6„t- would be determined at the subnanosecond level. The explanation is Mi Ml that fi„t, is determined from the satellite-station dynamics, whereas 6„t,-6^t, Ml MlMl results from continuous phase tracking. Although slightly more involved, the same 1 M approach could be applied to p« Another point to stress is the distinction between the nonlinear model given in eq. 6 and the linearized version to be discussed later. The nonlinear model should be used for the computational model and the linearized version of the model used for determining the analytic partial derivatives for the design matrix in the normal equations. A practical advantage is that the data reduction can be handled should receivers inadvertently take measurements many seconds apart. FORMING LINEAR COMBINATIONS OF RAW OBSERVABLES Depending on the objective, there are significant advantages and disadvantages to forming certain linear combinations of the basic phase measurement mr^d). One- station combinations do not require common satellite visibility between geodetic locations. When common satellite visibility is imposed (as in single differences), and the GPS receivers are part of a global network, one sometimes discards valu- able data. Also, if the optimal estimation of the phase profiles of the GPS satel- lites is desired, one-station observables may be preferred. On the other hand, the requirement of intervisibility is not overly restrictive due to the 20,000 km altitude of GPS satellites. When observations are formed using nearly simultaneous measurements from two stations, the <|> (t.) term drops s 1 out of the model; the behavior of the satellite clock only appears by way of the f factor over, at most, a fraction of a second. When observations are formed 9 using nearly simultaneous measurements from two satellites, at one station, the station clock term &„(i) drops out of the model. The behavior of the receiver n clock, *t , appears, therefore, in a relatively harmless role (see eq. 4) and it can be replaced by a linear model. Whereas hundreds and easily thousands of un- knowns must be determined when modeling the raw phase observation, only a few need to be determined when two-station, two-satellite combinations are formed. One 331 must account for the correlated nature of such observations for precise applica- tlons. The three most useful one-station observables are mr,(i), m^(i)-mr:(i) , and mrj(i+l)-mrj(i) , where M Is the receiver, j and k are satellites, and 1+1 Is the epoch number which follows epoch 1. Although single-station combinations are advantageous for certain applications, only two-station applications will here- after be considered. SINGLE DIFFERENCES Using eq. 6 as the fundamental model, define the single difference obser- vation (Goad and Remondl 1984; Remondl 1984) using station 1 and station 2 as follows: S(j,l) = m^(i) - m](i) where N^(l) = N^(l) - N^(l) and e^(i) = e^(i) - e^(i). If the receiver oscillators are highly stable, „(t +6t ) = 'l>t»(t,) + f„6t.. If the receiver R 1 1 R 1 R 1 oscillators have been tuned with respect to f , then s The minus sign stems from the convention established when St was defined, (i.e., 6t is negative vjhen the clock runs fast because the measurement would be taken too soon). The single difference model, under these assumptions, reduces to: s(j,i) = f3-(«2ti ■ s^i - "^i^^^ * ""i^^O ^ ^^^^^ ■*" ^^^^^ ' This model is nonlinear in the 6t. in that the x (1) must be evaluated at the true signal receipt time t +6t . To form the normal equations, one linearizes eq. 8 as follows (see eq. 4): (7) (8) S(j,l) i f^(«,t, - fi,t,) + N^(l) + e^(l) s z 1 11 c s c s P^(t^) + (>^^it^)(s2t^-Pj(t^)/c\ P^(t^) + Pi(t^)(«jt^-Pj(t^)/c) (9) where p is range rate. The partlals of S(j,l) with respect to 6 t, are M 1 ^i(i-;^i T c s I »-♦ ^-^ \ c s 2^ c s VPo/ \_dx^ 9x„J 3x„ ^ 2' c s I ^-> ^-* 1 c s „-♦ c s \p,/ I9xj axjj axj K -> T (10) Notice that the partial derivatives of the station components are components of the station to satellite unit vectors times a constant (f /c). In practice one avoids a singular solution by solving for the differences 6 t -6 t, (which come from continuous phase tracking) and the reference S.±^ (whXcn comes from M 1 satellite-station Doppler) rather than ^wt . • It may also be useful to define a relative clock drift parameter 6.=6^t,-6-t and a common drift parameter C.=(6^t +6^t,)/2. The advantage of this is that C, can be replaced with a con- stant or linear model thus reducing the number of unknowns. In such a case, 6. and the ^.-^i would still be estimated. If the receiver clock differences are measured Before and after data collection, then S^ can be computed a priori and need not be estimated. Simplifications to the data reduction can be found in Remondi (1984: 49). When more than two stations are involved, one should ac- count for the correlated nature of the single differences. One aspect to single differences, not yet addressed, relates to the N (1). In the least-squares process they are treated as real (noninteger) numbers. The coefficient of N (1) is constant; the coefficient of fi-t--6.t^ is very nearly constant. Thus, there may be insufficient geometry to distinguish N (1) from 6^t -6 t^ . Thus, the integer value of N (1) cannot be isolated — even for short base lines. The integer difference between satellites will be apparent, however, because f"^(5^t,-6, t, ) will subtract out (reducing the effect of 6-t,-6,t, by a s 2 1 11, ki 2111^ factor of 10 to 10 ). Once the N (1)-N (1) have been established, they can now be fixed in a subsequent reduction. Taking advantage of the Integer nature of the N (1) is important if one is to achieve millimeter accuracy — especially for short base lines. It should be pointed out that if tracking is interrupted, the integer number of cycles from that point will likely be wrong once tracking is resumed (the fractional phase measurement should be unaffected). One can account for these lost cycles during processing however. More will be said about this, later, in the triple difference discussion. DELTA SINGLE DIFFERENCES Let us define the delta single difference as follows (Remondi 1984: ch. 4): DS(j,l) » S(j,l+1) - S(j,l) . (11) The model and partlals can be taken from subtracting those from the corresponding single differences. Notice, however, that there are no integer ambiguities N (1) in this model. The advantage is the insensltivity of the model to loss of lock; 333 the disadvantage is one cannot exploit the integer nature of the ambiguities. Thus, for short base lines, the ultimate in accuracy may not be achievable. For many applications this is not a serious loss (e.g., industrial applications). Other disadvantages are the correlated nature of the observations (Remondi 1984: 108-114) and the requirement to solve for the epoch time parameters (the 6^.t,-6,t.), Mill DOUBLE DIFFERENCES The double difference observable is defined using satellites j and k at epoch i as follows (Bossier et al. 1980; Bock et al. 1984; Remondi 1984): DD(j,k,i) = S(k,i) - S(j,i) . (12) The model and the partials are taken from corresponding differences of single differences. In this scheme one satellite, say j, becomes the reference satel- k 1 lite, and the integer unknowns are N (1)-N (1). For short base lines these integ- ers can be isolated since the contribution made by the clock drift terms, 6t., has 6 ^ been reduced by the order of 10 . Thus it is satisfactory, even for precision applications, to use a linear clock model for the station clocks. The double- difference method is much like the single difference method. The slight disadvan- age to using single differences is that one must either determine or eliminate the clock drift parameters (for time Interval transfer this would be an advantage); a slight disadvantage of double differences is their correlated nature. TRIPLE DIFFERENCES The triple difference observable, using satellites j and k, at epochs i and i+1 , can be defined (Remondi 1984) as either DS(k,i) - DS(j,i) or DD(j,k,i+l) - DD(j,k,i). In either case: T(j,k,i) = f^T^t^d+D-T^Ci-*-!)) - (x^(i)-T2(i))l - f^|(TJ(i+l)-tJ(i+l)) - (TJ(i)-tJ(i))l . (13) The main advantage of the triple difference method is its robust nature. When a loss of lock is encountered only data at a single epoch will be edited, and process- ing will continue. In fact, numerous losses of lock can be handled with ease. For this reason, hundreds of base lines can be processed in (unattended) batch mode. If the receiver oscillators are synchronized and tuned, and if the station 1 coordinates are sufficiently well known, then as few as three parameters need to be estimated (namely, the coordinates of station 2). The main disadvantages of this scheme are: (1) the correlated weight matrix is more complicated; and (2) as with delta single differences, one cannot exploit the integer nature of the biases. It has been shown (Remondi 1984: ch. 7) that when one accounts for the correlated nature of triple differences, relative geodesy can be performed at the 1 ppm level; when one does not, 10 ppm (or better) is achieved. AN AUTOMATIC APPROACH TO LOSS OF LOCK AND CYCLE SLIPS When a satellite signal is obstructed, it can no longer be tracked. When the satellite reappears, tracking can resume. The fractional phase, then measured, would be the same as if tracking had been maintained; the integer number of cycles 334 would be wrong, however. There are numerous possible approaches to dealing with this problem. A common approach is to hold the stations fixed and to edit the data manually. This has proven to work, but it can be tedious. Another approach is to model the data with piecewise continuous polynomials on a satellite depen- dent basis (Beutler et al. 1984). To implement this approach the data would have to be examined to find the breaks, which could be tedious. This would be followed with some manual editing at the few cycle level. Although many approaches are possible, I shall herein sketch an automated ap- proach which is easy to implement. Use the triple difference processing method to determine station location(s). Once convergence has been achieved, automatic- ally search through the triple difference residuals to isolate "large" discontinui- ies in double differences, where the choice of what is deemed large is Important. For example, 2 cycles or 10 times the root-mean-square (rms) of the residuals might be the criteria. The triple difference method is ideally suited for this task because (1) it is not confused by clock drift, and (2) it knows, based upon its own very good station solution, how many cycles to expect over any time interval. One would evaluate all such triple difference residuals over an epoch interval and determine which satellites had integer jumps and by how many cycles. (For example, if the SV-6 minus SV-8 residual was 10.02 cycles, and the SV-9 minus SV-8 residual was 12.97 cycles, one would remove 10 cycles from SV-6 and 13 cycles from SV-9 at all epochs from i+1 to the end. True, this might result in a common in- teger error for SVs 6, 8, and 9 at this epoch; it would drop out, however, in double difference mode.) Finally, the single- or double-difference method would be used to complete the processing. After convergence, a first difference approach could be used to isolate any 1-2 cycle discontinuities. With this approach, single or double difference processing would be as hardy as triple difference processing. REFERENCES Beutler, G. , Davidson D. A., Langley R. B. , Santerre R. , Vanicek P. and Wells D. E. , 1984: Some theoretical and practical aspects of geodetic positioning using carrier phase difference observations of GPS satellites. Department of Surveying Engineering, University of New Brunswick, Fredericton, N. B. , Canada. Bock, Y., Abbot R. I., Counselman C. C, Gourevitch S. A., King R. W. , and Paradls A. R. , 1984: Geodetic accuracy of the Macrometer Model V-1000. Bulletin Geo- desique 58 (2), 211-221. Bossier, J. D. , Goad C. C, and Bender P. L. , 1980: Using the Global Positioning System (GPS) for geodetic surveying. Bulletin Geodesique , 54 (4), 553-563. Counselman, C. C. and Gourevitch S. A., 1981: Miniature interferometer terminals for earth surveying: ambiguity and multipath with Global Positioning System. IEEE Transaction on Geoscience and Remote Sensing , GE-19, No. 4. Counselman, C. C. and Steinbrecher D. H. , 1982: The Macrometer: a compact radio interferometry terminal of geodesy with GPS. Proceedings of the Third Interna- tional Geodetic Symposium on Satellite Doppler Positioning , Physical Sciences Laboratory, New Mexico State University, Las Cruces, New Mexico, February 8-12, 1982, 1165-1172. 335 Goad, C. C, 1985: Precise relative position determination using Global Positioning System carrier phase measurements in a non-difference mode. Proceedings of the First International Symposium on Precise Positioning with the Global Positioning System , (NOAA), Rockville, Maryland, April 15-19, 1985. Goad, C. C. and Remondi B. W. , 1984: Initial relative positioning results using the Global Positioning System. Bulletin Geodeslque 58 (2), 193-210. MacDoran P., Spltzmesser D. J., and Buennagel L. A., 1982: SERIES: satellite emission range inferred Earth surveying. Proceedings of the Third International Geodetic Symposium on Satellite Doppler Positioning , Physical Sciences Labora- tory, New Mexico State University, Las Cruces, New Mexico, February 8-12, 1982, 1143-1164. MacDoran P. F. , Miller R. B. , Buennagel L. A., Fliegel H. F., and Tanida L., 1984a: Codeless GPS systems for positioning of offshore platforms and 3D seismic surveys. Navigation , 31 (2), 57-69. MacDoran P. F. , Whitcomb J. H. , and Miller R. B. , 1984b: Codeless GPS positioning offers sub-meter accuracy. Sea Technology , 10-12. Remondi B. W. , (Center for Space Research, The University of Texas at Austin, Austin, Texas), 1984: Using the Global Positioning System (GPS) phase ob- servable for relative geodesy: modeling, processing, and results. Ph.D. Dis- sertation. 360 pp. Remondi, B. W., 1985: Performing centimeter accuracy relative surveys in seconds using GPS carrier phase. Proceedings of the First International Symposium on Precise Positioning with the Global Positioning System , (NOAA), Rockville, Maryland, April 15-19, 1985. Spilker, J. J., Jr., 1978: GPS signal structure and performance characteristics. Navigation , 25, 121-146. Van Dlerendonck, A. J., Russell S. S., Kopitzke E. R. , and Blrnbaum M. , 1978: The GPS navigation message. Navigation , 25, 147-165. Ward, P., 1982: An advanced NAVSTAR GPS geodetic receiver. Proceedings of the Third International Geodetic Symposium on Satellite Doppler Positioning , Physical Sciences Laboratory, New Mexico State University, Las Cruces, New Mexico, February 8-12, 1982, 1123-1142. 336 OASIS— A NEW GPS COVARIANCE AND SIMULATION ANALYSIS SOFTWARE SYSTEM S. C. Wu and C. L. Thornton Jet Propulsion Laboratory California Institute of Technology 4800 Oak Grove Drive Pasadena, CA 91109 ABSTRACT. A new covariance and simulation analysis software system for earth orbit- ing satellites, especially the GPS, is currently under development at JPL. This software system is called Orbiter Analysis and Simulation Software (OASIS). The system is de- signed to provide a flexible, versatile and efficient accuracy analysis tool for earth satellite navigation and GPS-based geodetic studies. The OASIS system is implemented on a Dig- ital Equipment Corporation VAX computer, but with portability in mind so that with minor eff'ort it can be implemented on different types of computers. The software has a miodulsir structure to facilitate modifications and enhancements. A number of new ca- pabilities have been included which are not now available in the widely used analogous system ORAN/COVAN. A key feature of the system is a new filter formulation providing either a U-D or a SRIF mechanization of a factorized Kalman filter. This dual formula- tion enables the users to select the more efficient algorithm for each specific application. A number of alternative approaches tire provided for analyzing multiple-station GPS ob- servations contaminated by clock errors. Clock-like errors can be individually modelled as a polynomial up to second order or can be represented as a stochastic process such as white noise, colored noise or random walk. Coding on Version 1.0 of the system with basic analysis capabilities is expected to be completed by June, 1985. Certification and documentation will be completed by October, 1985. The complete system (Verstion 2.0) will be implemented by January 1986. This paper describes the OASIS capabilities and reports on the status of system development and testing. I. INTRODUCTION Over the past few years, the Jet Propulsion Laboratory (JPL) has performed extensive analyses involving earth orbiting satellites. These include the navigation of low earth orbiters such as the proposed NASA Ocean Topography Experiment Satellite — TOPEX, and geosynchronous satellites such as TDRS, as well as geodetic applications of the NAVSTAR Global Positioning System (GPS). The analysis tool has been the ORAN/COVAN system. The ORAN software was developed by the Wolf Research and Development Corporation under contract with NASA's Goddard Space Flight Center (Hatch and Goad 1977). While it is capable of orbiter trajectory generation and covariance analysis, it has three major limitations: (l)its filter is not a square-root mechanization and, hence, ill-conditioning and degraded accuracy may occur on computers with limited dynamic range such as a VAXll/780; (2)it cannot process differential GPS data types; and (3)it is inefficient to do repeated analyses with the same trajectory and observing geometry because the integration of orbit variational equations and the computation of partial derivatives have to be repeated for each run. The COVAN softweire is a covariance analysis filter. It was developed at JPL (Bierman and Hamata 1977) to supplement ORAN. It makes use of the orbit trajectories and the partial derivatives generated by ORAN and performs covariance analyses. f The filter in COVAN is a square-root information filter which is known for its numerical precision and stability relative to the classical information matrix approach (Bierman 1977). Another supplementary program, executed prior to COVAN, can be used for combining multiple-station GPS observations by direct differencing. Hence, all three major limitations of ORAN are alleviated when it is used in conjunction with COVAN. However, the ORAN/COVAN system still cannot fully satisfy many of the modern covariance analysis needs. These include better dynamic models (especially GPS solar pressure) and non-dynamic models for cm-level geodesy, new data types that cannot be formed by simple differencing (such as VLBI observations on extra-galactic radio sources. t One version of COVAN can also perform data reduction. 337 altimetry, and gradiometry), sequential filtering allowing for stochastic parameter models, worst-cjise analysis (in which the absolute values of the effects of all error sources are summed linearly, instead of quadratically) , and flexibility to be modified for special needs (such as the inclusion of a specific gravity model and atmospheric drag model). The above capabilities are unavailable from the ORAN/COVAN system and need for such has led to the development of a new covariance and simulation analysis system. The OASIS system is designed to provide a flexible, versatile and efficient tool to perform covariance and simulation analyses involving multiple earth orbiting satellites, especially GPS-based geodesy and satellite navigation. In this paper, the capabilities and key features of this new analysis system are described. The status of its implementation and system tests are reported. II. GENERAL DESCRIPTION The OASIS system is implemented on a Digital Equipment Corporation VAX computer; however, portability is maintained so that it can be transported to other types of computers with minimal eflForts. This is made possible by the use of standard FORTRAN language throughout, with occasional exceptions to reduce coding complexity and to avoid the use of ambiguous parameter names (a parameter name can be as long as 16 characters). All non-standard FORTRAN extensions can be transformed into standard ones automatically using a simple sorting program, so that line-by-line examination of codes will not be needed when transporting to a different computer. The system has a modular structure so that modifications and enhancements can later be made with ease. Its main body consists of six major modules: (l) PATH/VARY generates satellite trajectories and integrates varia- tional equations to compute satellite state transition matrices and dynamic model partial derivatives; (2)REGRES defines observation sequences and forms measurement peirtial derivatives; (3)PM0D forms singly and doubly dif- ferenced data types, generates simulated residuals and performs data editing; (4) FILTER/SMOOTHER performs various modes of covariance and simulation analyses and smoothing, including an algorithm for weighted linear combination of measurements using Householder orthogonal transformations to optimally eliminate clock-like errors; (5)INPUT PROCESSOR allows the users to define the problems to be analyzed with concise input and converts it into a unified input file containing information required by all other major modules and (6)0UT- PUT PROCESSOR translates covariance analysis results into user desired, easy to read, quantities and performs mappings of orbit covciriances and simulated solutions. Supplementary but essential modules include FORCE MODELS, NON-FORCE MODELS and PV INTERPOLATER. The FORCE MODELS compute variational partiab for dynamic parameters. The NON-FORCE MODELS compute measurement partiab for non-dynamic parameters. The PV INTERPOLATER converts the PATH/VARY generated file into a time sequence which can be efficiently read by the FILTER/SMOOTHER when stochcistic dynamic parameter estimation is involved. Data files that interface between major modules are random-access un-formatted files. These files have a unique NAVIO structure (Collier 1984) which has proved efficient and has lately been adopted by JPL's Orbit Determination Program (ODP) (Moyer 1971). Figs. 1 and 2 present examples of typical runs showing how these modules can be incorporated in various stages of a covariance analysis involving GPS. The run as shown in Fig. 1 generates an INPUT file, a GPS trajectory and variational partial file (PV file) and a measurement partial file (REGRES file) for a specified measurement scheme. The INPUT file can also be used in the subsequent stages of the covariance analysis if there is no instruction change. Fig. 2 describes a run to modify the REGRES file, to interpolate the GPS PV file and to perform covariance analysis. Note that the same GPS PV file and modified REGRES file can be used repeatedly for different filtering strategies; only the INPUT file needs to be modified. Because of the uniform geometry of the GPS constellation, a GPS PV file can be used not only in the analysis for which it is initially generated, but abo in other covariance analyses involving a similar geometry. m. SYSTEM CAPABILITIES AND FUNCTIONS The basic data types that can be processed by the OASIS system include range and range rate between a transmitter and a receiver. The transmitter and the receiver can either be a ground station or an earth orbiting satellite. Derived data types that can be generated in the PMOD module include singly and doubly differenced 338 INPUT PROCESSOR REGRES major module NON-FORCE MODELS suppl. module C J data file data flow Fig. 1. Generation of INPUT file, GPS PV file and REGRES file range, range rate and integrated dopplerfdelta range).^ Data types that are not now available but will later be added into the system include angle meaisurements, QueiScir VLBI observations, and satellite altimetry and gradiometry data. There are no limits on the maximum numbers of satellites and of ground stations that can be involved in any single analysis; these will be limited only by the computer storage size and the processing time. The functions of the major and supplementary modules are described in the following subsections. PATH/VARY Module A large part of the PATH/VARY module is adopted from JPL's existing Orbit Determination Program (Moyer 1971) with modifications. The nominal trajectory for each satellite specified by the users is generated by numer- ically integrating the equations of motion. All integrations are performed in the inertial reference coordinate system, J2000 (Kaplan 1981). Variational peirtials of satellite current states with respect to the epoch states and to all force parameters involved are calculated. The forces to be applied to each satellite are specified by the users and are obtained from the FORCE MODELS module. The trajectory and the variational partials for each satellite are written onto a PV file in terms of "difference line" representation — an efficient representation that uses discrete time differentials of varying order and at Vcirying time intervals. When such a file is later read, the PV reader will interpolate the trajectories and their variational partials to any time specified. FORCE MODELS Module The FORCE MODELS module defines the forces (dynamics) that govern the motion of a satellite. As an integral part of the PATH/VARY module, a majority of force models are adopted from the ODP. Force models that are available in the OASIS system include the earth's gravitational field represented by a spherical harmonic t Integrated doppler measurements are formed by generating a common bias for each continuous pass of phase (i.e., ambiguous range) measurements; these biases are to be estimated later in the filter stage. 339 REGR PMOD PV INTERPOLATER FILTER/ SMOOTHER y Y (ud/srif) (eval^ (smooth) Fig. 2. Covariance analysis with modified REGRES file and interpolated PV file expansion up to degree and order 100 (which could easily be increased),! local gravity anomalies in terms of mascons, solar and lunar point-mass gravity and their tidal effects, solar radiation pressure and its earth surface reflection (albedo), atmospheric drag, satellite gas leaks, and instantaneous thrusts. Also, lumped models of the geopotential field can be included by the users to replace the nominal model. The effects of atmospheric drag and solar radiation pressure depend heavily on the shape of the satellite body. In the ORAN/COVAN system the simplest model, a sphere, is used. To furnish a realistic model in PATH/VARY, the composite shape of each satellite can be defined in terms of a sphere, a sun-tracking and an earth-tracking panel. The area to mass ratio and the specular and diffuse reflectance for each elementary shape are user specified. For the convenience of precision analyses involving GPS satellites, the GPS solar radiation pressure t Currently, un-normalized harmonic coefficients are used; some of the higher degree and order terms may appear to have a null value as a result of the limited dynamic range of a VAXl 1/780 computer. Normalization of these coeflicients will be implemented in the future. 340 model developed by the Rockwell International Corporation (Moore and Grafton 1983) is also implemented. For atmospheric drag, the Jacchia model (Jacchia 1977) is available to furnish atmospheric density, temperature and velocity. REGRES Module The REGRES module generates, within a specified time period and geometrical constraint, measurements and their partials with respect to satellite epoch states, station locations, and a specified number of force and non- force parameters. These parameters are to be either estimated or "considered" (Bierman 1977) in the covariance analysis. Measurements are assumed to be instantateous {i.e., no light time). At any measurement time, REGRES converts station locations, obtained from a station log file, into the inertial reference coordinate of date. It reads PV files to obtain satellite states and variational partials. The geometry of the measurements is then specified. Measurement partials with respect to satellite epoch states and force parameters are calculated from variational partials; those with respect to non-force parameters are calculated using the models defined in the NON-FORCE MODELS module. The nominal values of satellite states, station locations, and measurement partials are written onto a REGRES file in a chronological order. To make efficient use of the REGRES file space, partials having a zero value are not recorded. Such zero-valued partials may account for up to 90% of all partials; hence the space saving can be significant. Non-zero partials are referred to by table indexing. The extra computer time needed for such indexing is compensated for by the time that would be needed to read the large number of zero-valued partials. NON-FORCE MODELS module The NON-FORCE MODELS module includes geometrical models that affect the measurements. Their effects on the satellite dynamics, if any, are separately modelled in the PATH/VARY module when satellite trajectories are computed. The NON-FORCE MODELS will be called only by the REGRES module when measurement partials are generated. These models include station location, polar motion, UTl-UTC offset, clock parameters (clock bias, frequency bias and frequency drift), troposphere delay, ionosphere refraction, solid earth tides, ocean tidal loading of the crust, offset between coordinate frames. Quasar angular position (on VLBI only), and satellite attitude (on gradiometry only). The primary data types that will be affected by these models are summarized in Table 1. Derived data types, such as singly and doubly differenced range, range rate and integrated doppler, are generated directly in PMOD from primary data types and, therefore, do not need models of their own. Station location can be defined in earth-fixed cartesian coordinates {X-Y-Z), in geographic coordinates (Longi- tude, Latitude and Radial), or in topocentric coordinates (Vertical, East and North). Polar motion and UTl-UTC offset change the locations of all stations systematically. The troposphere delay model of Chao (1974) is adopted which remains non-singular at all elevation angles; the zenith delay is the scaling factor with respect to which troposphere partials are generated. The ionosphere refraction model has both elevation angle and zenith-sun angle dependence with zenith columnar electron content (in 10^^ electrons/m^)being the scaling factor. For the solid earth tides, only the Love numbers of the second and the third kind (Melchoir 1966) are included. The model of ocean tidal loading of the crust is adopted from Pagiatakis (1982) where only the M2 tide effects are retained. PMOD Module The major functions of PMOD include forming derived data types, data editing, re-assigning data weights, and generating measurement residuals for simulation analyses. Derived data types that can be formed are singly and doubly differenced range, range rate and integrated doppler. Data editing can be performed for selected measurement time spans, stations, satellites, data types and cut-off elevation angles. Data weights can be re- assigned according to elevation angles (to account for random troposphere delays), or transmitter-receiver distance (to account for space loss). Simulated residuals include the effects of data noise consistent with the assumed data weights, as well as the effects due to user assigned uncertainties in force and non-force parameters included in the REGRES file. After each run of PMOD, a new REGRES file of the same format is written. PV INTERPOLATER Module The PV INTERPOLATER reads a PV file that is written by the PATH/VARY module in terms of discrete time differentials at varying time intervals and performs interpolation so that satellite trajectories and variational 341 Table 1. Non-force models that apply to the primary data types RANGE RANGE ANGLE VLBI ALTIMETRY GRADIO- RATE (Ocean) (Land) METRY Station Location Polar Motion, UTl-UTC Clock Bias, Frequency Bias Frequency Drift Troposphere Delay (Wet and Dry) Ionosphere Refraction Solid Earth Tides Ocean Tidal Loading of the Crust Offset Between Coordinate Frames Quasar Anguleir Position Satellite Attitude partials axe interpolated to each batch time for sequential processing involving stochastic dynamic parameter estimation. A new PV file is written for use by the FILTER/SMOOTHER module. FILTER/SMOOTHER Module The FILTER/SMOOTHER module is key to all estimation, simulation and covariance analyses. The filter works either in a batch mode or a sequential mode according to user specification. It is an epoch-state filter when no stochastic process is involved; otherwise, it is a pseudo-epoch state filter (Bierman 1977). For epoch-only covariances and/or estimates without any process noise modelling, it needs to read only a REGRES file. A PV file is needed by the filter only when process-noise parameters are involved. In addition to the basic consider covariance analysis capability, the FILTER/SMOOTHER can treat any force or non-force parameter as process- noise and perform smoothing for all dynamic parameter estimates and covariances. This feature is especially useful in modelling non-deterministic effects such as clock instabilities, satellite gas leaks and other non-gravitational forces. A filter evaluation mode is available so that the effects of mismodelled data noise, stochastic parameters 342 and a priori parameter uncertainties can be studied. The FILTER/SMOOTHER includes a dual factorized Kalman filtering mechanization — a square-root infor- mation filter (SRIF) and a U-D factorized filter (UD) (Bierman 1977). This feature enables users to select the more efficient filtering algorithm for each specific problem. For instance, SRIF is best suited to problems with large numbers of measurements at each observation time and for combining estimates and covariances from in- dependent data sets. The UD formulation is preferrable for performing the filter evaluations as described in the preceding paragraph. There is available in the SRIF formulation an algorithm for weighted linear combinations of multiple-station, multiple-satellite observations using Householder orthogonal transformations. A special case of such linearly combined data (i.e., no a priori clock information and uniform data weights) is equivalent to explicitly differenced data wherein clock-like errors are totally eliminated (ignoring the light time effects). However, the Householder approach is superior to the explicit double differencing alternative in that the derived data remain uncorrelated and, depending upon the differencing algorithm employed, more information is retained (Wu 1984; Melbourne 1985). Upon completion of the filter process, a SRIF or UD array file is written, which is re-read during the smoothing or evaluation mode. Smoothed estimates and covariances are written on a separate SMOOTH file. When the evaluation mode is used, an EVALUATION file is also written. The display of these files is performed by the OUTPUT PROCESSOR module. INPUT PROCESSOR Module The INPUT PROCESSOR module is designed to provide the user with a simple and convenient way to define input quantities. Duplicated inputs, such as the observation scheme involving multiple stations and/or multiple satellites, need not be repeated. This is made possible by the use of macros (i.e., function definitions) to expand the user input (which is free-formatted), into standardized inputs required by each of the major modules. A single unified INPUT file will be written which will contain all instructions and quantities needed by the subsequent modules. With such a unified INPUT file, consistency between all modules will be maintained. For instance, instructions in the INPUT file will ensure that same PV file will be used to generate the measurement partials in REGRES, to perform smoothing in FILTER/SMOOTHER, and to map the covariances and estimates in OUTPUT PROCESSOR. OUTPUT PROCESSOR Module The OUTPUT PROCESSOR module interprets and displays the contents of files generated by the FIL- TER/SMOOTHER. It produces computed and consider covariances, and perturbation matrices for any subset of parameters specified by the users. It has the capability to determine reduced-state filter estimates and co- variances, produce mapped satellite state estimates and covariances, generate worst-case errors (absolute sum of effects from all error sources), form differenced estimates and covariances between pairs of stations for geodetic interest, and display estimates and covariances in different coordinate systems. When an EVALUATION file is generated by the FILTER/SMOOTHER, it will produce covariances for re-assigned data noise and parameter uncertainties, including the a priori uncertainties of estimated parameters. All outputs are written on a printable file which can be either displayed on a CRT screen or sent to a printer for a hard-copy print. A graphics package will also be available which will plot out key results contained in an OUTPUT file, such as post-fit residuals, error bar charts, etc. IV. STATUS OF SYSTEM TESTS Out of the seven primary data types listed in Table 1, only range has been coded. This limited capability allows for studies involving both range and integrated doppler data types (see footnote in the first paragraph of Section III). All completed modules have been individually tested using test data. Data files and their interfaces with different modules have been checked out. GPS trajectories generated by the PATH/VARY module have been checked against the Aerospace Corporation's TRACE program (Mercer, et al.) with 9 cm agreement over a period of 14 days for non-eclipsing orbits, and 14 cm over a period of 8 days for eclipsing orbits. Covariance results using OASIS filter (U-D formulation only) with partials generated by ODP and ORAN have been compared to 343 the corresponding results using COVAN and ODP filters. They all agree to better than eight significant figures when the test cases are well conditioned and identical models are used in the comparisons. When different models are used, the covariance results are confirmed to agree within the limits of model deviations. Further tests involving new data types and new features such as smoothing involving process-noise modelling, SRIF/UD intercomparison, filter evaluation mode, combining information from independent data sets, and map- ping of satellite state estimates and covariances will be performed within the next few months when these new features are implemented. V. SUMMARY A flexible, versatile and efficient covariance and simulation analysis software system has been designed and is now near completion. This system is designed to analyze problems involving earth orbiting satellites, and is especially well suited to GPS-based geodesy and navigation. Most basic features have been implemented and partially tested; these include a U-D factorized Kalman filter and multiple models for clock errors (including bias, linear and quadratic drifts and stochastic models such as white noise, colored noise and random walk). Currently, the only data type available is range. By October 1985, a system (Version 1.0) with basic capabilities will be available. The complete system (Version 2.0) is projected to be fully implemented by January 1986. Additional implementations by January 1986 include new data types, a SRIF formulation of the filter, filter evaluation mode, and expanded capabilities in the OUTPUT PROCESSOR. Normalization of geopotential harmonic coefficients will start soon after. Although REGRES and its associated NON- FORCE MODELS module calculate measurement partials without including light time effects, they are accurate for covariance analyses. Other modules in the OASIS system use high precision (to sub-cm level) models and computation algorithms. Hence, with a replacement of the REGRES module, it can be converted into an operational data analysis system. The modular structure of OASIS greatly simplifies such a conversion. In fact, such a GPS data analysis software system is currently under development in parallel with the OASIS system effort and will be used to process data from the NASA GPS measurement system demonstration, performed in late March to early April 1985 (Davidson, et al. 1985). ACKNOWLEDGEMENT The near completion of the OASIS software system development in a relatively short time is due to the efforts of all OASIS Development Team members. The following members, in particular, have spent enormous time in the design, implementation, and testing of the entire system. They are B. C. Beckman, W. I. Bertiger, G. J. Bierman, J. S. Border, C. S. Christensen, S. M. Lichten, A. P. Louie, R. F. Sunseri, B. G. Williams, P. J. Wolff and J. T. Wu. Valuable suggestions from V. J. Ondrasik, C. S. Christensen and C. E. Hildebrand are acknowledged. The work described in this paper was carried out by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. 344 REFERENCES Bierman, G. J., 1977: Factorization Methods for Discrete Sequential Estimation, Academic Press, New York, NY. Bierman, G. J. and N. E. Hamata, 1977: "A Brief Description and User's Guide for COVAN (Covariance Analysis Program)," Eng. Mem. No. 314-129, Jet Propulsion Laboratory, Pasadena, CA. Chao, C. C., 1974: "The Troposphere Calibration Model for Mariner Mars 1971," Tech. Rep. No. 32-1587, Jet Propulsion Laboratory, Pasadena, CA, March 1974, pp. 61-76. Collier, J. B., 1984: "NAVIO User's Guide," Internal Doc, Jet Propulsion Laboratory, Pasadena, CA. Davidson, J. M., C. L. Thornton, C. Vegos, L. E. Young and T. P. Yunck, 1985: "March 1985 Demonstration of the Fiducial Network Concept for GPS Geodesy: A Preliminary Report," First Int. Symp. on Position with GPS, Rockville, MD. Hatch, W. and C. Goad, 1977: "Mathematical Description of the ORAN Error Analysis Program," Wolf Resecirch and Development Corp., Riverdale, MD. Jacchia, L. G., 1977: "Thermospheric Temperature, Density, and Decomposition: New Models," Special Rep. No. 375, Smithsonian Astrophysical Observatory, Washington, D.C. Kaplan, G. H., Ed., 1981: "The lAU Resolutions on Astronomical Constants, Time Scales, and the Fundamental Reference Frame," United States Naval Observatory Circular, No. 163, U.S. Naval Observatory, Washington, D.C. Melchoir, P., 1966: The Earth Tides, Pergamon Press, New York, NY. Melbourne, W. G., 1985: "Algorithms for Obtaining the Minimum Variance Estimate from Multiple Differenced Global Positioning System Observations," IEEE Trans. Geoscience and Remote Sensing, Vol. 19 (in press). Mercer, R. J., R. H. Prislin and D. C. Walker, 1971: "TRACE 66 Trajectory Analysis and Orbit Determina- tion Program. Volume 1: General Program Objectives, Description and Summary," The Aerospace Corp. TOR- 0059(9320)-l, Vol. 1. Moore, A. N. and J. Grafton, 1983: "Solar Force Model," in Orbital Model Report, Tech. Oper. Rep. No. SSD 83-0029, Rockwell International Corporation, Seal Beach, CA. Moyer, T. D., 1971: "Mathematical Formulation of the Double- Precision Orbit Determination Program (DPODP)," Tech. Rep. No. 32-1527, Jet Propulsion Laboratory, Pasadena, CA. Pagiatakis, S. D., 1982: "Ocean Tide Loading, Body Tide, and Polar Motion Effects on Very Long Bciseline Interferometry," Tech. Rep. No. 92, Dept. Surveying Eng., Univ. New Brunswick, Fredericton, NB, Canada. Wu, J. T., 1984: "Estimation of Clock Errors in a GPS Based Tracking System," AIAA/AAS Astrodynamics Conf., Seattle, WA. 345 Precise Relative Position DetGrmlnatlon Using Global Positioning System Carrier Phase Measurements In a Nondlfference Mode Clyde C. Goad National Geodetic Survey Charting and Geodetic Services National Ocean Service, NOAA Rockville, Maryland 20852 ABSTRACT. With the advent of less expensive carrier tracking instrumentation, it has become clear that an easily implementable algorithm to process carrier phase measurements from many receivers tracking simultaneously is essential. Previous methods which were developed to process phase measurements in single-, double-, and triple-difference modes are easily implemented when only two receivers are employed. However, when three or more receivers operate simultaneously, these data types require more complex algorithms if information is to be extracted from these data in an optimal manner. This paper presents an algorithm which will handle the carrier phase measurements in an undif f erenced mode thus allowing any number of stations to be analyzed without additional complexities. This phase-only approach possesses all the advantages of the differenced data approaches and has the added properties of generating the proper covariance matrix and yielding receiver and satellite clock difference histories. INTRODUCTION The National Geodetic Survey (NGS) took delivery of its first two Global Positioning System (GPS) phase tracking receivers in the spring of 1983. After delivery, computer programs were upgraded to handle the new "real" data rather than simulated data. Several months later NGS received its third GPS receiver, at which time the problem of just what algorithm to use with three receivers collecting data simultaneously was discussed. It was recognized that stronger solutions should be achievable due to the vector closure. One algorithm that others have used to process data from three or more stations is to generate uncorrelated (orthogonalized) double differences using a Gram-Schmidt orthogo- nalization scheme (Bock et al. 1984a, Remondi 1984). While this is a completely valid approach to use, this investigator has stayed clear of such orthogonalization schemes that generate linear combinations of the original data for fear that cycle slips and data editing would be more problematic when analyzing data combinations rather than the original data. As data from more receivers are added to the data set to analyze, the linear combinations of uncorrelated data become further removed from their original forms and thus harder to analyze. The introduction of much cheaper second generation GPS receivers which will track the standard position service code (C/A) is 347 advertised to be only a few months away; this will create an added demand for an improved multi-receiver (three or more) algorithm. For this study, it was considered mandatory to find an analysis technique which could process multi-receiver data in a mode that does not destroy the original form of the data, while maintaining the same ease and integer bias resolution that processing the data over single base lines has rendered. These constraints have been satisfied in an algorithm that processes the undif f erenced phase measurements made at individual GPS receivers. Since the undif f erenced phase data is used, the data remain uncorrelated no matter how many receivers collect data simultaneously. By using the base station - base satellite concept (to be described below) , biases exactly like those estimated in double-difference processing, which theoretically are integers, are part of the solution parameters. Dual frequency measurements are also easily handled with this new algorithm. First the basic phase observable will be described mathematically. Then the differenced data types will be discussed. The algorithm for the phase observables using the base station-base satellite concept will be given along with dual frequency enhancements. Finally, a technique for handling missing data which is crucial to the overall scheme will be discussed, and a summary describing an actual computer implementation will be given. THE PHASE OBSERVABLE The basic observable for precise determination of base line components (position differences) is the phase difference between the carrier signal transmitted at the satellite and a local receiver's oscillator. Mathematically this is expressed as .(tj^) (1) where superscripts refer to a particular satellite; subscripts refer to a particular ground receiver; and the argument is either the transmit time, t , or the received time, t . R Equation (1) as it is written is errorless. That is, no assumptions have been made yet in the process of simplifying it. Also, when the first measurement of phase difference is made, .(t^), the measurement value is only known to within one cycle or 21? radians. Now eq . (1) is rewritten in a more usable form. The right hand side is written so that the times are expressed in terms of the received time, t . The distance from the i ° satellite to receiver is given by p,(t ). Therefore the travel time in a vacuum is given by p (t )/c where c is the speed of light. Assuming that the oscillators run at a constant frequency, f, eq. (1) is now rewritten as: 348 Notice that the distance still has the transmit time t as an argument. This distance function can be expanded in terms of the received time if desired, but most investigators choose to solve a nonlinear equation for the transmit time given the received time and then evaluate p.(t^) directly. Also notice i J '^ that an integer N. has been inserted into eq. (2) to acknowledge that ^ (t^), the phase observable at the first measurement time, is determined modulo one cycle or 27r radians. If lock is maintained thereafter, the same N. will appear in every phase observable between receiver j and satellite i. Some small terms have been ignored in the derivation of eq. (2) such as the effects of relativity, ionospheric and tropospheric refraction and time tag errors. Some of these will be addressed later. Since all time arguments in eq. (2) are implicitly or explicitly a function of the received time tag, t , the R designation will be dropped with the understanding that hereafter the time tag refers to the receipt time. Thus, eq. (2) is rewritten ♦5 - '"" "j - ♦j'^fc) * "1 (3) where k refers to the k-th sample time, hereafter referred to as the k-th epoch. DIFFERENCED DATA TYPES Geodesists are mainly interested in using these phase observables for base line vector recovery. This information is extracted only from the term -f/c p in eq. (3) which is a function of the satellite and receiver locations. The other terms in eq. (3) are the clock difference term, ^ ( t, )-(|> .(t, ) , and the 1 k j k initial integer ambiguity, N.. Selectively differencing these phase observables is one way to eliminate these non-geodetic terms and thus simplify the reduction algorithm . Goad and Remondi (1984) first showed results from differencing phase observables over a common satellite to eliminate the satellite phase (or clock) term. For example, two stations, 1 and 2, at the (almost) same instant, t, , measure the phase difference between satellite 9 and the local oscillators. Using eq. (3), this is expressed as ♦2.i (t,), but now contains differences in phase (or clock) values between ground receivers 1 and 2, initial ambiguity differences, and distance differences. The clock differences do not necessarily have a known relationship from one epoch to the next and thus must be estimated on an epoch-by-epoch basis. Furthermore, the receiver clock difference , ( t, )-«j)-( t, ) will be the same should another satellite 1 k 2 k participate in the difference processing. 349 9 9 The term Involving the p.-p- can be calculated based on a knowledge of the I Z 9 9 station and satellite positions. N- - N.. is the same for all epochs. Thus these two terms are "common" contributors and need not be considered on an epoch-by-epoch basis. The least-squares normal matrix possesses certain structure which allows one to solve for the epoch receiver clock difference values rather easily. This structure will be given later. For a given base line, no phase observable appears more than once, thus the measurements are uncorrelated and no special treatment is required. But when more than one base line is considered, the phase observables will appear more than once, and thus these measurements will, in general, be correlated. Some investigators have given results using double differences ( for example. Goad and Reraondi (1984), Bock et al. (1984b) ). These are obtained by taking differences of two single difference observables at a common epoch from two receivers to two different satellites. For an example, receivers 1 and 2 and satellites 4 and 9 at epoch k are chosen. Then 4499 9944 » f/c (Pj - P2 - Pi + P2^ + N2 - nJ - N^ + N^ . (5) Now all satellite and receiver clock differences are removed. The right hand side contains four ranges and a linear combination of four ambiguities. Unlike the single-difference observables, the double differences are less complicated to handle (no epoch-to-epoch clock differences to model or estimate), but on the other hand phase observables now appear more than once even for a single base line and therefore the single base line data sets are correlated. To optimally process this information one must decide on whether to go with a more complex model as given by eq . (4) for the single differences, or to choose the simpler double difference model given by eq. (5) and then be forced to model the correlated nature of the double difference observables. Triple differences are generated by differencing two successive double differences in time. This has the effect of removing the bias and increasing the number of ranges to compute in the model to eight. Losses of lock will cause a spike in the triple-difference data rather than a step as in double-difference processing. These spikes (or outliers) are easily removed bj' an automatic editor or outlier detection scheme. This is an extremely desirable characteristic, especially when looking at the data initially or when the most precise results are not required. This was discussed by Goad and Remondi (1984) where actual comparisons between single-, double-, and triple-differencing results were given. When double differences are chosen, there are two techniques in common usage to model the correlations. The first is simply to evaluate the correlations and include them in a weight matrix in the generation of the least-squares normal system of equations. This matrix has a banded structure since no correlations exist between epochs. Such banded structures are routinely handled on today's computers. Another advantage is that residuals of the yet unmodified double differences are analyzed for determination of data outliers. 350 An alternative scheme Is to decorrelate the double difference data (at an epoch) . A transformation Is found (by solving a very small set of equations) to generate a linear combination of the double difference observables which are no longer correlated. This has the advantage that the newly transformed data values can be reduced by a least-squares process with the desirable diagonal weight matrix structure. It has the disadvantage that the automatic detection of outliers may be done on a linear combination of the double dif- ferences rather than the original data set. A problem common to both schemes is that the differencing algorithm must be devised to make sure that duplicative observations are not introduced. For example 4 9 49 49 49 (j> ' » ^"i^ ~ ^ii' thus q'9 should not be introduced if the other two measurements on the right hand side already have been considered. This can be problematic especially when data dropouts occur. In both cases, single- and double-difference processing becomes even more complicated when additional base lines are observed at the same time. Since a phase observable will, in general, contribute to more than one phase differ- ence observable, the correlated nature of the data is increased. DOUBLE-DIFFERENCE CHARACTERISTICS Referring again to eq. (5), the double difference is seen to possess a very desirable quality — the integer nature of the bias. Since all clock terms are removed in the differencing process, only base line and integer bias effects remain. The results of processing data from many base lines whose lengths are less than, say, 30 km are that the estimates of the biases are indeed very close to integers. This integer nature will deteriorate as the base line lengths are increased and non-cancelling effects such as ionospheric and tropospheric refraction and satellite orbit errors contaminate the solutions . If the integers can be determined, then these biases should be forced to keep their integer values and be excluded from the set of solution parameters. This greatly strengthens the recovery of base line components. Thus, any scheme for processing phase data should be capable of determining and then holding the biases to their integer values. As described, the integer nature of the bias is inherent in double-difference processing and can be incorporated into single-difference processing by expressing biases as differ- ences from one reference bias. This reference bias in single-difference processing can have any real value. WHY PHASE OBSERVABLES? As carrier phase tracking receivers become more available, the opportunity to simultaneously collect data from several locations will become more routine. Not only is this desirable from a economical point of view, but with 3 or more receivers collecting data at the same time, vector closure is an important characteristic of the data reduction scheme when all data are processed to- gether. 351 This is, in effect, a small network adjustment whose output will be a nonredundant set of base line vectors and associated (full) covariance matrix. As the number of receivers collecting data is increased, the correlat- ed nature of differenced data types becomes more complex. One data type scheme whose least-squares weight matrix will remain uncorrelated (diagonal) no matter how many receivers are collecting data simultaneously is one which analyzes the raw undifferenced phases. It is quite obvious that a phase-only algorithm will consider uncorrelated data, but how does one exploit the integer nature of the biases? This question will now be answered. THE BASE STATION - BASE SATELLITE CONCEPT The base station - base satellite concept can best be presented by an example. Suppose that at the k-th epoch a sufficient number of phase measurements are collected to constitute a double difference. Again let us assume there are two stations, 1 and 2, and two satellites, 4 and 9. Then from eq. (3), the measurements are given as follows: l(tj^) - ♦^(tj.) - f/c pj - <>j(t^) + Nj ♦2<^> - '^^^ V - 'f' 'I - *2^ V * ^2 . Again it should be emphasized that these four phase measurements could be used to generate one double-difference observable. Now the above relations are rewritten substituting N »N +<|) -<|> in each equation. One gets ♦^(tj^) - - f/c Pj + Nj(t^) ♦2 ■ - '^^ 4 * ^2< V ♦|(t^) . - f/c pI + N^(tj^) Arbitrarily, station 1 and satellite 4 will be chosen as the base station and base satellite, respectively. Then let us define ^2 " ^ *^^*^k^ " K^\^ ^ ' ^ ^l^V ' ^1^\^ ^ • ^^^ Notice that no time argument is included in the K variable. This is done intentionally. After substituting for the N's, one gets 9 9 4 9 4 K2 - N2 - N2 - N^ + N]; . (7) 352 That is, the K variable consists of the linear combination of the initial integer ambiguities. It remains the same throughout an observation session if lock is maintained. This is the essence of the algorithm. Now the four mea- surements are rewritten with only the fourth measurement actually changed. f/c f/c f/c f/c 9 -4 (8) 5^1 <\> 5j-(t, ) is the only phase observable which has neither a base station subscript nor a base satellite superscript. When this occurs, the N is replaced with the K formulation. The K values are Indeed the same integer biases one would obtain if double differences were generated. But this formulation allows the data to remain uncorrelated and thus simplify the overall process, no matter how many stations collect data simultaneously. Some base station and base satellite must be chosen. The selection algorithm is not at all crucial to the data reduction. In my computer processing code, I have chosen initially the station which has the maximum number of measurements as the base station, and similarly the satellite which contributes to the maximum number of data as the base satellite. This will be replaced with a scheme which chooses the satellite (station) as base which occurs jointly with the most other satellites (stations). Now the technique can be stated formally. (1) Choose the base station and the base satellite. (2) When a phase measurement is encountered, if either the satellite is base or the station is base, then the mathematical formulation free of the K's is used. Should both the satellite and the station not be base, then the K formula_tion given in the last equation of (8) is used. Epoch-to-epoch values of N must be estimated. The station positions and K variables are common contributors to all epochs. This formulation allows for a very particular structure of the set of least-squares normal equations as follows: B/B, B/A B,'B, r^ B/A b;b, V^ b;a b;b. B/A ^^-\ BjB. B/* o B/B. Bj* • • • • • • A'e, A'B, A'B, a\ *^B, A^B. • • • aU B'r B/V B.'V 353 The matrices B. contain measurement partial derivatives with respect to the epoch-to-epoch parameters (N) , and the matrix A consists of measurement partial derivatives with respect to the common parameters (station positions and K's). This is the same scheme used by Goad and Remondl (1984) for single difference processing where the block diagonal submatrlces are scalars. Thus T T T only the common block (A A) and one epoch pair (B. B. , B. A) need to reside in memory at any one time. This vastly reduces the size of the memory require- ment. Under optimal conditions, the K's should be very close to Integers, \fhen this turns out to be the case, or when a search of all possible combinations of Integers reveals one combination that is obviously the correct combination, these biases can be constrained to their integer values. This will Improve significantly the base line vector recovery for short base lines. IONOSPHERIC REFRACTION At radio frequencies the effect of the ionosphere on group velocity is to retard it Inversely proportionally to the square of the frequency. A corresponding advance is created in the phase. Thus eq. (3) must be augmented to account for this effect. The GPS satellites transmit at two frequencies, L. and L». The L. frequency Is 1575.42 mHz which is exactly 154 times the fundamental P-code chipping rate of 10.23 mHz. The L_ frequency is 1227.6 mHz which Is exactly 120 times the P-code rate. Equation (3) is now augmented to account for the ionospheric effect, 4>j(tj^) « «j>^(tj^) - f/c p^ - ^^(t^) + Nj + A/f . (9) Equation (9) must now be written twice, once each for the L, and L- frequencies. At this time we recognize that both the station and satellite hZ phase values should be equal to the corresponding L, phase values scaled by the frequency ratio f^/f^ since they are both based on the same fundamental rate of 10.23 mHz. We desire to eliminate the ionospheric effect by combining the two observations above in a linear comblninatlon as follows: Choosing 999 "2 - -hh'^'l - *2> yields the following "corrected" observation: 354 Equation (11) now looks exactly as the original L. phase equation given In (3) except the integer bias term is replaced with tne linear combination of the L, and L„ integer biases. Thus when ionospherically corrected data are processed, no programming changes except to linearly combine the dual frequency data into one measurement are required. Once combined, the data reduction continues without change. Prior to combining the data, all cycle slips must be corrected on each L. and L^ channel. MISSING DATA Occasionally data at an epoch may be missing. If this happens to the phase observables for the base station or base satellite, then there will be an insufficient number of data to complete the set of four measurements given In (8). This situation is not only a problem for phase processing, but also any of the non-temporally differenced data types. However, even if the base station or base satellite is not present, a sufficient number of measurements may be present to generate other double-difference observables. So, much useful information could be present. The technique used by this investigator is to do nothing until the least-squares normal matrix is reduced. At that time missing base station or base satellite data will cause singularities to appear when the epoch-to-epoch N values are being computed. But if enough phase observables are present to generate other possible double differences, then a certain linear combination of the N's can be estimated. The particular combination is of no special interest to one interested in base line determination. Thus when encountering these singularities, one zeros out the corresponding nondiagonal row and column elements of the normal matrix system. Or to put it another way, we let the normal matrix tell us what parameters can be estimated. This simple algorithm is preferred to a more involved accounting algorithm which must analyze the data that are present, and then take appropriate action when data for the base or reference satellite or station are missing. With this technique, no data are ever excluded which means all possible information is extracted from the available data. Compare this with double-difference processing of data collected simul- taneously atthree receivers. Normally some station is chosen as the reference station, say station 1, and then all double differences are generated between stations 2 and 1, and between stations 3 and 1. These measurements are then orthogonalized over the stations since station 1 measurements appear in both sets. But what happens when measurements from station 1 are missing? Double differences could be generated between stations 2 and 3. But how would these measurements fit into the orthogonalization scheme just described? Very possibly these data would not be considered. But in contrast, the phase technique would not even be aware that the data dropouts occurred. The normal matrix is generated without regard to the missing data. Singularities are detected at the reduction step; they are accommodated, and processing proceeds . Should a cycle slip or loss of lock occur, the integer offset or difference upon reacquisition obviously would be present in all double-difference observations in which it contributed. Also, should orthogonalization be used to generate uncorrelated double difference observables, then the cycle slip would be present in all orthogonalized double differences in which the correlated double difference appeared. As additional stations collect phase 355 data simultaneously, the cycle slip Is propagated to more and more orthogonallzed observations. The coefficients of the linear transformations used to generate the uncorrelated double difference measurements are convex. Thus the original cycle slip will be multiplied by a number less than one in magnitude destroying the integer nature of the cycle slip (as well as the integer biases). SUMMARY The mathematical basis for an undifferenced phase observable processing scheme has been given along with a singularity detection scheme to handle those cases when data are missing. The use of this singularity detection scheme is essential if involved computer code to detect and substitute other nonsingular solution parameters is to be avoided. In practice, cycle slips are detected by analyzing the double differences prior to data reduction. Since they do not have either satellite or receiver oscillator phase terms, double differences are the easiest measurement to use in the detection of cycle slips. Once a consistent double-difference data set is available, a successful phase reduction is guaranteed. Such a scheme has been programmed by the author. The program, PHASER (for Phase Reduction), has been given an automatic cycle slip fixing algorithm. It is based on using a preliminary triple-difference result which should be very close to the actual base line vector. Successive differences of the double-difference residuals are studied for unacceptable jumps in the residuals. These jumps are "repaired" by adding an integer which "smooths" the residual trend. Also, when studying double-difference residuals to which the base station or base satellite contribute, an integer offset is used to keep all estimated biases close to zero. Keeping the biases close to zero seems to help based solely on my experience. Very large positive or negative numbers soon lose significance while variations about a nominal (zero) value seem to be a little more meaningful, especially in an integer search situation. REFERENCES Bock, Y., R. Abbot, C. Counselman, R. King, S. Gourevitch, 1984a: How consistent are GPS surveys?, EOS, Transactions, American Geophysical Union, p. 854. Bock, Y. , C. C. Counselman, S. A. Gourevitch, R. W. King, A. R. Paradis, 1984b: Geodetic Accuracy of the Macrometer^ Model V-1000, Bull. Geod., 58, 211-221. Goad, C. C. , B. W. Remondi, 1984: Initial relative positioning results using the Global Positioning System, Bull. Good., 58, 193-210. Remondi, B. W. , 1984: Using the Global Positioning System (GPS) Phase Observable for Relative Geodesy: Modeling, Processing, and Results. Ph.D. Dissertation, 360 pp.. The University of Texas at Austin, Austin, Texas. MACROMETER™ is a trademark of Aero Services Division, Western Geophysical Company of America, 8100 Westpark Drive, Houston, Texas 77063 356 GPS CARRIER PHASE AMBIGUITY RESOLUTION OVER LONG BASELINES Peter L. Bender Joint Institute for Laboratory Astrophysics University of Colorado and National Bureau of Standards Boulder, Colorado 80309 USA and Douglas R. Larden Survey Division, Department of Lands Box 1047, G.P.O. Adelaide SA 5001, Australia ABSTRACT. As GPS satellite orbit determination accuracy improves, carrier phase ambiguity resolution over base- lines 100 km to 1000 km or more in length will be desir- able. With phase delay single differences for both the LI and L2 frequencies from the j-th satellite, two par- ticularly useful linear combinations can be formed. One is dj , a measure of the difference in geometric distance to the ground stations plus the clock correction. The other is g j , a measure of the difference in integrated electron content along the two paths. For correlation- type receivers which do not effectively square the re- ceived signals, errors Anjj and An2j in assigning the integer parts of the phase delays will result in biases for dj and g j . For particular integer error combinations (Anjj, An2j) such as (3,4) and (7,9), the resulting values of B(dj) are only 0.298 Xj and 0.033 Xj. If LI and L2 pseudorange (group delay) information is avail- able, it can be used to eliminate such cases by putting limits on |B(gj)|. In particular, if the pseudorange information is accurate enough to rule out integer error combinations giving either B(dj ) = or B(gj) B(dj) > 2.133 Xj = 40.6 cm, then 2 0.562 Xi = 10.7 cm. This information should make possible ambiguity resolution over long baselines if the orbits, phase measurements, and tropospheric corrections are sufficiently accurate. If pseudorange information is not available or not accu- rate enough, integer error combinations giving |B(g4)| ^ 40.6 cm still can be ruled out for some moderately long baselines by considering information on the maximum plausible difference in ionospheric electron content. * Staff Member, Quantum Physics Division, National Bureau of Standards. 357 INTRODUCTION It is generally recognized that the accuracy of geodetic baselines determined from differential GPS carrier phase measurements at two or more sites will be best if the phase ambiguities can be removed. We consider particularly the case where two-frequency receivers, water vapor radiometers, and surface pressure measurements are used to make accurate corrections for ionospheric and tropo- spheric propagation delays. As accurate GPS satellite tracking data from re- ceivers at a good distribution of known sites becomes available, it is expected that accurate orbits can be calculated over at least regional areas. It thus is important to know what additional information is needed in order to resolve the GPS carrier phase ambiguities over distances of up to 1000 km or longer. The analysis method we use is based mainly on single differences of phase for two ground stations observing the same satellites. Observations of the phase differences over perhaps a couple of hours as the geometry changes can be used to attempt to solve for the phase ambiguities. However, some incorrect phase as- signments may fit the phase difference observations but give appreciable errors in the baseline components. We thus consider pseudorange (group delay) measure- ments as supplemental information and discuss the accuracy they need to have in order to yield reliable results. Finally, for cases where pseudorange measure- ments are not available, we discuss the use of ionospheric electron density gra- dient model information instead. ANALYSIS OF CARRIER PHASE DIFFERENCES The results of carrier phase difference measurements for the j-th satellite can be written as: ^^21 " ^"21 "^ *2i^ ^2 • ^^^ Here n^ and <|>i-j are the differences in the assumed whole fringe number and the phase, respectively, for the two ground stations at the frequency f^i; ^i is the wavelength for fLi; and the corresponding quantities with index 2 are for fre- quency fL2» Neglecting tropospheric, electronic, antenna pattern, and multipath errors, as well as Doppler corrections, and assuming n^^ and n2-j are correct: "ij - ^JG ^ ^ - hj (3> ^2j - -'JG ^ = - hi ■ (*> Here djg is the geometrical difference in path length; C is the product of the speed of light and the clock difference between the two stations; and 1\a and I2-J are the differences in ionospheric corrections at the two stations at fre- quencies f^i and fL2' Two particularly useful linear combinations can be formed from (1) and (2). These are: d^ = K d^^/(K-l) - d2^/(K-l) (5) g. = d,. - d^. (6) where K = (fLi/fL2^^ = 1.6469 . ^7) 358 Rewriting (5) and (6) gives: d. = X,{2.5A6(n,.+jj) - 1.283(n2^+(t)2j)} . Neglecting higher than second order terms in the frequencies: l2j = K • Ijj . (10) Hence, from (3) and (4), if nij and n2j have their correct values, and still neglecting measurement and tropospheric errors: d. = djg + C (11) gj - I^^ - I,^ . (12) The quantity d-; thus is an ionosphere-independent expression for the difference in geometrical distance to the two stations from the j-th satellite plus the clock correction, and g-; is proportional to the difference in integrated electron density along the two paths. AMBIGUITY RESOLUTION One approach to the ambiguity resolution problem is to pick initial values for nj-j and n2-j from a priori information on the station locations and/or integrated Doppler solutions. Any errors Anjj and An2j then will cause biases B(dj) in dj and B(gj) in g j : B(d.) = X, {2.546 An,. - 1.984 An„.} (13) B(g.) = Xj{Anj. - 1.283 An2.} . (14) The size of these biases for different values of An^j and ^^2i ^i^® given in Table 1, (Larden and Bender 1980), in order of increasing values of | (An2j-Ani j ) | . For each value of (Ano^-Anj-s) , the listing is in order of increasing |Ani-j|. All cases where B(d.)T < 1.6 X^ and B(g.)| < 5.0 X^ are included. With the assumed values of n^-j and n2j for each satellite, the phase difference data can be converted to values of d^ and g4. The dj values as a function of time as the satellite configuration geometry changes can be used to solve for the coordinates of the observing stations, clock differences, and differences in the biases in the d j . However, it seems very unlikely that the level of systematic measurement errors and atmospheric correction errors can be made small enough to rule out the cases (Anij,An2j) = (±7, ±9), where B(dj ) = +0.033 X^. For this reason, we must be able to rule out cases with |B(gj;| > 4.550 X^ in order to eliminate these cases. Also, it would be highly desirable if we could rule out |B(gj)| 2 2.133 Xj. Then we could eliminate the cases (±3, ±4) and (±4, ±5), and only require enough accuracy to rule out B(d-j ) ^ 0.562 X^ in order to fix An^^ and An2-? uniquely. In summary, it is sufficient if we can rule out cases where JB(dj)| ^ 0.562 \\ = 10.7 cm and JB(gj)| > 2.133 X^ = 40.6 cm. To be specific, although not complete- ly general, we consider a satisfactory solution to be one where nij and n2-j are such that the following conditions hold: 1) the values of |B(dj)[ and JB(gj)| 359 Table 1. Ambiguity resolution cases with |B(d.)| < 1.6 X, and |B(gj)| < 5.0 Xj. (An2j-Anjj) Anij ^"2j B(dj)/Xj B(gj)/Xi ±1 ±1 ±0.562 +0.283 ±2 ±2 ±1.124 +0.567 ±1 ±2 +1.422 +1.567 ±2 ±3 +0.860 +1.850 ±3 ±4 +0.298 +2.133 ±4 ±5 ±0.264 +2.417 ±5 ±6 ±0.827 +2.700 ±6 ±7 ±1.389 +2.983 2 ±5 ±7 +1.157 +3.983 2 ±6 ±8 +0.595 +4.267 2 ±7 ±9 +0.033 +4.550 2 ±8 ±10 ±0.529 +4.833 are less than one-third of the limits given above, or 3.6 cm and 13.5 cm respec- tively; and 2) the total uncertainties in B(dj ) and B(g^) are less than twice these values with very high confidence levels, so that the chances of having fixed njj and n2j incorrectly are extremely small. As discussed elsewhere (Larden and Bender 1982, 1985), the chances of being able to meet these criteria for determining B(dj) even over baselines with lengths of 1000 km or possibly longer seem good provided that high-quality data for determining the satellite orbits is available and that correlation-type receivers which do not effectively square the received signals are used. Thus it is useful to consider how well B(gj) can be determined. For short baselines, the difference in the ionospheric corrections for the two stations is small. Thus the calculated value of gj can be compared with appro- priate model values to find B(gj). However, for long baselines it is desirable to use LI and L2 frequency pseudorange data (i.e., group delay information) if it is available. If Dh and D2J are the measured pseudorange differences to the two ground stations from the j-th satellite, and if tropospheric, electronic, antenna pattern, and multipath errors are neglected, then: Defining '2j C + I C + I 2j G. = D^. 2 2j - D Ij (15) (16) (17) we can estimate B(g4 ) from the average difference of gj and Gj over a long enough 360 time interval so that the statistical uncertainty due to the pseudorange measure- ments is small: B(gj) = <(gj-Gj)> . (18) The systematic measurement error in Gj is likely to be considerably larger than for g-j, so our requirements on B(gj ) become: 1) that values of n^j and n2-; exist which give B(g^)| < 13.5 cm; and 2) that the measurement uncertainty for 64 be less than 27.1 cm at a high confidence level. The main obstacle to achieving this accuracy appears to be errors due to multipath. However, the necessary ac- curacy hopefully can be achieved by careful control of the antenna and its sur- roundings. Thus the prospects for fully resolving the ambiguities over long baselines by using pseudorange information appear to be good, when accurate satellite orbits are available. In cases where pseudorange information is not available, it still is possible to resolve the ambiguities over moderately long baselines by using estimates of the maximum plausible differences in the integrated electron density along the two paths. For example, we can use Figure 1 of Clynch and Renfro (1982) to find gradients in the vertically integrated electron content during September in a typical year when the sunspot number is 50. Maximum gradients of about 2 x 10^^ electrons /m^/deg are found at southern latitudes in the daytime, which correspond to 0.1 m/deg gradients in l2-j-Iij for vertical paths. Allowing a factor 2 in- crease for slant paths, and assuming that averaged differences from modeled gra- dients over periods of a couple of hours during magnetically quiet to moderately disturbed periods might be comparable with the typical gradients, there could be problems with ambiguity resolution even for 100 km length baselines. The gradi- ents during pre-dawn hours from Figure 1 of Clynch and Renfro (1982) are typi- cally a factor 5 or 10 lower, so ambiguity resolution over substantially longer distances should be possible if data are available at appropriate times. On the other hand, the typical gradients may be roughly a factor 3 worse than shown at times of maximum solar sunspot numbers. More careful studies of ionospheric gradients and their time variations will be needed if ambiguity resolution over longer baselines is attempted without the aid of pseudorange information. REFERENCES Clynch, J. R. , and B. A. Renfro, 1982: "Evaluation of ionospheric residual range error model," in Proceedings of the Third International Geodetic Symposium on Satellite Doppler Positioning (Physical Science Laboratory, New Mexico State Univ., Las Cruces), Vol. 1, pp. 517-537. Larden, D. R. , and P. L. Bender, 1980: unpublished manuscript. Larden, D. R. , and P. L, Bender, 1982: "Preliminary study of GPS orbit determina- tion accuracy achievable from worldwide tracking data," in Proceedings of the Third International Geodetic Symposium on Satellite Doppler Positioning (Physical Science Laboratory, New Mexico State Univ., Las Cruces), Vol. 2, pp. 1247-1252. Larden, D. R. , and P. L. Bender, 1985: "Expected accuracy of geodetic baseline determinations using GPS carrier phase measurements," Jour. Geophys. Res., in preparation. 361 EVALUATION OF GPS CARRIER DIFFERENCE OBSERVATIONS; THE BERNESE SECOND GENERATION SOFTWARE PACKAGE W. Giirtner G. Beutler I. Bauer sima T. Schildknecht AstronomicaJ. Institute University of Berne Sidlerstrasse 5 3012 - Berne Switzerland ABSTRACT. Niomerous tests with GPS carrier phase difference obser- vations have been performed dioring the last few years, but only few mutually independent processing techniques have been developed so far. In this report we present the second generation of a soft- ware package, the first generation of which was jointly developed by the Universities of Berne (Switzerland) and New Brunswick (Ca- nada) . The new Bernese program package comprises preprocessing- and para- meter estimation-procedxires. The resxolt of preprocessing are (a) a receiver-type independent representation of the phases and (b) a priori orbits in our standard format. The parameter estimation pro- gram processes double differences. Phases of the L-]_-, the Lp-carrier, or the ionosphere free linear combination of L^ and Lg may be ana- lyzed. Moreover the phases of Lj_ and L2 may be processed in the same program run, in which case the parameters of a simple ionosphere mo- del have to be estimated. Our estimation program inay be used for pure differential positioning, for pure orbit estimation or for a combination of both. Networks or baselines may be analyzed. We il- lustrate the main features of the program system using the obser- vations of typical observation campaigns. 1. INTRODUCTION Our institute has taken an active interest in the civil applications of GPS since 1982, when Bauersima published the first of meanwhile five reports on GPS in our institute series (Bauersima I982-8I+). The next step was the development of an experimental software package for processing measiorements of the V-IOOO Macrometer surveyor by Beutler during his one year visit to the University of New Brxanswick, Fredericton (Beutler et al. I98U). This software package has been restructured and essentially generalized. The result is what we call a second generation software package which we present here. Programs for the evaluation of GPS differential carrier phase measurements have to cope with the following difficulties: - The observables are biased by many different sources in a magnitude far above the system's internal precision (clocks, atmosphere, orbits, ...). - The amount of data varies very strongly between different types of receivers (Macrometer: 0.5-I obs/min, SERIES-X -v h obs/min, Tl-UlOO '^' 15 obs/min). Usual- 363 ly the data has been preprocessed by receiver-internaJL software that could alter its statistical properties. - The data can be affected by gross errors and/or cycle slips of varying magnitude and frequency. - The functional model contains in its rigorous form elements of celestial mechanics as well as elements of geodynamics. - The number of unknowns can be very large (dependent on data processing method) . 2. THE BERNESE SECOND GENERATION GPS SOFTWARE PACKAGE The package consists mainly of 3 different parts : - Receiver dependent data preprocessing software - Standard Orbit Generation Program - Parameter Estimation Program 2.1 Preprocessing Software Since the raw data representation varies between the different receiver types programs are needed to reformat the observations into a unified, receiver inde- pendent representation. These observation files contain in a header receiver and station related information and subsequently all single difference phase obser- vations between two receivers simultaneously stationed at the end points of a baseline. If n receivers have been operating during the sajne session n-1 linearly independent single differences per satellite and epoch have to be formed, so we get n-1 observation files per session. For dual frequency receivers we store the L]_ axid L2 single differences and the ionosphere-free linear combination of L-, and L^ on three different files. Figure 1 shows the header and the first few single differences of an observation file. ALASKA EXPERIMENT BASELINE STATION NAMES; FREQUENCY: RECEIVER-TYPES*. UNIT-NUMBERS: WAVELENGTH-FACTOR: REFERENCE EPOCH: CLOCK OFFSETS AT R.E. : DRIFTS: INTERVAL: NUMBER OF SATELLITES: SPACE VEHICLE NUMBERS NUMBER OF OBSERV. : 1 ^5909.00347222222 2 45909. 00381944is a single or double differenced observable, or is a linear combination of phase measurements obtained from observations of a number of SV's by a number of receivers. In this case certain delay offsets are eliminated and the quantities p, N^, n^j and n.-^2 ^^^ should be interpreted as the differenced or linearly combined versions. The "small terms" in Equation (1) allude to small effects not included here, due to kinematics, relativity, higher order ionospheric effects, etc. Equation (1) is adequate to discuss sensitivities but no such truncations are made in the actual data reduction process. The measured values of (J)ti and t2 ^^ ^^^ initial epoch are modulo 27r. Hence, the quantities n^t and n,2 are tne number of integer cycles between the measured (error freeT and actual carrier phases. These quantities are nominally considered as unknown and are called cycle ambiguities. The cycle ambiguities on the phases of the P-code are assumed resolved. For a receiver using the P- code there is, of course, no ambiguity. For a codeless receiver, a priori range information more accurate than the 30M wavelength of the P-code is assumed to be available from earlier orbit determination. This may be an annoyance during episodes of very high (Ng>2.8xl0 ) ionospheric activity. Implicit in Equation (1) is the assumption that the dispersive instrument induced phase errors (particularly on the P-code) have been correctly calibrated and that no differential multipath effects exist. (Actually, multipath appears to be the dominant error source in this approach.) Equation (U may be considered to hold for a continuum of measurements in which the cumulative count of cycles for^ each of the four tones is tracked without loss of any cycles. In this case, ^, the measured phase at any epoch, is the exact number of zero crossings accumulated since the initial phase measuremenj^ plus the fractional phase at the epoch of the measurement. The quantities 4>, are said to be phase connected. While P and N are time variable and partially stochastic, the quantities nj^j^ and Ti,2 are constant integers. Solving the system in equation (1) yields estimates for Uti and nL2 tCrow et al, 1984] of 376 V = -*u- l^^^il^J V \2 ° -♦l2 ^ M .2 2 J It^I V which, for receivers using the P-code, reduces to (2) "l1 = -*L1 -^ 630 i^^ - 476 $p2 \2 = -*L2 -^ 611 *pi - ^91 $p2 (3) For codeless receivers that track the second harmonics of the carriers, the coefficients multiplying the P-code phases are doubled. The additional factors of roughly 4 multiplying each of the P-code/carrier frequency ratios in equation (2) arise from the proximity of the Ll and L2 carriers and from the opposite ionospheric signatures on the phase and group modulation arrival times. A time sequence of N estimates of nj^j^ and of nj^2 ™*y ^^ assembled from the set of phase measurement quadruplets obtained from a pass of GPS observations. From the sequence, (Sti» ^t?^* ^^® ensemble means of n,i and n-jn ™^y ^^ formed and the maximum likelihooa integer estimates of n,i and nT2 may be obtained. The a priori probability density for (n^i. ^t 2^ "^^ expressed as f^Ll'V) 'ff V^l^-Yl) «Hl2) (4) where 6 is the dirac delta function and the ot],g is the probability coefficient based on prior orbit determination information, hand over information from other participating terminals, etc. In the case of unbiased gaussian statistics, the a posteriori or conditional probability density of ^^Ll» ^^12^ given (n^i, *iL2^» ™*y ^® expressed as r r V exp[-Q(k,s)/2] S (k-nj_^) 6 ( s-n^^^) / I- - \ k s ^ ' ^ ' (5) P('^Ll»^L2l^l*''L2; == X J a^g exp[-Q(k,s)/2] k s where Q(k, s) is the quadratic form 2 Q(k,s) = X^^(k-S^^) + 2X^2Hli) (-^2) ^ ^22(-v)" (6) and where the X^* is an element of the inverse of the covariance matrix of n^i and &L2» which may be obtained from equation (2) when the statistical properties of the phase measurement sequences are provided. For independent statistics X-' would increase linearly with N; hence, the standard deviations for n, J and n, 2 would decrease as 1/\/nI The integer values of n, , and nx2 377 that maximize equation (5) provide the maximum likelihood estimates. In the case of uniform values for the aj^g, it can be shown from equation (5) that the standard deviations of the mean estimates, (nTj, ^to^* must be less than about 0.25 for this technique to reliably (p > 95%) provide the correct values of k and s. Equations (2) and (3) clearly demonstrate the requirement for sub-mill icy cle accuracies in the phase measurements on the P-code if one is to resolve carrier cycle ambiguities by this approach alone. The dilemma is that the large ft/fp ratio forces one to make P-code range measurements for cycle ambiguity to nearly the same accuracy as one is trying to attain through the carrier range observable. These P-code accuracy requirements would be major cost drivers in the receiver and antenna design. In addition to requiring high C/N values, corresponding control must be maintained of multipath effects and phase calibration. Reliable control of multipath induced phase error below a few millicycles is probably an unrealistic goal with low gain omni-directional antennas. Nevertheless, these algorithms were applied during the SERIES-X campaign of 1983-84 [Crow et al, 1984 and Melbourne, 1984], to assess their limitations and to evaluate the inherent phase stability of the SERIES-X receiver/antenna system. SERIES-X includes a calibration assembly that enables sub-centimeter relative phase accuracy on the P-code. From SERIES-X one obtains simultaneous and connected phase observations from all visible SV's of the five tones corresponding to the C/A code, PI, P2, and the second harmonics of LI and L2. These sequences of uninterrupted and phase connected observations, lasting over a pass, were examined for multipath effects. From a series of tests over a variety of controlled environmental configurations discussed in [Crow et al, 1984], we concluded that these particular receivers experienced multipath effects at the level of 0.003 - 0.03 cycle RMS. Figure 4 exhibits the best multipath results that were obtained with SERIES-X; the antennas in this test were well isolated and shielded by an extensive RF absorbing ground plane, and had an elevation cut off at about 20°. The spectral distribution of the multipath effects in these tests have sufficient power at longer periods to not totally cancel over a pass. Even without multipath, the SNR induced phase jitter in the SERIES-X receivers (e.g., '^0.03 cycle @ 1 sec on Ll) limits this technique to bounding the cycle ambiguity range rather than isolating it. Although reliable cycle ambiguity resolution by this method alone appears doubtful, on the contrary, resolution of n, ^ - nj^2 appears quite feasible. It may be shown from equation (2) for unbiased gaussian statistics that the ratio of the principal axes of the covariance ellipse for n-ti and n|^2 ^^ about 100 to 1 and that the ellipse itself is rotated about 45". The correlation coefficient between n^j and n^o ^^^ ^® shown to exceed 0.99995. This near linear regression reduces the domain of (n^^t , nT2) space to be searched for cycle ambiguity resolution to nearly a straight line. It suggests the use of transformations of the observables that exploit the small eigenvalue of the covariance matrix. The difference, nrj-nLo* ^^ aligned to within I*' of the smaller eigenvector. From equations (2) or (3), the instantaneous estimate of nTi-nT2 is given by n. Ll " \2 ^Ll ^L2 ^Ll ^ ^LZJ -( Ll ^2, (7) 19.1 *p^ + 14.9 *p2 - (*L1 - *L2, 378 and thus involves coefficients of the F-code phases that are some 30 times smaller than those in equation (2). If differential multipath effects on PI and P2 can be controlled to a few hundredths of a cycle, equation (7) suggests that Ot i-Ut? ^^^ ^® determined by a well calibrated receiver continuously tracking tlie P-code and carrier tones. The error in range (i.e., its differential or linearly combined version) due to errors in the estimates of n^ and nL2 is given by Ap = 43.2A/n^^-nj^2) + 10.7a( ^^ ^ ^^ ) (cm) (8) If n* 1 - n, 2 has been resolved, the remaining parameter, (n^i + 0^2^ /2, leads to ambiguities inP with a 10.7 cm granularity. THE UTILITY OF INTERMEDIATE FREQUENCIES Introducing additional tones at intermediate frequencies between the carrier and the clock frequencies, would greatly facilitate resolution of carrier cycle ambiguities. One possibility is the use of the L3 carrier planned for the operational GPS satellites. The L3 frequency is at 1381 MHz, which is exactly 135 fp. L3 will be coherent with Ll and L2. The principal function is for telemetry, but it will carry the C/A code and a data stream of the order of a kilohertz in bandwidth. The current plan is to transmit on L3 daily, but for only short intervals. The transmitted power is 20.1 dbw which is comparable to the L2 power level. L3 is roughly 40 MHz below the hydrogen hyperfine line, an indispensable tool in astronomy. The prospect of continuous operation of L3 is problematical. However, if L3 could be operated for a sufficient interval it would be very helpful. One implementation scheme would combine at baseband the tracked L3 tone with those at Ll and L2 to obtain intermediate tones at f^ = fj^^ - fj^g *^^ ^5 "^ ^12 - fjo which would be continuously tracked and jjhase connected. In this case, the quadruplet of measured phases C^^, ^n2* ^4* ^5^ would be used to obtain estimates of the cycle ambiguities, Ua and Ue, or the intermediate tones. Using the analogous approach as in equations (1) and (2), it may be shown that the instantaneous estimates of n^ and n^ are given by n. 2 LSV^Ll f,,(f - f L2j ^4(^11^13 f f2 Ll 5 L2. hA f5(^L2^L3 - ^Ll) fp / ^Pi fp / "*'p2 t (9) Equation (9) reduces to ^ = lA.87^p^ + 4.13ct)p2 - *4 n = 4.24^ , + 10.76$ 2 " ^^ (10) •^Pl Grand estimates of n. and ne would be obtained by averaging n^ and n^ over an ensemble of phase connected observations. The diminutive size of the coefficients in Equation (10) results from f^ and fj being only 19 and 15 times fp, respectively. Also, these tones all effectively carry the same sign for the ionospheric effect. For receivers that track the second harmonics of the carriers, these coefficients would be doubled. In either case, a P-code 379 phase measurement accuracy at 1% of a cycle should he sufficient to resolve the cycle ambiguities on the intermediate tones. Equation (7) also provides an additional condition on ii* + nc. One could use these intermediate tones and their resolved cycle ambiguities to obtain estimates of the range and ionospheric corrections. However, the proximity of the tones leads to considerable magnification of errors. It may be shown that the measurements of P and KNe from the intermediate tones are given by p = 698$, - 689*^ 4 5 (11a) KN /r = 615*, - 779*, e 4 5 (lib) Here, the coefficients are in cm, f = '^^Ll^L2^L3^ » *^<^ *^4 and $5 are the reconstituted phases including n^ and Uc. Of course, the physics of Ne versus time can be utilized to filter Equation (lib) over a limited time interval, which may be fed back into Equation (11a) to somewhat improve the statistics on P. Thus, the intermediate tones should yield a vacuum range observable that is about an order of magnitude more precise than that provided by the dual band P-code pseudoranges. Even so, the data noise (e.g., 10 cm @ 1% phase error) is likely to dominate other error sources. To reliably eliminate data noise as a significant error source, (e.g., so that it is well below the 1-3 cm error level of tropospheric water vapor), the carrier range would be of utility. To obtain carrier range^ one would apply the cycle ambiguity procedure again to the phases ('J'ti* ^l2*^L3* *^4' ^5^ ^° obtain the individual carrier cycle parameters. In tnis case, it may be shown that fij^j, nj^2 ^^^ ^L3 ^^^ given by 'LI 'L2 ^Ll -^ ^12^ L3/ ^L2{ '4(^11 'l2) LI ) - f L2 fu(fL2 ^ 'l3 L"uj |_f^( LI ^u) '12(^0 -^ fL3 S(fLl-f L2 + f, ,f. ^5 ( ^Ll - 'li) ) 'Lli'Ll^^-i) '5 { f LI - f L2 ) - 1 -1 -1 For TLj^i and 11^2 » Equation (12) yields 'LI ^L2 ''L3 (12) n^^^ = 61.8$ - 68. 0$ - ^^i. (13) It is noted that these coefficients are not doubled for receivers tracking the second harmonics of the carriers. Equation (13) still requires moderately stringent phase measurement accuracies on the carriers, but they are roughly a 380 factor of 5 relaxed over those associated with Equation (2) and an order of magnitude relaxed for receivers tracking the second harmonics. Another possible useful tone is the downlink S-band carrier used on the GPS for monitor and control. It is at 2227MHz, but it is not coherent with the navigation tones. COMBINED RANGING AND COMMENSURABILITY APPROACHES The combined group delay, carrier tracking, and possibly also the L3 tracking, may fall short of providing definitive values of the carrier cycle integers. Instead, equation (5) would provide a domain of discrete values within which the integers must lie. This would provide valuable a priori information to proceed with the commensurability approaches It is convenient to separate the geometric delay and ionospheric terms through a transformation of the basic observations. Let the new phase observables ^andXbe defined in terms of observables through the transformation the basic P-code and carrier i>. \ I Ll - f L2 \ } "Ll - f L2 hi - ^Ll ° " 'l2- hi I Ll pi p 'li^i^^ 'Ll ^2 (14) This transformation leads through equation (1) to the "diagonal" form for the equations of condition /*.\ / vl \ -f f 0\ Ip/C + T -1 -1 ^e/^Ll^L2 m V (15) where f is defined by f*= (fLl2-f2L2) /y^l2 + fL22 The transformed cycle ambiguity parameters, m and t^ are given by (16) 381 (17) From equation (15) it follows that only one cycle ambiguity parameter (m) is required to recover carrier based vacuum range, and similarly, only one parameter (-£) for the carrier based columnar electron content. They are constrained to discrete values through equation (17) by the integer constraints on n, , and ^-rn' Equation (17) is equivalent to rotations of the (nyj^* "l2^ axes of 38° for m and 52° f or £. . Hence, only about 10% of the major eigenvector of the covariance ellipse of n,i and nT2 is projected into the standard deviations of m and Z, The ambiguity granularity in vacuum range is 10.7 cm arising from errors in (n^^j + nj^2)/2 and 43 cm for errors in ^'^L1~'^L2^- If the time series of connected P-code and carrier phase observations is insufficient to resolve the cycle ambiguities, but is effective in narrowly bounding the probable range of integer values, then the following commensurability approach, which is an alternative to those cited earlier, may be useful. Also, if the L3 carrier is tracked and n# and nc are resolved but not Hti, njo or njo, then the vacuum range determination based on $a and $5 in equation (lla) sharply limits the possible integer values of the amoiguities. This technique may be practicable if GPS ephemeris errors could be adequately controlled. It is a lattice theoretic approach which is predicated on the overall system accuracy being a small fraction of the carrier wavelength over the observing session, and on the diophantine character of the resulting cycle ambiguity constraints. An outline of the technique is provided here for the single regional baseline case in which only relative position information is sought. The extension to multiple terminals involving position and GPS ephemeris determinations with fiducial point constraints is not addressed. Let the quantity ^^ ^^ '^^ linear combination of the Lj^ and L2 differential carrier phase defined in equation (14) to the k^" SV. Treating ^, as a residual differential observable between the two terminals plus known calibrations (actual minus model and hence a nominal value of 0), it may be expressed as a linear function of the residual baseline components and clock offset between the GPS terminals in matrix notation as Y = AX - M + € (j3) where /= *i ♦[ "'' and A is the information matrix given by A= f* ^2 ^3 1 r r . ^2 ^3 ^' (20) where the a^ are the differential direction cosines to the k SV (plus small 382 terms due to parallax, refraction, relativity, etc.) The index r is the total number of SVs under simultaneous observation. The vector X is defined by xT = (x, y, z,t) (21) and contains the residual components of the baseline expressed in a terrestrial reference frame (in light-seconds) and the clock offset between the two GPS terminals. The quantity M is the residual cycle ambiguity vector defined by M^ = (m^ . . . , m^) (22) where m is the differential ambiguity parameter for the k SV and defined by equation (17). The quantity £ is the lumped error vector due to possible instrumentation errors, calibration errors and imperfections in the model used to form the residual observables. Define the r x r symmetric matrix E by E = I - A(a''^A)"^a'^ (23) Operating on equation (18) with E yields E H* = -EM + E £ (24) thereby eliminating the baseline components and the clock parameter. It can be shown that E is an idempotent matrix (E =E) of rank r-4 (provided A is of rank 4). The non-zero eigenvalues of E are unity. Each of the r-4 associated eigenvectors V^ satisfies the 4 conditions defined by A^Vi =0, i = 1, . . . ,r -4 (25) Diagonalizing equation (24) leads to the system of linearly independent diophantine equations vTm = -vTt + vTc i = 1 , . . . , r - A (26) which must be satisfied by the ambiguity parameters as defined by equations (17) and (22). Actually, there are only r-1 linearly independent ambiguity parameters. Equation (25) requires that Vjl = i = 1 ...... r - A (27) where 1 = (1,...,1). It follows, without loss of generality, that equation (26) may be rewritten in the form 1 (M-mh) + i^-i-i) - (.-e^) =0 i=l,...,r-A (28) Thus, it is the double differenced ambiguity parameter that formally enters the constraints in equation (28). This result could have been directly obtained by eliminating the clock term through a redefinition of 'i^ and M in equation (18) as double-differenced quantities. Equation (28) must hold at each observation epoch which may total into the hundreds for a typical session involving simultaneous observations of the same SVs. One could subject equation (28) to the usual least squares approach to 383 obtain estimates of the tnJ-m , This might be useful in the case where the time variable parts of (x, y, z) have significant stochastic or unmodeled components. But the power in equation (28), when the system errors are very small compared to a carrier cycle, is derived from invoking the constraints that the m^-m are confined to a set of discrete values as defined by equation (17) and the integer constraints on n^^ and nT2* Equation (28) may be considered as a r-4 system of hyperplanes cutting through a r-1 dimensional quasi-uniform lattice. The coordinates of the points of the ^lattice are the values of the r-1 double differenced ambiguity parameters, m^-m , j=2, ...,r. Only coordinates of lattice points lying in the intersection space of the hyperplanes are allowable values of the ambiguity parameters. At each observation epoch equation (28) defines a new system of hyperplanes which will be only slightly displaced from the previous ones provided E is small. Furthermore, the changing SV geometry with time causes the eigenvectors V- to change which in turn change the orientations of the hyperplanes passing through the lattice. These rotations of the hyperplanes cause different lattice point coordinates to satisfy equation (28). If the axes of rotation of the hyperplanes themselves vary with time, then the only lattice point satisfied at all observation epochs is M=0. In a practical computer developed histogram of lattice point successes, £ is set to zero, but one would assign a gate within which equation (28) would be considered satisfied; in effect, the hyperplanes of equation (28) assume a finite thickness and a set of moire-like patterns corresponding to successes would develop. These patterns would change with SV geometry leaving M=0 as a preferred coordinate. The gate size should be chosen to balance the need for adequate sample size in the histogram and, on the other hand, to obtain maximum resolution. A number of limitations to this scheme are evident. One is the potential size of the problem. For r=5, one obtains a 4-dimensional lattice. If R is a three-sigma bound on the ambiguity integers, i.e., n, = 0, + 1, ... + R, then, ± keeping in mind the near linear regression between n^j and nL2» ^^^ number of lattice points for small R goes as (2R+1)^, a dramatically increasing function of R. It is apparent that minimizing R from the time series of P- code and carrier phase measurements is crucial. Another problem is the potential magnitude of C . From the foregoing discussion, it follows that the lattice theoretic approach requires maximum system accuracy, significantly smaller than the spacing between lattice points. The instrumental and propagation media errors should be controllable to about 15% of a lattice spacing. The GPS ephemeris errors probably limit the effectiveness of this technique to baselines below a maximum length. Ephemeris errors of 100 nrad (2M orbit errors) map into an equivalent error of 1 cm in differential delay on a 100 km baseline. From computer simulations, the effectiveness of the lattice technique appears to diminish when the system errors exceed 30% of a lattice spacing. For accurate ephemerides in the 1-2 dekameter range, the technique may be extendable to continental baselines. Also, the notion of using the strong VLBI-based fiducial point information to control the smearing effects of SV ephemeris errors should be considered. Another possible limitation which might have a more serious impact is the existence of direction dependent phase errors originating at the SV due to multipath from antenna array. This effect would be roughly proportional to baseline length and is probably small for regional baselines. Further investigation of this error source and techniques for its calibration should be undertaken. 384 (J ^/M -iQOC 3 HI is a>rot s « « W u « »= a u >o < a I •-) •a u aoi-t •3 §v S W CB X -o e I 3 41 09 « e « 09 o •»4 a. " M iJ u r (UO) Miao ivnaisau 3 ao Z < UJ o o a. O < (tea) aoniiivi 385 ACKNOWLEDGEMENT The research described in this paper was carried out by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. REFERENCES Bossier, J.D., Goad, C.C., Bender, F.L., 1980, "Using the Global Positioning System (GPS) for Geodetic Positioning," Bull. Geod., 54 pp. 553-563. Counselman III, C.C, and Gourevitch, S.A., 1981, "Miniature Interferometer Terminals for Earth Surveying: Ambiguity and Multipath with Global Positioning System," IEEE Transactions on Geoscience and Remote Sensing, GE-19. No. 4, pp. 244-252. Crow, R.B., Bletzacker, F.R., Najarian, R.J., Purcell Jr., G.H., Statman, J.I., and Thomas, J. B., 1984, "SERIES-X Final Engineering Report," JPL D- 1476, August 1984, Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California. Dixon, T.H., Melbourne, W.G., and Thornton, C, 1985, "A GPS Measurement System for Regional Geodesy in Mexico and the Caribbean; Science and Technical Plan," JPL 1710-4, Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California. Goad, C.C. and Remondi, B.W., 1984, "Initial Relative Positioning Results Using the Global Positioning System," Bull. Geod., 58., No. 2, pp. 193-210, Kroger, P.M., 1984, "GPS Geodesy in the Caribbean: Evaluation of Data Types for Baseline Determination," Internal JPL Communication, Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California. Melbourne, W. G., 1984, "GPS-Based Tracking System for TOPEX Orbit Determination," Proceedings of SPIE, Recent Advances in Civil Space Remote Sensing, Vol. 481. pp. 181-192, May 3-4, 1984, Arlington, Virginia. Melbourne, W.G., Thornton, C, and Dixon, T.H., 1984, "GPS Measurement System Development for Regional Geodesy in the Caribbean; Operating Plan," JPL 1710-3 Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California. Remondi, B.W., 1984, "Using the Global Positioning System (GPS) Phase Observable for Relative Geodesy: Modeling, Processing, and Results," Doctoral Dissertation, University of Texas at Austin. Yunck, T.P., Melbourne, W.G., Thornton, C, 1985, "GPS Based Satellite Tracking System for Precise Positioning," IEEE Trans, on Geoscience and Remote Sensing, in press. 386 CONCBPT OP THE GEODEriC INTERFEROMETER "RYSY" POR BASELINE DETERMINATION WITH GPS Zdzls3:aw J. Kryslnski Krzysztof K.Vorbrlch Polish Academy of Sciences Space Research Center 01-237 Warsaw, Poland ABSTRACT. A concept of an GPS interferometer is described, GPS radio signals are treated as noise and the cross-correlation method for their detection is applied* Signals in a reference and a remote baseline points are received and amplified with frequency conversion. The directional antennas with the moderate gain factor are used, Pour video SSB signals from L-i and L2 frequency ranges are obtained at separate outputs of a double chsumel receiver. At least three signals are extracted from the total GPS spectrum for the removal of a fringe phase ambiguity. Next they are registered by means of the MARK II technique, A software correlator preprocesses the data in order to get a complex cross-corelation function. Primary observable s: a fringe phase and amplitude, a fringe rate and the group delay are extracted. At present the main stress is put on the proper hardware and software design, INTRODUCTION New possibilities for geodesy and the Earth surveying appeared after GPS has been introduced, VLBI techniques designed for radioastronomy can be easily applied to baseline determination with GPS, The GPS constellation makes possible to observe continuously at least four satellites at arbitrary time and place* Wide signail spectrum and pseudorandom signal modulation make it possible to process GPS radio signals similiarly to quasar signals processing im VLBI, Received GPS signal power is relatively high and this extremally reduces the sizes and costs of antenna arrays and interferometer receivers* Small, mobile GPS interferometers were developed /MacDoran 1982, Counselman 1982/* GPS INTERFEROMETER DRAFT The GPS signal spectrum /Spilker 1980/ enables the use of ihe bandwidth synthesis technique /Rogers 1970, Thomas 1973/. Thus it iis- possible to eliminate fringe phase ambiguities within a moderate signal-to-noise ratio* It is obvious to choose from the total GPS spectrum four frequency bands centered at f^ =f£^ +fo/2, f^^fz-y -fo/S, fjsif^^ +^0/2 and :C?r«fiz -fo/2, where f^.^^^ are carrier frequencies of 387 both Li and L2 ranges and fg is a standard Trequtncy. Simlliar idea is described in /MacDoran 1979/. We may synthetize two effective frequency bands: B^^^ af ^ -f^ "f^ -f^ af o and Ba^f/s =f^-f4a35fo* GPS radio signals are treated as noise. The pseudo-random coherent modulation for the SNR improvement is not taken into account. The four choosen bands have 2MHz bandwidth in order to minimize requirements for SNR prameters. Such bandwidth involves sufficient angle resolution of the interferometer with an omnidirectional antenna. In the model, however, the directional one is used first. The receiver pseudo-random signal is synehronically down converted and single side-band detected, and then converted into binary form to further registration. The MARK II registration technique is use4 /Clark 1973/. Frequency quartz standards and LO synthetyzers have sufficiently low level of phase instabilities, Differentialjphase drifts of LO can be easily extracted by the quasi -simultaneous observation of the 4 satellites. The receivers are phase calibrated in order to measure their own phase delays. Two registrations from the two separated points of the baseline are used to further computer processing. The correlation method of the detection of observables is used. Signals from all respective channels are cross-correlated and a fringe stopping procedure is used. For many particular time periods the complex correlation functions are defined. The estimates of measured fringe amplitude Ro » fringe phase 0o» group delay r^ and fringe rate F^j are obtained, MBASUREMBNJ? ERRORS The principal factor of measurements accuracy of an interferometer is the signal-to-noise ratio, /< • It may be expressed /MacDoran 1979/: where: S is a radio signal flux /Jy/, 71 is a wavelenght /m/, Gx and Gj/ are antenna gains in a reference and a remote baseline points, Tsx and T^^ are system temperatures, B is a signal bandwidth, T is coherent integration time. Factor |5 expresses information losses caused by digitalization £md data processing. For MARK II ^s2,3. Results of the correlation process are estimates of the Ro»0o»tj and F|^ . Sometimes it is convenient to measure the time derivative of the delay, i&a • Standard deviations of the int erf erome trie observables are expressed as follows /Nes 1981/: ^'^^ "" fiwr /2/ b/< — jji /3/ ^ = Trtfe /*/ 388 Wa may extract the measured time delay from phase estimates obtained for particular frequencies /Thomas 1973/: where: (^i,\ are measured at cO^y fringe phases, A(^iV)s^r represents a differential phase effects of an equipment ,5"0 represents all other phase effects, B^/f afc-f; • Instrumental phase effects may be eliminated after the proper equipment calibration. Other phase effects, like the ones caused by the signal propagation media or oscillator drifts, can be reduced in the data processing, REQUIREMENTS FOR AMBIGUITY REMOVAL The delay ambiguity of the fringe phase measurement may be easily eliminated in three steps. At first, we assume fringe phase measurements at f^ , f^ ^^^ ^^ frequencies. We synthetize the first effectiye bandwidth By^^ aT0.2!^IHz /'^4»9l •l^T^s/ and calculate the rough time delay f^ from equation /6/, The correct value of 2kTris determined from rough baseline coordinates. In the next step we synthetize the ^ze4f =358.05MHz /T2»2,79ns/ and calculate the intermediate accuracy time delay, tl. The ambiguity of this calculation may be eliminated when the standard delay deviation of the previous result is smaller than T2 /2,79ns/, that is, according to /4/, for the signal-to-noise ratio/i>20. In the third step we measure the fringe phase with the highest accuracy of the single channel interferometer. The former result,e,g, delay f 2. may be used for ambiguity removal if only the standard deviation of theTz. is smaller than 0.63ns /for f^^ =1,58GHz/. Such deviation is obtained for/4 «2.5, So, we may determine the formal instrumental error of the single fringe phase measurement as smaller than 18 /or about 30ps of the delay for Ai^«.19m/, In these computations instrumental and other phase errors were not taken into account, REQUIREMENTS FOR COHERENT INTEGRATION TIME AND AMOUNT OP INFORMATION From equation /I/ we determine minimal amount of information Ns2BT and the necessary coherent integration time. We assume /for Li range/ values: S«280000Jy, 7l«.19m, Gx«Gy=500, Jlsx ^Tsy «200K, B=2MHz,^a2.5 and/i a:20. So, we obtain N«20kbits and Ti*5ms for the single channel observation of one satellite. For the four frequency channels and the four satellites we have 320kbitff of data and we may define single estimates of measured observables. For better accuracy much more data must be used, "RYSY" RECEIVER PREDESIGN GPS radio signals from both L^ and L2 frequency ranges are received, Except for the receiver front-ends, the transmission channels of inteimediate frequency are symmetrical. 389 The first LO frequency is placed in the middle of the f£^=154fo and f/.2. = 1 20fo , and is equal to 137fo« The first intermediate frequency is then 17fo« The second LO frequency is 12fo and the second IF frequency is 5fo • Orer 7096 of the total spectrum of the both L^ and Lz ranges is transmited in the parallel receirer channels with gain flatness better than ±1dB. Transmission phase nonlinear! ty is less than ±4° at the band edges. The receiver temperature is about 150K, The second IP signals are next transmitted to. the synchronic single side-band detectors. Signals from L^ and Lz channels, centered at 4.5fo and 5.5fo frequencies are down converted to the video band. Defined upper or lower bands are extracted. All signals are bandlimited to 2MHz. Pairs of orthogonal LO frequencies, 4.5fo and 5.5fo are synthet3rzed for SSB detectors. All the analog, video signals are then converted into binary form, formatted and registered. The receiver block diagram is shown in Figure 1. DATA SIMULATION AND SOFTWARE CHECKING Till today the GPS signal has not been to our disposal. It was necessary to simulate interferometer data in order to check the software. Pseudo-random fractional normals N/0,1/ are employed to imitate both, the source and the receiver temperature effects in the reference and the remote baseline points. The signal referred to the remote antenna is transformed to the frequency domain and simulato the efemeride controlled phase variations, caused by Doppler effect, is applied. After the inverse procedure the remote signal is transformed to the time domain and contains given phase changes, related to the reference phase. Incoherent "receiver" noise is added to the "antenna" signal in order to achieve adequate signal-to-noise ratio. Then the low-pass digital filters are employed to imitate the registered signals which have required spectral characteristics. Next, simulated signals are used to check software correlator. Signals are shifted and cross-multiplied. Products are integrated. The counter rotation procedure is applied. The sine and cosine channels are introduced in order to obtain the complex correlator. TEST RESULTS Figure 2 illustrates the cross-correlation function for Wa500 words /each of 32bits long/ and for initial signal-to-noise ratio SNRtv"oo and 1.0. Signals had been bandlimited. The filter bandwidth was equal to the half of the Nyquist frequency. The employed particular filter was one the simplest of FFT type. Van Vleck correction was accounted for. All software trials were carried out by an ordinary computer RIAD 32 /the IBM 360 type/. 390 4 X CM -I- O I o II CL 5: i II H W >-• tn s • 4* O o o H P4 CO /f i ^ /|\ -^ <4| ,-ll ~-» 1 -J ^ •< t 2 H ^i> 0. v/) VO 391 392 REFERENCES Clark, B, G., 1973: The NRAO Tape-Recorder Interferometer System, IEEE Proc, 61, 9, pp. 1242-1248. Counsclmaui III, C. C, 1982: The Macrometer Int erf erome trie Surveyor, Proc. Int'l Symp. on Land Information at the Local Lerel, UniT, of Maine at Orono, pp. 233-241. MacDoran, P.P., 1979: Satellite Emission Radio Interferometric Earth Surveying SERIES - GPS Geodetic System, Bull. Geod. , 53» pp. 117-138. MacDoran, P.. P., 1981: SERIES, CSTG Bull., No3, Nes, H., 1981: The Accuracy of Very Long Baseline Interferometry Observable 8, Radio Sci., 16, pp. 947-952. Rogers, A. E. S. , 1970: Very long baseline interferometry with large effective bandwidth for phaae-delay measurements, Radio Sci., 5» 10, pp. 1239-1247. Spilker, J. J., jr., 1980: GPS Signal Structure and Performance Characteristics, NAVIGATION , pp . 29-54, the Inst, of Navigation Thomas, J. B., 1973: An Analysis of Long Baseline Interferometry, JPL Tech. Rep. 32^1526, XVI, part III, pp. 47-64. 393 MULTI-STATION GPS WITH ORBIT IMPROVEMENT E.G. MASTERS A.STOLZ University of New South VJales P.O. Box 1, Kensington. 2033 AUSTRALIA ABSTRACT For regions such as Australia where the accuracy of currently available GPS ephenerides may be inadequate for precise surveying, improving position determinations using orbit adjustment may be important. Existing GPS positioning software was modified to permit simultaneous multi-station processing and orbit improvement. The software was tested on the data acquired during the FGCC campaign and calculations were done to assess whether the method gives improved baseline measurements. For networks of less than 50 km in extent, orbit improvement is not warranted unless the orbit error exceeds 200 m or a baseline a few hundred kilometers long is included in the network. The results of the study are presented and current plans for software development are briefly described. INTRODUCTION Two options for processing GPS phase observables are: (1) the data can be processed as single baselines which are then combined in a rigorous adjustment; and (2) a rigorous one-step multi-station adjustment can be computed. There are good practical reasons for first processing the data as single baselines, not the least of which is that cycle-slips are easier to edit out. An advantage of the multi-station approach is that the correlations which exist between differenced observations can be more easily accounted for. The multi-station procedure is also readily modifiable to include orbit improvement. Kouba (1983) demonstrated that the latter approach improved positioning accuracy obtainable with the TRANSIT system and one would expect the same to apply to GPS. In Australia there is presently some doubt about the availability of accurate GPS ephemerides to the general surveying community. This is of particular concern to potential users of uncoded instruments. Moreover, interest in GPS for crustal movement studies and for control surveys is high. Accurate orbital data is essential for both these applications. Australia could establish its own tracking network for orbit determination to overcome this obstacle in which case Australia should also develop its own GPS baseline and orbit processing software 395 (Stolz et al, 1984). Similar conclusions were reached by investigators in other countries (Beutler et al, 1984; Nakiboglu et al, 1984; Goad, 1985). In this paper we describe our earlier attempts at developing an Australian GPS baseline and orbit determination package. MULTI-STATION POSITION DETERMINATION WITH ORBIT IMPROVEMENT The general mathematical model describing simultaneous orbit improvement and position determination can be written as: f(x,x',l) = (1) where x is the vector of unknown parameters including ground station coordinates, x' is the vector of satellite coordinates at observation epochs, and 1 is the vector of observations. The solution of the satellite equations of motion together with initial conditions constitute an additional constraint for the vector x' , given by g(x',x^) = (2) where x is the initial state vector comprising either the initial values of the osculating elements or the initial position and velocity components of the observed satellites. The system of equations (1) and (2) together with the relevant a priori covariance matrices form the basis of the orbit improvement and multi-station positioning method. The equations of motion can be solved using numerical or analytical techniques. Beutler et al (1984) summarise the relative merits of these methods. In essence the numerical methods provide the maximum flexibility and accuracy, both of which are required for high-precision applications. On the other hand, the analytical methods are generally less demanding on computer time. Nevertheless, for GPS orbits numerical methods are appropriate. Indeed, we find that the computations can be performed interactively. The orbit of the satellite depends on various forces of gravitational and non-gravitational origin. The perturbing forces which contribute to the GPS satellite motion at the 1 ppm level are the Earth's gravity field, luni-solar attraction and solar radiation pressure. SOFTWARE DEVELOPMENT We modified the single-difference software developed at the United States National Geodetic Survey (NGS) by Clyde Goad to include a numerical orbit integrator and models for the forces due to the Earth's gravity field, luni-solar attraction and direct solar radiation pressure. A predictor-corrector type numerical integrator was incorporated, as were the gravity field model of Lerch et al (1983) 396 truncated at degree 8 and a two-plate model to account for solar radiation pressure. Analytical expressions for the partial derivatives of the satellite state vectors were derived assuming Keplerian motion. VJe consider this approximation adequate for the results presented below. However for high-precision applications, numerical methods and more accurate expressions for the partial derivatives will be necessary. NUMERICAL TESTS At this point in time, no GPS surveys have been carried out for geodesy in Australia. Accordingly, we tested our programs on the data acquired during the FGCC tests (Hothem & Fronczek, 1983). Three baselines of length 750 m, 18 km and 42 km were selected. Our software yielded baseline measurements which agreed to within 2 ppm with the values provided by NGS. Since the orbital data made available to us comprised a single state vector of unknown accuracy for each satellite for each day we believe these differences were the result of orbital uncertainty and not programming error. The baseline precisions obtained from our software are given in TABLE 1. A priori orbital uncertainties of 0, 40, 200 and 2000 m, corresponding to baseline errors of 0, 2, 10 and 100 ppm respectively, were considered. The values in brackets refer to the root-sum-square (RSS) baseline precisions obtained from the solution with the orbit held fixed and the precision calculated from the well known rule-of- thumb for which a given error in the satellite orbit introduces an error in baseline reduced by the ratio of the baseline length to the satellite's altitude. The orbital integration process was assumed to be error free over the arc length considered and the single-difference observations were assigned precisions of 1 cm. These assumptions seemed plausible to us. None of the baselines used in this study were observed simultaneously. A calculation was performed to simulate this case. The results are given in case E of TABLE 1. If the figures shown inside the brackets in TABLE 1 are less than those outside the brackets, then orbit improvement is not warranted. For the small network considered, multi-station positioning with orbit improvement is not warranted unless the orbits are worse than 200 m. Better accuracies are obtained when a longer baseline is part of the network. A comparison of the cases D. and E. in TABLE 1 shows a slight improvement in baseline precision for simultaneous observations. However, the improvement obtained is insufficient to advocate that networks be only observed simultaneously. The improvement of baseline precision obtained by including longer baselines in the smaller network was examined more closely. FIGURE 1 shows the effect of a long east-west baseline. The effect of a long north-south baseline is shown in FIGURE 2. Including a baseline with long east-west or north-south components improves the precision of the shorter baselines. 397 In FIGURES 1 and 2, the satellite state vectors were assumed known to within 2000 m (lOOppm) and the components of the long baseline were estimated along with those of the smaller network. In retrospect these orbits were pessimistic and selected solutions were therefore repeated with better orbits. With 100 m (5ppm) orbits the baseline precisions improved approximately by a factor of two. This shows that in practice baseline solutions will be much improved with the proposed method. Since the satellite laser ranging and VLBI techniques are now well established and since these techniques are more accurate than GPS over long baselines, it would be more realistic to constrain the long baseline components to an accuracy of a few centimeters. This case was also studied, with the result that the precisions of the components of the short baselines improved by approximately a factor of two over those in FIGURE 1. PLANS FOR THE FUTURE Our software became much too cumbersome to use, difficult to modify and unsuitable for all observation types. VJe therefore decided to start from scratch and develop a package which is, easy to modify, flexible with regard to observation type and estimated parameters, machine independent as far as possible, and satisfies a whole range of surveying needs from low to high precision applications. The program outline is sketched in FIGURE 3. We decided to adopt a modular approach, so that the program will run on a large personal computer. A prototype is expected to be completed by June 1985. Acknowledgements We have benefitted from discussions with Chris Rizos and Bob King. The data for the FGCC tests and NGS software were made available by Clyde Goad. The Australian GPS software package described in this paper is being developed jointly with the Division of National Mapping, Ewan Masters is supported by a Program Grant under the Australian Research Grants Scheme. REFERENCES BEUTLER, G., DAVIDSON, D.A., LANGLEY, R.B., SANTERRE, R. , VANICEK, P.B., & VJELLS, D.E., 1984: Some Theoretical Aspects of Geodetic Positioning Using Carrier Phase Difference Observations of GPS Satellites, Mitteilungen der Satellitenbeobachtungstation Zimmerwald . Nr. 14 . Bern. GOAD, C, 1985: Precise Relative Position Determination Using Global Positioning System Carrier Phase Measurements in a Non-Difference Mode, These proceedings. HOTHEM, L.D. & FRONCZEK, C.J., 1983: Report on Test and Demonstration of Macrometer Model V-IOOO Interferometric Surveyor, U.S. Federal Geodetic Control Conmiittee. Rept. FGCC-IS 83-2 . NGS/NOAA. 398 KOUBA, J,, 1983: A Review of Geodetic and Geodynaraic Satellite Doppler Positioning, Reviews of Geophvs. Space Phvs.. 21 . 27-40. LERCH, F.J., KLOSKO, S.M. & PATEL, G.B., 1983: A Refined Gravity Model from LAGEOS, NASA Tech. Mem. 84986 . Goddard Space Flight Center, Greenbelt, Md. NAKIBOGLU, M,,BUFFETT, B., SCHWARZ, K.P., KRAKIWSKY, E.J., & WANLESS, B., 1984: A Multi-pass, Multi-station Approach to GPS Orbit Improvement and Precise Positioning, Proc. IEEE . 153-162. STOLZ, A., MASTERS, E.G. & RIZOS, C., 1984: Determination of GPS Satellite Orbits for Geodesy in Australia, Aust.J.Geod.Photo.Surv. .40 . 41-52. 399 TABLE 1. BASELINE PRECISION Solution Oi cbit error (ppm) Baseline 0. .75 km 18 km 42 km Precis: Lpn, ppm A. 1 baseline (3-hour arc) 2 10 100 36 36 38 86 ( 36) ( 36) ( 37) (106) 1.5 3 20 67 (1.5) ( 3) ( 10) (100) 0.4 2 5 24 (0.4) ( 2) ( 10) (100) B. 2 baselines (1-day arc) 2 10 100 36 37 80 ( 36) ( 37) (106) 3 11 71 ( 3) ( 10) (100) - C. 2 baselines (1-day arc) 2 10 100 - 3 7 32 ( 3) ( 10) (100) 2 5 26 ( 2) ( 10) (100) D. 3 baselines (2-day arc) 2 10 100 36 37 64 ( 36) ( 37) (106) 2 7 27 ( 2) ( 10) (100) 1 5 21 ( 2) ( 10) (100) E. 3 baselines (3-hour arc)^ 2 * 10 100 36 36 43 ( 36) ( 37) (106) 2 6 24 ( 2) ( 10) (100) 1 3 16 ( 2) ( 10) (100) Values in brackets give the RSS precision obtained from solution holding orbit fixed and precision calculated from rule-of- thumb. * observed simultaneously 400 FIGURE 1. 500 1000 EAST -WEST BASELINE LENGTH, km Baseline precision obtained when a long east-west baseline is included. 500 1000 NORTH-SOUTH BASELINE LENGTH, km FIGURE 2. Same as FIGURE 1 but with the long baseline in the north- south direction. 401 CO o •H m bOx: f-i c o. g^ •^ CO (0 V4 T3 C 9 00 •H CO (0 CO 0) H q; CO D. > M Vi (^ • <-( ••-1 a o r-t 4-t > 0) (U M f-4 r-t (U CO V4 U 4J d o >» a CO <+^ U '.-• i i-i V CO ■u a CO O Vl -H 00 4J a; CO CO 4J •r^ M C M oei •H CO U > r-l T3 M r-< e M PU CO CO C M o o •iH CO '<■* Wl 4J .U « 'H CO S -Q 3 3 M cr coo; as o M H H O O g o .< M CO a> 1— 1 i-i CO JQ •H H-( CO CO 4J O > 13 M MO CO 0) (U •<-! O. O. CO 4-1 >»XI -H 01 4J O CO ^ CO O CO >%-0 O. h4 ^ C (U o O. CO U (U CO a a a; a o> -^ C M M s •■-I o q; C jO >M U-l (U S >M 4J o o -^ w o *j 73 -a CO i-t (0 •H "O *J a M CO CO ?HI 0) a otf CO OJ o CO I-I « u J= 43 *J g O. CO CO > ^ <-* u s (U Oi u no CO rH O J3 CO S O o CO O M 402 SOFTWARE DEVELOPMENTS FOR GEODETIC POSITIONING WITH GPS USING TI 4100 CODE AND CARRIER MEASUREMENTS Gerhard WQbbena Institut fur Erdmessung Univeritat Hannover Nienburger Strasse 6 3000 Hannover 1 Federal Republic of Germany ABSTRACT. With phase measurements on the carrier signals of GPS satellites a highly accurate relative geodetic position- ing is possible. A main problem concerns the determination of the phase ambiguities. A method which helps to solve this problem using simultaneous P-code and carrier measure- ments is presented. After a sufficient time of observation pseudoranges with a noise level of a few millimeters are obtained. Software developed at the University of Hannover for the simultaneous detennination of absolute and relative positions using these ranges is described. GPS RECEIVER CODE AND CARRIER MEASUREMENTS A GPS receiver reconstructs either the code, the carrier or both signals of an incoming satellite signal. Measurements are made on these signals through the code and carrier tracking loops. The code tracking loop correlates the incoming code with a code replica generated by the receiver. If maximum correlation is reached the phase of the code replica is a measurement of the received code phase at a time event of the receiver clock. In the carrier tracking loop the relative phase between the reconstructed carrier signal and a reference signal generated by the receiver is measured: where «p - is the measured relative phase, 9 - the received carrier phase and 9 - the phase of the reference signal. wkh the carrier phase can be computed by It is tj. ^- the receiver time at the time of the carrier reception ai f ' - the nominal frequency of the reference signal. ind 403 If the receiver time and the reference signal are derived from the same oscillator there will be no error in the computed phase of the reference signal. Once the carrier signal is acquired and no loss of signal occurs, the phase change can be measured, including whole cycles. Since the phase of a received signal equals the phase of the transmitted signal (Remondi 1984), the receiver measurements are observations of the signal phases at the satellite and the corresponding transmission times. The transmitted signals are derived from the satellite oscillator. Thus, the phase of a signal represents the satellite time. From a code phase the code transmission time can be computed by .' t = ♦ / f (4) p,s P P Here ♦ - is the (p-) code phase (*p (tr=0)=0 ) f ' - the nominal code frequency and tj 5- the satellite time of code tranmission. Tn6 carrier transmission time is given by t, = ♦, / f, (5) c,s c c where « - is the carrier phase since t =0 (• (t =0)=0 ) and f - the nominal carrier frequency. Thus, both the code and carrier phase measurements can be treated as ob- servations of the satellite time at the corresponding time of phase trans- mission. A first difference between the two phases is that the code phase can be measured without ambiguity but the carrier phase is ambiguous. There is an integer number of cycles unknown in the first observed carrier phase. This is the ambiguity problem. The second difference is the ionospheric propagation time delay. Let n be the refraction index for carrier phases, then the group refraction index for the code is ng = n +^f (7) So the difference in propagation times of code and carrier phases is t aT, = /•■ An dt (8) with 404 An = n - ng (9) AT = T^ - Tp where T., Tp are the propagation times. Another difference is the noise level of the measurements. For example, the noise of TI 4100 p-code measurements is about 2 nsec (- 0.60 m), the noise of the carrier phases about 0.01 nsec { - 3 nun ). PHASE AMBIGUITY DETERMINATION FROM CODE AND CARRIER MEASUREMENTS The following equations are derived from the above relations: S.I =S,i*^^,i = *f' %* ^^,1 and \^'z- ^/^-^/^^^^, 1-^^,1 ^''^ It is t^ , - the space vehicle time corrected for ionospheric propagation time ' delay, AT. .- the ionospheric time delay for the carrier phase and ATp'j- the ionospheric time delay for the code phase. The' accumulation of equation (11) for all times of observation yields \/ f, - x(., /f , -»c/f c -AT, , -AT^j ) /n, (12) with m - the number of observations. To evaluate this equation the sum of ionospheric time delay has to be known. If one neglects higher order effects the ionospheric model AT^_, = -A/f^' (13) where A - is a factor varying with time and location, results with ( 7 ) in AT,_, - ^/fl (14) and ^\.l- ^Tc,I=2A/f/=2AT, , (,5) 405 With two-frequency code measurements the ionospheric delay can be computed from AT, (subscription 1,2 for LI, L2 respectively). M.1=-(S,S,l-S,S.2)/( '-fc.1* 'ha ) ('6) The standard deviation of the ambiguity computed from equation ( 12 ) with uncorrelated code and carrier measurements is %/f '50, (17) where a is the standard deviation of the code measurements. With a standard deviation of about 2 nsec for TI 4100 code measurements this results in o ,= 14.4 cycles. The accumulation of 1000 measurements is neccessary to get the ambiguity with a standard deviation of 0.5 cycles. The mean output rate of the Tl 4100 is about 4 seconds. Thus, a continuous observation of one satellite over 1.2 hours is required to compute the ambiguity with the above accuracy. A higher output rate would be worthwhile for reducing observation times. Figure 1 is a plot of the determined ambiguities for one satellite versus time at two simultaneously observed stations. The dotted curve is the ambiguity and the continuous line the standard deviation. It is obvious that there is a high correlation between the two stations. Similar behaviour can be observed with other satellites. There seems to be a systematic error in the model. The above model does not account for phase delays and phase center differences between the different carrier and code signals. However, phase errors due to satellite hardware will affect all simultaneously observing stations in the same manner. These errors are independent of station locations and should vary slowly. For multiplex receivers like the TI 4100 phase delay errors are more or less the same for all observed satellites because there is only one hardware channel for all tracked signals. Nevertheless there are possible differences between different frequencies, so further analysis is required in this respect. Two different receivers of the same type may have similar errors, however, the change with time should be uncorrelated. Another error in the described model is caused by the neglected ionospheric effect of higher orders. There is no complete agreement among many people concerned with this problem about the order of magnitude of these effects. With simultaneous code and carrier measurements the change in first order ionospheric refraction can be computed using the two-frequency model in two independent ways. But again the accuracies of the two determinations are separated by about two orders of magnitude. It can be seen from carrier measurements that the change in the refraction is very smooth. Figure 2 shows a second order polynomial fitting of the change in the ionospheric refraction determined from carrier as well as from code measurements on the two simultaneously observed stations (with a distance of 5 km). Significant coefficients were obtained from both approximations. The third plot shows the elevation angle of the satellite. The residual error sum of the two-frequency correction in the change of the ionospheric refraction was about 2 nsec here. The first order refraction amounted to 15 nsec at the beginning of the interval. The absolute error in one time correction can not be computed from these measurements. To estimate this quantity a model has to be adopted. 406 Through the algorithm about twice the mean residual error in the code refraction minus the error in the carrier refraction will be contained in the ambiguity. It seems that this can result in some cycles. However, if short baselines are observed the error should be the same on both sides. With the computed ambiguities one gets the satellite transmission times with the noise level of the phase measurements ( a few millimeters ) and with a possible bias of a few cycles. From these times corresponding pseudoranges can be computed and used in an adjustment procedure similar to a model using pseudoranges obtained from code measurements. THE GEONAP SOFTWARE Software for geodetic positioning using the described model is being developed at the Univerity of Hannover. Some parts of the software depend on the TI 4100 data s'tructure, others do not. The data flow chart gives a general view of this GEONAP ( GEOdetic NAvstar Positioning ) software. A brief description of the function of the modules follows. TIDECO: This program uses files with the raw data collected from a TI 4100 NAVSTAR Navigator. It decodes the binary data stream and separates different data types like the raw measurements, the NAVSTAR navigation message, TI 4100 user solutions and other information. CYCLAM: This software automatically edits the raw measurements, detects cycle slips in the carrier measurements and computes the ambiguities of carrier phases. One option for this program is to use one or both carrier frequencies. The cycle slip detection works in a way that the carrier phase is predicted for the next observation time and compared with the actual measurement. The prediction model is a polynomial computed from the previous measurements. The prediction accuracy is good enough for the short measurement intervals of the TI 4100. Thus, for this receiver the program works without knowledge of station coordinates and satellite orbits. For receivers with lower output rates a modified model may be neccessary. The output of CYCLAM is a file with edited measurements and another file with control information about the ambiguities. lOCORR: This module adds the computed ambiguities to the carrier phases and computes and corrects for the ionospheric refraction. The output rate for the corrected measurements is controlled by an input parameter, so a reduction of the number of measurements is possible. A further option is installed to choose the use of LI, L2 or two-frequency measurements. This allows an analysis of uncorrected ionospheric effects in station coordinates. The software is prepared to work with an adopted ionospheric model. This will probably be neccessary if only one-frequency measurements are available and longer baselines shall be determined. MSSORT: MSSORT uses the NAVSTAR navigation message files- from all stations observed at the same time, checks the decoded messages for completeness, reduces redundant information and outputs a file with sorted messages. 407 The output file of MSSORT is used in this software to compute smoothed satellite orbits using least squares fit algorithms with polynomial models. The first reason for this is to represent the satellite coordinates without jumps as they occur in the navigation messages every time a new message set is transmitted. The second reason is to have the possibility of interpolating orbits if a navigation message is missing. A third reason is to have no interference with other software parts if different orbit information is available or different orbit modelling is desired. SINCOR: The SINCOR program uses the ionospheric corrected measurements, the smoothed orbits and an optional weather file as inputs. Corrections like satellite clock offsets, relativistic time effects, earth rotation effects and tropospheric refraction are made on the measurements or satellite coordinates respectively. A single station solution for every observation time and an accumulated least squares solution for station coordinates and a polynomial receiver clock model are produced. Orbit parameter partial derivatives, with respect to ranges, are determined and written to an output file together with the corrected measurements and satellite coordinates. GEONAP : This final software is a multiple station adjustment program. The output files of SINCOR are used to do a modified least squares adjustment of the satellite time observations. The parameter vector contains - 3 coordinates / station, - polynomial clock parameters for receiver clocks, - tropospheric parameters, - up to 6 keplerian orbit parameters / satellite - polynomial clock parameters for each satellite clock and - 1 ambiguity parameter / station / satellite. There is no fixed length for this vector. Options are used to choose parameters to be estimated. The program is prepared for the introduction of additional parameters. A covariance model for receiver and satellite clock errors is used to describe integrated random noise oscillator errors. A priori variances or covariance matrixes for single parameters or parameter blocks are optional inputs. This allows the usage of prior adjustments and the fixing or constraining of parameters. The detailed observation equations and covariance models for pseudoranges shall not be discussed in this paper. There are a lot of publications dealing with this subject. 408 REFERENCES Davidson, D.; Delikaraoglou, D. ; Langley, R. ; Nickelson, B. ; Vanicek, P.; Wells, D. 1983. Global Positioning System Differential Positioning Simulations. University of New Brunswick, Technical Report No. 90. Fell, P.J. 1980. Geodetic Positioning Using a Global Positioning System of Satellites. Ohio State Uni verity. Report No. OSU-DGS 299. Remondi. B.W. 1984. Using the Global Positioning System (GPS) Phase Observable for Relative Geodesy. Modelling, Processing, and Results. Dissertation. University of Texas at Austin. Ward, P. 1982. An Advanced NAVSTAR GPS Geodetic Receiver. Proceedings of the Third International Geodetic Symposium on Satellite Doppler Positioning. Las Cruces N.M., USA. Wuebbena.G. 1983. Simulation und Auswertung von Messdaten im Strecken- und Dopplermodus arbeitender NAVSTAR-GPS Empfaenger zur absoluten und relativen 409 CYCLES 8- 7 6 5 4 1 3 2 1 AMBIGUITY STATION MSD - SV 12 * 1 01:00 23:00 00:00 TIME (UTC) CYCLES 7 • 6 ' 5 • AMBIGUITY STATION VEL - SV 12 23:00 00:00 TIME (UTC) Figure 1: Ambiguities and Standard Deviation 410 IONOSPHERIC VARIATION STATION MSD - SV 12 ■*-r "* 23: 60 ' 00:6o . IONOSPHERIC VARIATION STATION VEL - SV 12 :?( nsec 5 - 4 - 3 - 2 - 1 ■■ - 01:00 o 70 "* 23: do * ' ' 00: 60 ^ ELEVATION STATION MSD - SV 12 01 ^0 ' 23:00 ' ■ ' — WW TIME (UTC) Figure 2: Ionospheric Variation in Code and Carrier Refraction • "01:00 411 RAW .MEASUREM. CYCLAM /edited^ V measurem / lON&SPI CORRECTED^ .MEASUREM SINCOR ^ ^ SINGLE STATION .SOLUTION TI niOO RAW DATA1 13 — NAVIG. MESSAGES CONTROL FILE /weather \FILE measur. ^SV COORD. DESIGN I I ^100 RAW DATA 2 NAVIG. (MESSAGES NAVIG. .MESSAGES SMOOTHED^ ORBITS measur; !SV COORD. DESIGN MULTI STATION ;OLUTION Figure 3: The GEONAP Data Flow Chart 412 REDUCTION OF MULTIPATH CONTAMINATION IN A GEODETIC GPS RECEIVER Frank R. Bletzacker Computing Applications Software Technology (CAST) , Inc. 5450 Katella Avenue Los Alamitos, CA 90720 Submeter differential position measurements using the Global Positioning System satellites and omni-directional antennas ex- perience serious systematic accuracy degradation due to multipath contamination of the P-code. This paper presents the results of a study undertaken by the SERIES-X team(l) at the Jet Propulsion Laboratory to quantify the magnitude and time signature of the mul- tipath contamination. Computer analysis of field test results suggest that multipath contamination of the P-code measurement can be reduced to roughly 30 cm by a combination of the following tech- niques: digital filtering of the measured P-code delay, using an RF- absorbent antenna ground plane, proper placement of the antenna rela- tive to local site geometry, diplexing to obtain LI and L2 using a single wideband (L-band) antenna. For integrated P-code Doppler range, the systematic multipath contamination may not be reduced by averaging. SERIES-X continuously tracked all visible GPS satellites using an omni-directional antenna. Figure 1 shows the SERIES-X LI and L2 an- tenna gain patterns both with and without RF-absorbent material FIGUBE 1. RELATIVE ANTENNA GAIN PATTERN FOR DUAL STANDARD CONFIGURATION WITH AND WITHOUT RF ABSORBENT GROUND PLANE. U) U WITH ABBORBBR (b) LI WITH ABBORBBR (c) U NO ABBORBBR (d) U NO ABBORBBR placed around the antenna base. This dual antenna configuration (the "standard configuration") was selected to improve the overall signal- to-noise ratio and reduce multipath. Associated with the low eleva- 413 tion angle gain for an omni-directional antenna is a susceptibility to multipath signals being superimposed over the desired signals. This multipath superposition corrupts the carrier phase measurement and all subsequent observables based on that measurement. Figure 2 illustrates multipath geometry and the carrier delay error caused by a time-dependent, reflected signal arriving out of phase with the direct signal at the antenna phase center. The time depen- dence is due to the motion of the satellites in the sky relative to the antenna geometry on the ground. A simple model of specular GPS multipath from local objects is defined by Figures 2a and 2b. The model, albeit simple, does suggest, through computer simulations, features observed in field test data. FIGURE 2. RAY DIAGRAM FOR SPECULAR MODEL a) HORIZONTAL MULTIPATH SOURCE, b) VERTICAL MULTIPATH SOURCE SPECULAR MODEL For a horizontal source such as in Figure 2a, the model predicts a phase delay, ^ , given by: T = (2H/X) sin (e(t)) cycles, and for the vertical objects of Figure 2b by: T = (2H/X) cos (e(t) ) cycles. (1) (2) The derivatives of these delays give the expected time-dependent fre- quency of the multipath signals. As a satellite rises, long period (15 to 30 min) phase structure due to signal delay is caused by mul- tipathing from vertical objects. As a satellite traverses the sky towards the zenith at about 30*/h, horizontal objects become more im- portant for long period structure, as the vertically induced periods decrease to approximately 1 to 3 minutes. This suggests that, while multipath in the PI channel could be offset in relative phase from 414 the P2 channel (decorrelated) , the magnitudes should be similar, and the periods should scale according to the ratio of wavelengths (L2/L1) . Multipath delays can corrupt measured phase at any elevation angle. However, low elevation angles are the most affected for at least two reasons: (1) Long period (low frequency) and short period (high frequency) structure is present in both the horizontal and vertical models. Since the short period multipath interference can be reduced by integrating over several multipath periods, it is not a sig- nificant data problem except for instantaneous measurements. The long period (low frequency) multipath interference cannot be in- tegrated and does affect system accuracy. The long period struc- ture for multipath horizontal surfaces occurs at high elevation angles. Using RF-absorbent material as an antenna ground plane effectively removes all long period horizontal multipath inter- ference (as will be discussed) . However, the vertical model predicts a long period multipath structure at low elevation angles. This vertical structure cannot be removed by an RF-ab- sorbent ground plane. The SERIES-X camper parked near the anten- nas served as a vertical multipath object. (2) While not predicted by the specular model, the antenna gain pat- terns of the standard configuration are predominantly altered at moderate elevation angles (<40*) by ground plane boundary condi- tions. Figure 1 shows these effects for the LI and L2 antennas in two different ground plane conditions. The test results show some disagreements with the specular model and suggest some of its shortcomings. As discussed earlier, the LI (PI) and L2 (P2) channels were expected to be similar with regard to multipath. This was not the case in our standard tests. While the Pl-Ll channels behaved as expected, the P2-L2 channel did not behave similarly for the standard configurations. However, the expected Pl- Ll and P2-L2 behavior was observed for a nonstandard configuration (helibowl) , to be discussed in a following section. EXPERIMENTAL CONFIGURATION Since the received si^gnal can be distorted by ionospheric and tropospheric delay, as wei>l as multipath, the multipath tests (con- ducted during the spring of 1984 at the Jet Propulsion Laboratory an- tenna test range facility) were performed on a short baseline where the ionospheric and tropospheric delay are common and difference out during data reduction. The test site on the JPL antenna range was an excellent multipath environment because of the many reflective struc- tures and objects, affording conditions that one would normally ex- pect to find in the field. Four different configurations of the standard dual SERIES-X LI and L2 antennas were tested by mounting them on : (1) Camper tops without RF-absorbent material. (2) Camper tops with RF-absorbent material. 415 (3) Tripods without RF-absorbent material. (4) Tripods with RF-absorbent material. One further category exists, a nonstandard configuration, which uses an antenna having higher gain and less solid angle coverage (helibowl) . This device, developed by Don Spitzmesser at JPL, shows promise as a high-gain modified omni-directional antenna. DATA REDUCTION The multipath tests were processed by a Fortran algorithm called DIFFRANGE. A detailed description of DIFFRANGE is outside the scope of this paper; however, an overview of its theory of operation is ap- propriate. DIFFRANGE operates on calibrated fractional GPS phase (i.e., modulo 2 )and constructs a data type called double-differenced integrated Doppler range (DDIDR) . DDIDR is used to evaluate mul- tipath effects on carrier and P-code phase as follows: To isolate the P-code effects, DIFFRANGE scales the carrier DDIDR to P-code in range units and subtracts L from P as follows: ^^1= (29.3) ( (|)pi - ^) meters (3) ^^2= (29.3) ( <|>j£ - 2^^) meters (4) for LI and L2, respectively (Note: P2 is the P-code modulated onto the L2 carrier) . The P-code and carrier range are two measures of the same quantity, the double differenced range to the satellite. Thus, the P-code minus carrier differenced DDIDR values can be ex- pected to scatter about zero. Multipath signature can be seen as systematic wander of the differenced DDIDR about the expected zero value. MULTIPATH TEST RESULTS This section gives the multipath test results with the standard SERIES-X antenna configuration. Expected Performance The optimal values of the DIFFRANGE observables (P-L DDIDR) are estimated using the computed 14-second PI, P2, LI, and L2 residual phase errors for each GPS satellite from the SERIES-X phase extrac- tion software program and the algorithm of Equations (3) and (4). Because the independently estimated 14-second phase errors are insen- sitive to relatively low frequency phase wander (e.g., multipath), the resultant mean rms of the Pl-Ll and P2-L2 DDIDR values of the twelve multipath tests are used to estimate system performance based on random system noise. In Table 1 the mean value of the operations outlined above for each of the test configurations has been computed and also includes a helibowl test optimized to receive L2. It shows that the P1/P2 ratio roughly agrees with that expected due to the broadcast power of the LI and L2 channels from the spacecraft. Ex- cept for the camper/no-absorber tests, the system noise estimates are roughly independent of the test configuration. A possible explana- 416 tion of the low P2-L2 DDIDR values of the camper/no-absorber test is that the L2 antenna gain pattern is significantly distorted when the antenna is mounted on the reflective camper top. Measured Performance: Standard Configuration In Table 2 the P-code minus carrier DDIDR mean rms values of all tests for all visible satellite pairs are listed for each standard test configuration with a 20^ and 40* elevation angle cutoff. The errors in the computed means represent the variations from one satel- lite pair to the next due to the variations in AZ-EL geometry for particular pairs. Figure 3 compares the computed mean Pl-Ll and P2- L2 values of the four standard configurations for all satellite pairs to the expected performance based on the predicted system noise. The best results for Pl-Ll occur with those configurations using RF-ab- sorbent material as an antenna ground plane. The absorbent material eliminates horizontal low frequency multipath, which significantly contributes to the computed rms for the no-absorber cases. The tests with an RF absorber are discussed below. TABLE 1 PREDICTED DDIDR PERFORMANCE TABLE 2 MEASURED DDIDR PERFORMANCE r - TEST TYPE DDIDR OBSERVABLES (cm) TEST TYPE DDIDR OBSERVABLES (cm) CAMPER TOP/WITH RF ABSORBER 24.59 41 .76 CAMPER TOP WITH RF ABSORBER DATA >20O ELEVATION 30.51* 2.31 62.59*4.26 TRIPOD/WITH RF ABSORBER 22.46 35.98 DATA >40O ELEVATION TRIPOD/WITH RF ABSORBER 26 12*2.23 48.16*4.65 CAMPER/NO RF ABSORBER 21.87 29.57 DATA >20° ELEVATION DATA >40° ELEVATION 40.83*6.17 35.68i3.64 86.12*18.67 64.27*12.51 TRlPOD/NO RF ABSORBER 29.77 39.03 CAMPER TOP/NO RF ABSORBER DATA >20o ELEVATION 58.51*7.49 78.74*8.33 MELIBOWL/WITH RF ABSORBER 23.94 21.07 DATA >40° ELEVATION TRIPOD/NO RF ABSORBER 44.22' 8.12 60.80*7.57 DATA >20° ELEVATION 74 63*9.48 76 17*4.38 DATA > 40° ELEVATION 61 .18114.89 69.88*27.85 HFI.moWL/WITH RF ABSORBER ( L2 OPTIMIZED ) DATA > 20* ELEVATION 34.45±8.14 20.7517.66 DATA > 40» ELEVATION 12.1116.46 10.05±S.13 Camper with Absorbent Material Configuration As discussed previously, the systematic contamination of the P-code was assumed predominately due to satellite signals at low elevation angles multipathing off vertical objects and high elevation angle scattering off horizontal objects. The construction of SERIES-X is such that when the dual L1/L2 antennas with absorbent material are placed on the camper tops, they are removed from the "line of sight" of nearly all multipath objects. Thus, our best multipath configura- 417 tion is a camper top with RF absorber. Figure 3a shows the Pl-Ll DDIDR observable to be within 5 cm of the value suggested by system noise. Moreover, the very slight decrease seen in Figure 3b when the low elevation angle data are removed suggests this configuration to be minimally corrupted by multipath. The rms multipath contamination is 15 cm. FIGURE 3 COMPARISON OF MEASURED TO PREDICTED DDIDR WITH ELEVATION ANGLE CUTS (o) ODIOR RMS FOR MULTIPATH TEST CONFIGURATIONS FOR ELEVATION ANGLES >2V (b) DOIDR RMS FOR MULTIPATH TEST CONFIGURATIONS FOR ELEVATION ANCLES >40' -1 r— —T ---J— --■ 1 ELEVATION ANGLE > 20» ^» MEASURED P2-L2 80 " ^ ^ J" - MEASURED r\-\.\,„f^ - K ^y^ ^<^ §40 " y,^ ^^"^^-^^.^ PREDiaEOP2-L2_,.^^'* 20 Jr • PREDICTED PI -Ll 1 1 1 1 1 HELIBOWL CAMPER + ABSORBER TRIPOD * ABSORBER CAMPER - ABSORBER ^40 S Q Q 40 ~l 1 ELEVATION ANGLE > 40° T MEASURED P2-L2 ^^' PREDICTED P2-L2 PREDICTED PI -LI TRIPOD - ABSORBER HELIBOWL CAMPER * ABSORBER TRIPOD » ABSORBER CAMPER - ABSORBER TRIPOD - ABSORBER The P2-L2 DDIDR data do not behave as suggested by either system noise or the expected similarity of Pl-Ll to P2-L2 based on the specular model. Figures 3a and 3b show the P2-L2 DDIDR data to depend greatly on the elevation angle cutoff, whereas the Pl-Ll data did not. The asymmetry can be illustrated further in Figure 4a showing Pl-Ll DDIDR results for typical data integrated over 140 s. The Pl-Ll DDIDR value shows no systematic phase wander, and scatters as expected about zero. The P2-L2 DDIDR values have significant systematic phase wander about the expected value, inconsistent with our model. The 140-second integration removes the high frequency noise from the Pl-Ll DDIDR value, as previously mentioned. Figures 4b and 4c show the results of passing the Pl-Ll 14-second data through a digital filter designed to selectively remove frequency components from the raw double-differenced range. The absence of any low frequency Pl-Ll structure suggests that the systematic behavior found in the P2-L2 DDIDR of Figure 4a is probably not due to mul- tipath, but related to antenna asymmetry instead. The L2 antenna gain ratios at 90®/20® and 90®/40* are -3 dB and -1 dB respectively, compared to -0.5 dB and dB for the Ll antenna (Figure 1). This gain asymmetry of the L2 antenna, if associated with a nonlinear phase response, could offer a partial explaination of the low eleva- tion angle structure seen in all the P2-L2 DDIDR multipath data. The camper experiment can be summarized as possessing a very low frequency (about 1 to 2 h) and low elevation angle structure in the P2 channel, which could be due to the L2 antenna gain pattern. In the next section, we discuss the tripod with absorber, which is more seriously corrupted by multipath. 418 FIGURE 4 DDIDR RESULTS FOR CAMPER WITH RF ABSORBER ODIDR WITH ELEVATION ANGLE CUTS 1 » B 51 3 ° O P\-U OOIM Eiev*IION >40' <^ PI-LI OOin ELEVATION <«)* • P2-L2 0010* ELEVATION > M* A l'2-LJ OOIW ELEVATION < «• 17 PI-LI IIUS: >40* ■ 16. S cm t «• ■ 23 .W c« P2-L2 (IMS: >40* > 61.06 o < 40* ■ » .74 cm -I. 18 UNIVtDSAL TIME (Kl l« RESIDUAL Pl-Ll DDIDR SPECTRAL CONTENT ALL FREQUENCIES LOW FREQUENCIES REF TIME 83:319: I6:36i]l RMS (c«.) 27.6 100 RELATIVE IIME {, 100 RELATIVE TIME (mini Tripod with Absorber Configuration The tripod with absorber is the standard SERIES-X configuration used for the baseline measurements reported in other papers (2). Figure 3 places the tripod test about 17 cm above system noise for the Pl-Ll DDIDR data and about 45 cm above the P2-L2 DDIDR system noise. The low elevation angle data contribute about 19 cm to the Pl-Ll observable and about 60 cm to the P2-L2. Unlike the camper test discussed before, the Pl-Ll channels are subject to systematic phase wander for certain AZ-EL geometries. Figure 5a shows an ex- ample of 140-second tripod-with-absorber data. The low elevation angle Pl-Ll data show a low frequency structure about 50 cm in am- plitude. The Pl-Ll frequency components are displayed in Figures 5b and 5c. The low frequency structure can be understood as multipath from a vertical object, possibly the SERIES-X camper structure, as the satellites rise; the multipath decreases as the satellites reach higher elevation angles. The high frequency structure of this pair begins with 3 -minute periods at the horizon, gradually broadening to 10-minute periods near zenith at mid-experiment. This behavior is consistent with specular multipath from a horizontal ground source. Figure 6 shows the same satellite pair (and geometry) for the tripod without absorbent material and shows the full effect of multipath contamination of the P-code. The P2-L2 data exhibit a much more serious systematic phase wander. Separating the observed P2-L2 behavior into multipath and antenna components would be very dif- ficult. However, both components contribute to the poor performance 419 FIGURE 5 DDIDR RESULTS FOR TRIPOD WITH RF ABSORBER DDIOR WITH ELEVATION ANGLE CUTS UNIVEISAl T(ME (h| 8 ALL FREQUENCIES r ■ ' ' ' I' ■ ' ' RESIDUAL Pl-Ll DDIDR SPECTRAL CONTENT LOW FREQUENCIES Uf TIMC M: tSi *: ft II IMS (a>) U.l 90 100 IM UUTIVt TIMC (laiKl I I I I I I — r— » — I I I I I I I I I I 1 I KF TIME a4: IS: 9: 0:16 •MS (ciK) 16.7 SO 100 ISO ULATIVE TIMC (mix) FIGURE 6 DDIDR SPECTRAL CONTENT FOR TRIPOD NO ABSORBER (o) H-L1 DOIDf AIL r^'^jiiMICV '. OMPrNtlJT' (W Pl-ll DOIDH FRCOUCNCY COMPONENTS < 1 'i mm (c) Pl-Ll DDIOH FICOUCNCY COMPONENT < 1/14 nin DEF TIME B3:33S: 12:30:9 SO 100 HEIATIVE TIME (-.m) SO 100 •ElATIVE TIME (mm) lEUTIVE TIME (mix) 420 of the P2 channels seen in Figures 4, 5, and 6. The tripod with absorber significantly reduces the multipath con- tribution over the nonabsorber case. The PI channel multipath ef- fects are less than 40 cm. Inclusion of a 40* elevation angle cut off reduces the multipath effect to 27 cm above system noise values. The P2 channel suffers from multipath structure in a similar fashion; however, as is the case for the camper, the P2 channel probably suffers from a systematic wander that cannot be attributed solely to multipath. In the next section, we investigate this structure. Anomalous Behavior of Test Results In previous sections we have implied that the P2-L2 test results of all the SERIES-X standard antenna configurations have been inconsis- tent with expectations based on the performance of the "sister" Pl-Ll data and the specular model. Figure 7 shows an example of the P1-P2 differences for a typical test. In this section we document various Investigations into this behavior. FIGURE 7 P1-P2 DDIDR FOR TRIPOD/WITH RF ABSORBER ALL FREQUENCY COMPONENTS (1) RELATIVE UNIVERSAL TIME (h) Standard Configuration. In the standard configuration of the LI and L2 SERIES-X antennas, the antennas are separated by 30.5 cm, with the L2 antenna taller than the LI by 1.9 cm. The mounting flange for the antennas was designed with a circular ring about 3 cm wide at the antenna base, which cannot be easily covered by RF-absorbent material. In two tests, we compared the P2-L2 DDIDR results with and without a special piece of RF absorbent placed over this open ring. We found the P2-L2 DDIDR rms aproximately 20% to 35% smaller with the extra absorber than without. The LI carrier (Pl-Ll DDIDR) was affected negligibly by the additional absorbent material. We concluded that the use of a single anten- na would be preferable to a dual configuration. We tried such a configuration, the results of which are reported below. (2) Helibowl. On March 6, 1984, we installed the first of a series 421 of three helibowl antennas. The helibowl is an L-band helix mounted in a reflective bowl. The design, while increasing the gain at zenith by about 10 dB, decreases the effective beam width of the antenna and, accordingly, the susceptibility to low eleva- tion angle signals. Table 2 reports the Pl-Ll and P2-L2 DDIDR results for a typical GPS satellite pair from the helibowl series (reported values are for an L2 -optimized helibowl) . The DDIDR observables were consistent with the system noise estimates for the helibowl given in Table 1 for all satellite pairs of all helibowl tests. The helibowl can shed considerable light on the nature of the discrepancy between the PI and P2 channels. (3) Variation of test parameters. Using the helibowl, we ran several tests trying to reproduce the anomolous P2 behavior. These tests consisted of varying the L2 zenith gain, AGC/MGC control and various elevation angle cuts. The conclusion we reached was that the helibowl tests could not reproduce the anomalous P2 channel behavior. We expect the anomaly was caused by the dual standard configuration antenna structure itself and suggest a single feed, wideband antenna for GPS measurements. CONCLUSIONS For omni-directional antennas, multipath is a systematic P-code contaminant which can be reduced, but not eliminated, by filtering. Isolation of the antenna phase center from the line-of-sight to reflective objects is of course the single most effective multipath reduction measure. RF-absorbent material and a single wideband an- tenna will also prove to be very effective. The best P-code perfor- mance was found to be about 15 cm averaged and 25 cm instantaneous when all multipath measures were incorporated. (1) The SERIES-X team consisted of F.Bletzacker, R.B.Crow, R.Najarian, G.Purcell, J.Statman, and J.Thomas (2) SERIES-X Final Engineering Report, JPL, TDA Progress Report, D-1476, 1984, and SERIES-X Test Results, PLANS Sym- posium, November 1984 422 GPS SATELLITE MULTIPATH: AN EXPERIMENTAL INVESTIGATION L . E . Youncr R. E. Neilan F. R. Bletzacker'^ Jet Propulsion Laboratory- California Institute of Technology Pasadena, CA 91101 '^Currently at CAST, Inc., Los Alamito, CA ABSTRACT. Differential GPS measurements promise to allow hicrhly accurate baseline determinations. The achievement of accuracies of a few cm over distances of thousands of km has been predicted for GPS based geodetic systems. These systems would use receivers operating in the differential mode, a fiducial network to allow accurate orbit determination, and on-site collection of media calibration data. A key assumption in the predictions of hiah accuracy is the cancellation of errors which originate at the GPS satellites, by differencing the range observations to a given satellite between two receivers. An example of a satellite error which would not be removed is the effect of multipath at the satellite antenna. If this multipath is present, it is expected to contribute different error signatures to receivers at separate locations. It appears to be impractical to calculate this effect with the required accuracy. This paper describes an experiment currently underway at the Jet Propulsion Laboratory designed to measure the size of anaie dependent delay errors originatina at the GPS satellites. DESCRIPTION OF GPS SATELLITE MULTIPATH EFFECT The use of high precision GPS receivers is expected to enable measurements of baselines up to thousands of km in length with accuracies of a few cm. A key to such accurate measurements is common mode rejection of instrumental errors originating at the GPS satellites, achieved by differencing the measured pseudo- ranges (or integrated Doppler signals) from a given satellite to a pair of receivers. Because of the importance of differencing, it is important to look for satellite based errors which are not removed bv this technique. Multipath in the satellite antenna is an example of this, because the additional signal delay caused by multipath is dependent on the angle between the antenna centerline and the line of sight to the ground receiver, also called the angle off boresight. See Fig. 1 for an illustration of multipath geometry. Fig. 2 shows the expected form of the effects of multipath on the P-code and carrier observables for a SERIES tvpe (delav and 423 multiply) GPS receivei:. (The effects on a code correlation receiver are expected to be similar.) The calculations leadina to Fig. 2 assumed a single multipath surface giving specular reflection, and that the ratio of multipath to direct sianal power is 1%. The formulas used to generate Figure 2 are (2) and (3) in the appendix. (Please note that the assumptions made in this paper to determine possible levels of multipath errors are meant to be realistic, however the current estimates of the sizes of these errors may, in fact, be wrong by an order of magnitude. The larcre uncertainty is what motivates the measurement, at JPL, of this effect. The formulas derived in the appendix are meant to be used as an aid to experiment design rather than as a ricrorous expression for the multipath effect!) Figs. 3a and 3b show the variation of the multipath effect over a 300 km baseline for a satellite at the local zenith, and for a satellite at 45 decrree elevation. To produce this figure an additional assumption was made, that the distance d on the satellite (see Fia. 1), from the antenna to the multipath surface is 1 meter. Formulas (2), (3), and (6) from the appendix were used to obtain Fig. 3. This figure shows that multipath can be a several cm differential effect between the carrier and P-code, even over fairlv short baselines. For the current Block I GPS satellite antenna array elements, 1% power in the multipath signal is probablv a reasonably good assumption, judging from the published antenna patterns of the GPS satellites (Rockwell 1981). Thie number of multipath surfaces on the satellite, however, is certainly more than one, and the relative importance of these surfaces will probably change as a function of satellite elevation. The presence of more than one multipath geometry is expected to reduce the overall effect, as the various multipath signals should be non-coherent. The reflection involved in the multipath geometry pictured in Fig. 1 causes a flip of the signal polarization from RCP to a left hand elliptical polarization. The partial rejection of this signal by a RCP antenna at the receiver also reduces the relative strength of the multipath signal. Although this paper concentrates on multipath, other effects may well be present in the satellite signal which cause an apparent variation in pseudo-range as a function of satellite to receiver aeometry. An example would be variations in the far field phase pattern of the GPS satellite antenna array. In any case, it is the combined effect that we are sensitive to, and the combined effect will be measured by the experiment. Based on the results shown in Fia. 3, there is a reasonable expectation of an effect with a macrnitude of a few cm which is not removed by differencing, and which cannot be calculated with confidence. Therefore, it is important to conduct experiments to quantify the effect, in order to determine if it can be ignored, must be modeled, or presents a fundamental obstacle to the use of P-code measurements to resolve carrier cvcle ambiauities. 424 USAF TEST OF GPS ANTENNA A measurement was made of the P-code delay versus boresight angle using a GPS antenna at the Autonetics antenna range. (Wong 1984) The antenna was mounted onto a ground plane, and used to transmit P-code ranging signals toward a GPS receiver placed at a distance of 800 feet. By measuring the received signal's delay, as the GPS antenna was pointed through angles of to 16 degrees, the delay variations of 0.2 to 6.3 ns were measured for the P-code at the LI frequency, and variations of 1.5 to 2.0 ns were measured at L2. These experiments were only designed to validate the antenna performance at the IjO m ^3.3 ns) level, and should be regarded as upper limits on the GPS satellite antenna delay variations. JPL EXPERIMENT The experiment being performed to detect the size of any angle dependent delay variations in the GPS satellite antennas uses the two SERIES (Buennagel 1984) high-gain antennas, with each antenna output going into the RF portion of a SERIES-X (Crow 1984) receiver. The data taking procedure is to track one GPS satellite continuously through a large range of elevation angles, and to search for the presence of a variation of pseudo-ranae as a function of elevation angle. This multipath effect would be present in any observation of pseudo-range from a receiver to a GPS satellite, as the elevation angle to that satellite changed. The challenge is to separate the multipath effect from the much larger variations in pseudo-range caused by ionospheric and tropospheric delays, ephemerides errors, instrumental variations on the satellite and at the ground receiver, etc. Fortunately for our test design, the delay changes originating from multipath are expected to be quite different for the P-code and carrier signals (see Fig. 2), with the effect much less for the carrier data in most instances. Our experiment is designed to exploit this fact by making observations in which the differential range change between the carrier and P-code is monitored as a function of the satellite elevation. (Because the satellite antenna centerline is kept pointed toward the center of the earth, the angle off boresight is a function of the satellite elevation. ) As is usually the case in experimental physics, a differential measurement allows an increase in accuracy, due to cancellation of common errors. In this case, the geometric delay between the receiver and satellite is common to the carrier and P-code signals, and so it cancels when these are differenced. The same is true for the tropospheric delays, and for clock errors at the satellite or ground receiver. On the other hand, the ionosphere causes a group delay for the P-code and an advance of the carrier phase, which does not cancel in the difference, but is calibrated 425 usina dual frequency data to form both the carrier and P-code observables. Note that the dif f erencincr to be done is between the carrier and P-code data from a sincrle station. The presence of the second receiver merely adds redundancy to the measurement. Some remaining sources of experimental error are considered below. System Noise Due to the "23 dB gain present in the SERIES 1.5 m diameter antenna, the Signal to Noise Ratio (SNR) is quite high. The expected contribution of system noise to the error in the dual frequency P-code pseudo-range change is approximately 1 mm for 100 seconds of data. Multipath at the Ground Antenna The effects of non-direct signal paths to the feed of the ground antennas will be minimized by the use of the highly directional SERIES antennas. The presence of some ground multipath is still possible. The experimental approach that will be used to separate satellite effects from ground multipath is to observe whether the residual pattern of delay is a constant function of satellite elevation anale in the presence of a variety of local ground multipath environments. Errors in Ionospheric Calibration Third and higher order terms in 1/f exist in the expansion of the group delay and phase advance due to the presence of ray bending and magnetic field effects. We truncate the expansion after the second order terms in our current dual frequency formulations. Estimations of the error due to this truncation show that it is unlikely to be larger than a cm. Non-Coherence of Carrier and P-Code Circuits at Satellite or Ground Receiver The effects of receiver instabilities will be distinguished from satellite multipath effects, because they will not be common to the two independent ground receivers. The incoh'^rence of the satellite circuits which produce P-code and carriet signals is expected to be small, and would produce a signature which would not repeat from day to day, distinguishing it from the antenna multipath effects. Possible Variation of Effect Among Satellites. It will be necessary to measure the effect for different satellites, to determine if it varies. In particular, the Block II GPS satellites are designed with different antennas than the current satellites. 426 Possible Delay Dependence on Satellite Antenna Azimuth Angle. In order to be able to confidently model the angle dependence of the GPS signal delay, if any, one must be able to measure the delay as a function of azimuth angle, as well as angle off boresight. This could, in principle, be done by repeating the measurements on a given satellite at different times of year, as the satellite follows the same ground track, but must rotate about its center line to enable the solar panels to track the sun. Satellite Orientation Errors The relation between satellite elevation angle and angle off boresight is in error if the satellite centerline is not directed toward the center of the earth. This effect is expected to be limited to less than 1 degree. APPENDIX Derivation of the Effect of Multipath on P-code and Carrier Signals in a SERIES Type GPS Receiver The following treatment is meant to give an approximate, qualitative view of the effect of multipath signals on the GPS receiver observable. The presence of the C/A and data codes in the GPS signal will be ignored in the following, and only the P- code and carrier signals in the LI band are treated. A single sample SNR <<1 is assumed. The use of optimum delays in the delay and multiply circuits are also assumed. The received GPS signal is represented by the following formula, where frequencies are given in radians per ns(10*'*f-9 second), and times are given in ns. S(t) = P(t-g)cosCw(t-g)]+eP(t-g-m)cosCw(t-g-m)+pi3 (1) P(t) = the P-code data modulation at a frequency of 0.01023 GHz t = the time time past some initial epoch g = the combined delay of the geometric signal path between the satellite and ground receiver, clock offsets and media delays w = the carrier frequency, 2 pi 1.57542 rad/ns e = the relative amplitude of the multipath signal m = the added delay due to the added pathlength traveled by the multipath signal ( from Fig. 1, m=(a+b)/c pi = the phase added to the carrier signal by reflection from the multipath surface 427 In the SERIES receiver, this signal is mixed to an Intermediate Frequency (Wif) of 2 pi 0.03542 rad/ns, split into 2 signal paths, and one path is delayed by approximately one half of the P-code period (p/2). The exact delay is taken to be a multiple of the carrier IF half period, in order to maximize the output of the SERIES delay and multiply circuit. (An even multiple is assumed below. The effect of an odd multiple would be to change the overall sign of equation (2).) The two paths are multiplied together, giving the following product. S(t)S(t-p/2)=P(t-g)P(t-g-p/2)cosCWif (t)-wg)3cosCWif (t)-wg)3 +eP( t-g ) P( t-g-m-p/ 2 ) cosCWif ( t ) -wg) DcosCw( -g-m) +Wif ( t ) +pi3 +eP ( t-g-m ) P ( t-cr-p/ 2 ) cosCw( -g-m ) +Wif ( t ) +pi]cosCWif ( t ) -wg ) 1 +eeP( t-g-m) P( t-q-m ) cosCw( -g-m) +Wif ( t ) +pi]cosCw( -g-m) +Wif ( t ) +pi] In order to extract the P-code signal, this product is filtered at the P-code frequency (0.01023 GHz), leaving a direct term at the P-code frequency, plus multipath terms with relative amplitude e, plus terms of order e squared which are dropped. Pout(t)'"AcosC2 pi 0.01023(t-g)-pi/2D +eAcos(-t-wm-pi)cosC2 pi 0. 01023( t-g-m/2 ) -pi/23 +eAcos(-wm+pi)cosC2 pi 0. 01023( t-g-m/2) -pi/2D +ee where A is a constant and the delays are in units of nanoseconds. Using the identities cos( A+/-pi) =-cos(a) , and cos( A) =cos( -A) , Pout(t)'"AcosC2 pi 0.01023(t-g)-pi/2D -2eAcos(wm)cosC2 pi 0. 01023( t-g-m/2) -pi/2D The phase error introduced by the multipath term is derived trigonometrically to be delta phase'^tan-l ] ■ 2eAcos(wm)sin(-2 pi 0.01023m/2) A+2eAcos(wm)cos(-2 pi 0.01023m/2) For e< 2: LU LU OC LU LU '■*' Li- Li- CSJ b es Z » LU E < LU CO -0.025 (A) \ \ GPS SATELLITE AT~90P ELEVATION CARRIER. P-CODE 100 200 BASELINE LENGTH (km) -2.5 GPS SATELLITE AT -45° ELEVATION I I 100 200 BASELINE LENGTH (km) Figure 3. This figure shows the amount of multipath error left after differencing single frequency pseudo ranges between two receivers, separated by to 300 km. A single multipath geometry is assumed, as shown in Fig. 1, with d = 1 meter. Multipath signal power is assumed to be 1% of the direct signal. 432 Absolute Calibration and Precise Positioning Between Major European Time Observatories and the U.S. Naval Observatory Using GPS J. A. Buisson, 0. J. Oaks Naval Research Laboratory H. Warren Bendix Field Engineering Corporation INTRODUCTION Historically precise time has been transferred from one site to a remote site by means of a method using portable clocks. The method entails the carrying of an active frequency standard and its associated clock from site A to site B. Personnel from the United States Naval Observatory (USNO), Bendix Field Engineering Corporation (BFEC), Naval Research Laboratory (NRL) , and others have made portable clock trips by airplane and surface vehicles for the past 15 years. Accuracy of the transfer of time ranges from a few nanoseconds (on a short surface trip) to hundreds of nanoseconds (on an extended overseas trip). Typically the origin of the portable clock trip is a major time keeping observa- tory, such as USNO, where the portable clock is initially synchronized as close as possible to the master clock (MC) time at that observatory. Upon return to the originating observatory, closure is again made with the master clock and a rate of the portable clock against the master clock is measured. Prior to departure a stationary rate is determined between the two clocks and these two rates (before and after) are compared. Assuming no major difference occurs, the time accumulation between the two clocks is estimated and linearly applied to results obtained from each location on the trip. The important thing to note in such a method is that the portable clock must be kept running during the entire trip; that is, transported "hot". Many logistics problems and additional costs result from this necessity. A new method called Remote Calibration And Time Synchronization (R-CATS), allows a Global Positioning System (GPS) single frequency clear acquisition (C/A) code time transfer receiver (TTR) to be used instead of the portable clock. The portable TTR can be shipped or carried as luggage with no continuous power requirements. The procedure is similar to the portable clock method. R-CATS performs three major technical functions, calibration of existing GPS TTR, time transfer, and navigation. The TTR is first calibrated against the originating observatory master clock by making observations at the originating observatory with the antenna of the transportable TTR located near the antenna of the GPS receiver currently in use at that observatory. The portable TTR to be used in the R-CATS method is driven by the same clock that is used by the perma- nent TTR. In the event that a site does not have a GPS TTR the R-CATS method will be used to perform time transfer and coordinate positioning. During December 1984, a team from NRL performed the first R-CATS trip using a Stanford Telecommunications Incorporated (STI) Model 502B GPS TTR. The trip included closure with major European time observatories and the USNO. Table 1 presents a list of participants in the first R-CATS trip. 433 TABLE 1 PARTICIPANTS UNITED STATES NAVAL OBSERVATORY (USNO) OBSERVATORIE DE PARIS, PARIS, FRANCE (OP) VAN SWINDEN LABORATORY, DELFT, NETHERLANDS (VSL) PHYSIKALISCH-TECHNISCHE BUNDESANSTALT, BRAUNSCHEIG, GERMANY (PTB) TECHNICAL UNIVERSITY OF GRAZ, GRAZ, AUSTRIA (TUG) UNITED STATES NAVAL RESEARCH LABORATORY (NRL) At the USNO site and the TUG site both GPS TTR were manufactured by STI, the same type TTR as the one transported in the R-CATS trip. At the OP, PTB and VSL sites a receiver either built at the National Bureau of Standards (NBS) or of similar design was used. The first consideration in using R-CATS at a site having a permanent TTR is the calibration, included measuring of all cable delays, pulse trigger levels and pulse widths to determine quantitatively the hardware associated influences on overall system delay biases. After the delays had been measured, data from NAVSTAR satellites was taken from each site over a period of three to four days to gain confidence in the resulting set of observations. The time synchronization portion of the R-CATS involved the near common view tracking of multiple NAVSTAR satellites between each remote site and the USNO. Results will be presented on both the calibration and time synchronization aspects of the project. The third technical objective of the trip was the navigation and coordinate determination of each remote site. Data was taken over an eight hour span, using all NAVSTAR space vehicles (SV), in a Kalman filter solution. Accurate positions of each GPS antenna were determined in an earth fixed XYZ coordinate frame on the WGS72 datum and then transformed to latitude, longitude and height coordi- nates. Results of the navigation determination will also be presented. Figure 1 presents a drawing showing the R-CATS method. Measurements are first obtained using the TTR STI025 driven by the USNO master clock (USNO MC) , and then driven by the MC at each remote site. Simultaneously, measuremnts are made by a permanent GPS receiver at each site. For discussion later, let the observa- tions from the permanent receiver at the USNO site receiver be designated R1, the observations from the transportable R-CATS receiver be RT, and the first remote site observations be R2. 434 R-CATS METHOD GPS GPS TTR TTR STI011 STI02S Ri UTC (USNO) USNO SITE GPS GPS TTR TTR STI025 REMOTE T UTC (REMOTE) REMOTE SITE Figure 1 TYPICAL R-CATS STATION CONFIGURATION 5 MHz OAA, 5 MHz Wl 5 MHz DISTRIBUTION T 5 MHz STATION REF CLOCK 1 PPS n 1 pps CABLE DELAY PORTABLE RECEIVER (STI025) n. REMOTE STATION GPS REC 1 pps CABLE DELAY 1 pps DISTRIBUTION AND TIME REF POINT Figure 2 435 CALIBRATION Figure 2 shows a simplified block diagram of a typical station hardware con- figuration. Care was taken to accurately measure each ccmponent of the system which could introduce any delay in the calibration. Table 2 presents the results of calibration measurenents made at each site. TABLE 2 R-CATS CALIBRATION PARAMETERS 1 pps 1 pps 1 pps STATION Level(v) Rise Pulse Time(ns) Width(jjs) A. With respect to STI025 TTR USNO 0-5 H 10 OP 0-8 150 20 VSL 0-2 HO 10 PTB 0-10 4 1 TUG 0-5 4 10 5 MHZ 5 MHz 1 pps REC + RF Receiver Level Wave- Cable Cable Calibration form Delay (ns) Delay (ns)' (ns) I.Ov rms sinewave 56 mi 88 50fl I.Ov rms slnewave »W1 114 -297 50n 3.0v p-p sinewave 677 111 -533 50n 3.^v p-p sinewave 13 111 131 50n I.Ov rms sinewave 38 144 106 50n B. With respect to permanent TTR USNO 0-5 4 10 I.Ov rms 50n sinewave 56 155 OP 0-8 150 20 1.8v rms 50 Ji sinewave 350 204 VSL 0-2 40 10 3.0v p-p 50n squarewave 15 746 PTB 0-10 4 .050 3.4v p-p 50n sinewave -50 259 TUG 0-5 4 10 I.Ov p-p 50n sinewave 38 82 99 -146 731 309 44 436 These values have been recorded and in the event components are either repaired, replaced, or levels changed, a recalibration should be performed. All pertinent measurements are believed to be accurate to 1-2 nanoseconds. It was reconmended to each participating site that they keep ccxnplete calibration records of any changes in configuration and that additional calibrations be performed on a yearly basis. A yearly check could determine if aging of syst«n components affects system calibration at the nanosecond level. The complete calibration procedure, referring to the notation in figure 1, includes the initial offset between observations from RT and R1 then the offsets at each remote site (the difference between RT and R2 . . . RN). To combine these two offsets the following derivation is presented. Measurements are made at site 1 using receivers R1 and RT. These measurements could be (local clock - GPS time) or (local clock - SV time). For this R-CATS trip, (local clock-GPS time) were used. Equation 1 shows the offset. RT - R1 = A1 (1) The TTR is then transported to site 2 and similar measurements are made. As the transportable receiver is moved from site to site during the R-CATS, phase differences are determined between it and each site (A1, A2, . . .AN). The offset calibration of one site to another site can then be determined. RT - R2 = A2 (-) RT - R 1 = A 1 R1 - R2 r A2 - A1 R1 = R2 + (A2 - A1) If each individual station offset is maintained, then any station calibrated during the R-CATS trip can easily be referenced against any other station, rather than only being compared back to the originating observatory (i.e., R1 + A1, R2 + A2, . . . RN + AN). Figure 3 presents the series of NAVSTAR tracks performed at each site using the R-CATS STI025 and the local TTR. Each plot in the figure presents the cali- bration offset, in nanoseconds, between R-CATS STI025 and the individual TTR being used at each site as determined by observing multiple GPS satellites over a period of 3-^ days. The statistics of each station offset is shown below each plot. The mean offset, X, is the number used by the remote site to calibrate against the R-CATS transportable receiver. At the conclusion of the R-CATS trip, the transportable TTR is returned to site 1 (the originating observatory) and additional measurements are made to insure that no offset occurred during the trip. In the traditional portable clock trips, a closure was made to deter- mine the drift of portable clock in frequency between the PC and the master clock. No such drift is possible with the R-CATS method. Figure 4 (upper left plot) shows that indeed a 10 ns shift, from +1ns before departure to -9ns on return, did occur. To have such a closure (10ns) after a three week European trip is an order of magnitude or so better than a typical portable clock closure. Since it is virtually impossible to determine when or how the shift occurred the best offset number to use is the average of the initial offset with the final offset at site 1. It was anticipated that closure in the 1-2 nano- seconds will be realized as additional R-CATS trips are performed. 437 « ° a crs T-K C'.IB-'T:.- . a s. :.»VA'. ORS!3.A10«» (1)5 SM*- 6 1 STic.-^ - s;:c:i S'.r.s- B j SVC9- e I Sil 1- A < svi?- e 1 SV13- C -^^ 30PTS X-I.ONS a-7.8NS 6017 OOIB 60ie 8020 8021 6022 6323 6024 6025 6026 6027 6028 6029 B Df-io -sc 6035 ssoe- 6 svoe- e SV09- e svi;. A SVl?. B sv;3- C C?S TTR C'-IB^ATIC. ORStBVATOSIC X P>o:S (OP) PS T7R C*L;aR'.T:o:. va:i Sk;::0EN lascratcs> c.sl) s::c25 - vsLO; SV06- 6 SV08- B SV09- B SVll- A SV12- e SV 1 3- c 13PTS(NO SV11) Xc4 0NS a==:8 9NS 15-20 L -70 ezti CPS T7R CALIBRATICI. PHYSIKALISCH-TECHSISCHE B'j::XS»Stf.V. BRA'jr.SCMWEIG CERKANY STIC25 - PTBl SV08- 6 SVOB- 8 SV39- e SVll- A SVi2- B SV13- c 18PTS INO SVllI X= -300 NS o=8.3NS 6C.;6 g-20 C I -30 0=^ 'T? c.«l:9=- =HYS:i'AL;SCH--rCHN;SCHE 9'^r^ b^/'ji.sck.e; J 3E^ st;c2e - p:= ES*::ST/LT IX e > (/) 1/) oi W) U) in - ^ ~~ U) CD .1 =-.fi (J u f*: •- < O 1- n rj m < :^ < o n: < K (/) m 1- o a> « u) -J i: -J o < b. u 1 (.) o (£ in (r 13 UJ !\j ffl O) t- < n o »- lU .1 •-• a 13 t- 10 -1 o m (J n. CD CD o . S B < . u ' *' . ■ ' 1 uJ AU UAi Lui •' 1 1 1 O -J — a CD ;: -I I& » - 10 (0 o," ' O 2 u , u cn (D . rj CD ■ (o a> OB < CD u A s A ■ I ■ CO a o ( ) r-« >■ > > (/> (0 10 tn u) (0 ' . • • xLi .uu mJ Uuui, LUJ UUliil 1. • . o soNoaasoNVN soNCoasorivr; % ■- >- _ •- O: II — « »- Q S < ui S , Q> 7 in a 03 a> a> < m u >>>>>> U> (0 (0 (0 U> (0 -, in _. n q: (O ^ z p (O (/> 0> M t I s 9IX e % tiiiiiiiiiii iii. I ...I... ...... I ^ I I f..ip, , f,,,J i/> 8 0000 00000 . ID g" CD ■ •-■ >- !^g" D gtd ■ < UJ 2 in CD TTR KL OE SHIN 1025 m - IfSi [;i ID ID u z ■ (0 3 «> CD < CD u s fi R 1 I m ■ > > > > > to to to 10 10 10 lilUl.Mlh mJ lui Ui. mJ o Si SCN033S0>iVri SONODBSONVN Figure 4 440 TABLE 4 (STI025 - SITE) Calibration Offset SITE DATE REG NO. PTS MEAN OFFSET (NS) (ns USNO USNO USNO 12-24-84 02-07-85 04-01-85 STI011 STI01 1 STI011 49 24 41 - 9 - 8 -10 5.6 7.7 5.9 TIME TRANSFER Another aspect of an R-CATS trip is to perform a time transfer (TT) between two sites after calibration has occurred. Figure 5 presents the time transfer from the participating sites involved in the first R-CATS trip, namely (USNO, OP, VSL, PTB, and TUG). Since the NRL team originated the trip from USNO each participating European observatory is referenced back to USNO, although this technique applies between any two tracking sites. The time transfer results were obtained from all passes observed by both the USNO GPS TTR (STI011) and corre- sponding passes taken at the European sites. The results are "near common view" but not exactly corrmon view to the minute. To include the calibration portion of the R-CATS trip, corrections were made in the following way before the results in figure 5 were determined: Time Transfer (TT) = (R1 +A1) - (R2 + A2) where R1 was USNO and R2 was each remote European site with A 1 and A 2 being the calibration offset described before for each site. A summary for each European site is listed in Table 5. TABLE 5 Time Transfer Between USNO and Remote Sites TT(USNO - RMT) Remote Epoch Time //PTS RMS Site (MJD) Transfer (ys) (ns) (ns) OP 6036. 2.340 13 20 VSL 6042. 3.563 13 14 PTB 6046.0 4.286 17 TUG 6050.5 -1.404 13 11 441 o m p) o ~| K! !8 "^ w o m -t IO ^ (n ^ *'2 a a UJ 0. • /-» u. •»' • o in >> z V z < o ^ »' n: z • ►- UJ c * I 3 <^ • O Z UJ V) % a. •-• a: z _l l»l UJ »- U. K 5 OJ a i < , 13 ra »- ^ ujS < > o s • • § 3 1 • 1 • • s 1 1 r- IO in •* m in « in o " •« . — in . tn — • IO ' • ^ m • S •-» z UJ 0. u. >^ ■ H- UJ C • . r> ^ u UJ a • z UJ in ■ % — a z m UJ )- u. a: o 3 , t- «\i (T '^ • UJ u , z < 1 & o! • • ' a: < o > OD UJ z O z ^ (D 1- ^ O o t- > 3 1 in 1 • « • * 1 1 ■ -, m _i o Q- ID Z Sai» r- . 10 m . o m . 1 i\j O I\j ID •. *» m • oc 0. UJ Q. u UJ a J - • UJ »- li. q: I n* • ' < o § 8 si > . 5 1 s; J * • • • • • 1 1 ■^ « (\j O ID O O 0) (O . 10 rj . c^ 'J o ^ ID 92 1 a.' " 2 a: a. uj a. ^^ n •-> z < u ^ ^^ i£ z a 1- UJ c I 3 ^ U Ul o o z UJ in -\ a « a z lu H u. ae J m «g 2 • . ANSFE - UTC GPS 8. U. * • • £ «° TIME VI SV 06. • , (J 1- 3 - • . « . 1 1 • 1 1 1 T —I O QC ID Z S0N033S0»3IW Figure 5 SONOOBSOdOIH 442 NAVIGATION Another important aspect of the R-CATS trip is the accurate position determi- nation of each site using the portable receiver (STI025) to determine the GPS antenna coordinates with respect to the World Geodetic Survey of 1972 (WGS 72). Figure 6 presents a typical phase 1 GPS constellation satellite coverage for the USNO and European observatories during December 1984. Included on the figure are the periods of time that each GPS satellite was tracked and used in the navigation solution. A time history of satellite ground tracks are shown in the azimuth - elevation presentation. The concentric circles are elevation rings from the horizon to 90 degrees in 10 degree steps. Each existing satellite is plotted with respect to the GPS receiver antenna position. Since the four European observatories were relatively close this figure can be roughly applied to each. Continuous solutions were obtained using the GPS satellites shown in the figure. The final solution was compared with coordinates supplied by each of the observing sites. For USNO, results are compared against survey markers obtained from the Defense Mapping Agency (DMA) doppler satellite survey team. For the OP site, an approxi- mate position had been obtained from the NBS04 receiver averaging results over 3 months of solutions. For the remaining three European sites (VSL, PTB and TUG) initial coordinates were supplied from the Institut Fur Angerwandte Geodasie (IFAG) European doppler campaign. For the European sites, the TTR STI025 positioning solution used observations for a period from 10 PM local time to 6 ^ local time on a single night. During this period the effect of the ionospheric uncertainties is minimized. This is important because the STI TTR is a single frequency receiver using a model to predict and correct for ionospheric effects. In addition no observations were made for any elevation angle less than 20 degrees, which also minimized the effect of the troposphere in the navigation solutions. Table 6 presents the R-CATS navigation solution for each site as compared against the initial coordinates supplied by the host observatory. TABLE 6 ■ R-CATS NAVIGATION SOLUTION OP VSL INITIAL NAV INITIAL NAV COORD SOLUTION A COORD SOLUTION A X(m) 14202786 052 1202778.119 -7.633 3923530 712 3923529.122 -1 .290 Y(in) 1713'48 005 171318.389 .381 300581 710 300573.287 -8 .123 Z(m) 1778651 18°50'8 161 1778618.877 18°50'9.058" -2.287 5002832 51°59'58 933 5002830.062 51°59'58.862" -2 .871 LAT 921" .137" 870" - .008" LONG(E) 2°20'1 782" 2°20'1.816" .031" 1°22'51 112" 1°22'50.707" - .135" HKm) 122 810 116.110 -6.730 66 550 63.100 -3 .15 PTB TUG INITIAL NAV INITIAL NAV COORD SOLUTION A COORD SOLUTION A X(m) 3811066 050 3811062.995 -3.055 1191125 806 1191127.329 1 .523 Y(m) 709612 380 709636.383 -5.997 1162693 155 1162686.063 -7 .392 Z(m) 5023113 780 5023111.202 .122 1617212 17 OI'OI 117 1617210.093 17 01*01.569" -2 .321 LAT 52°17'15 898" 52°17'16.011" .113" 608" - .039" LONG(E) 10°27'31 016" 10°27'33.761" - .282" 15°29'36 082" 15°29'35.725" - .357" HT(m) 121 190 119.025 -2. 165 537 601 535.561 -2 .010 443 SVia - C 07J5-J330 SVII - A O41O-II00 evoo - g 0Bcs-oa?5 Evoe - e 0300-CHX svoe - e CM3o-oe30 USNO 12 NOV 84 USED IN SOLUTION PTB GPS GROUND TRACKS DAT! W Die M NORTH TO SOUTH SOUTH Tt) NORTH ■vn- • •vu-t SVU-* infriKO Figure 6 --« - -.1 _ A NAV SOLUTION StMBOLS AfSIlOiS-SITE SUBVEYI t- 1 X _ L H H L H NRL NAVIGATION SOLUTION INITIAL ESTIMATE - GPS DERIVED COORDINATES 03/02/85 l \ m\ *\ u I m I 1*1 '*! ulMloalul nlulosl ulsvj I»4i UTC TIMt IHRS. MINI Figure 444 Figure 7 (left plot) presents in graphics form the results tabulated in Table 6. It can be seen that the USNO position solution agrees with the DMA supplied coordinates to within 2 meters in all three axis. For the three sites referenced to the same IFAG doppler campaign solutions, a definite longitudinal bias of approximately 7 meters (.35 arc sec ) exist, with the latitude results being less than a meter and a height bias of 2-3 meters. Many factors could contribute to the large longitudinal bias. It is understood that the IFAG campaign originally solved for the European coordinates in the NWL-9D (NSWC 9Z-2) datum and transformed to WGS72. The transformation matrix is such that an approximately 5 meters (.260 arc sec) shift occurs in performing the transformation. In addition a change of approximately M meters is applied to the height coordinate. Work will continue with IFAG personnel on verification of original coordinates. Another possibility is the method of data collection used in the R-CATS navigation solution. An on-line real-time Kalman filter was used in the STI025 TTR with NAVSTAR SVs being switched in 30 minute intervals over the 8 hours total track time. Subsequent solutions at the NRL site have shown that, if an optimum Geometric Dilution of Precision (GDOP) term is predetermined and satellites are switched every three minutes, a solution can be obtained that converges to a steady state over a one hour period (reference to figure 7 right plot). More detailed analysis is needed before it is recomnended that new Euro- pean site coordinates be adopted at the meter level. CONCLUSION The R-CATS method has been proven, and initial absolute calibration has been completed for a series of major European observatories as well as the USNO and NBS sites in the USA. The R-CATS method is both cost effective and technically more accurate than a traditional portable clock trip. Navigation solutions (to the 10 meter level) have been performed. USNO is continuing to investigate this method and will begin replacing the current method of portable clock trips. 445 SENSITIVITY OF GPS CARIBBEAN BASELINE PERFORMANCE TO THE LOCATION OF A SOUTHERLY FIDUCIAL STATION Peter M. Kroger, C. L. Thornton, J. M. Davidson, 5. A. Stephens, and B. C. Beckman Tracking Systems and Applications Section Jet Propulsion Laboratory California Institute of Technology Pasadena, California 91109 ABSTRACT. The NASA SPS Caribbean Initiative will involve a network of "fiducial" GPS stations, whose locations in an earth-fixed reference frame have been well established using an independent technique such as VLBI. The fiducial station network enables the joint determination of GPS satellite orbits and mobile GPS station baselines with accuracy suffi- cient to be of use for geodetic applications. For the NASA GPS Caribbean Initiative, fiducial stations will be estab- lished at existing VLBI stations in North America. In addition, one or more fiducial stations may be established in South America, provided such stations are justifiable in terms of improved system performance and available re- sources. In this work we report the results of covariance analysis studies, investigating the sensitivity of GPS Caribbean baseline performance to the specific location of a southerly fiducial station. This sensitivity is investi- gated both for the case of the integrated doppler (i.e., current system) and carrier range ^advanced 19B9 system) data types. Scenarios involving fiducial stations at the POLARIS sites in Te::as, Massachusetts, and Florida, as well as one additional site in Ecuador, Chile, Brazil, or French Guyana will be discussed. INTRODUCTION A complete understanding of the plate tectonics of a particular region requires a spatially and temporally dense set of geodetic measurements. This is presently being accomplished in some areas, such as southern California, through use of mobile VLBI systems (Davidson and Trask 19B5). These systems have the capability of measuring baseline lengths with 1 to 2 cm accuracy for baselines up to 1000 km in length. Over 300 baselines in the western United States have been measured with this technique since 19B0 as part of NASA's Crustal Dynamics Project (CDP) (NASA 1982). Satellite laser ranging (SLR) using transportable laser ranging systems also has the capability to measure regional baselines with accuracies comparable to mobile VLBI measurements. Measurements by this technique have also been made in southern California as well as in many other regions (Christodoulidis et al. 1985). While both of these technologies have the required accuracy for geodetic mea- surements of tectonic motion and are quite mobile, they do have certain drawbacks which may make them impractical for making baseline measurements in some regions. The mobile VLBI units, for example, are somewhat limited in their ability to occupy sites which are not accessible by fairly good roads. Although a recent series of measurements has been completed in Alaska (Clark 1984) they involved a great deal of expense in terms of both equipment and manpower to allow transporta- 447 tion of the mobile VLBI units to several remote sites in this region. While requiring less equipment than the mobile VLBI units, the transportable SLR units require fairly clear weather conditions in order to make measurements and there- fore, typically require much longer occupation times at a given site. For these reasons, use of the NAVSTAR/GPS satellites and receivers offers an attractive alternative to either SLR or VLBI. GPS receivers are relatively small and much more portable than either mobile VLBI or SLR systems. A GPS system is also an order of magnitude lower in cost and incurrs lower maintenance, operating and post-processing costs than either VLBI or SLR systems. These advantages make GPS technology much more suitable for the kinds of measurements needed to under- stand the tectonics of regions such as the Caribbean. This, of course, presumes that the GPS systems can provide the same level of baseline accuracies that SLR and VLBI have already demonstrated. We report the results of several covariance analyses of GPS baseline measurements in the Caribbean. These analyses indicate that the establishment of a fiducial station in the northern part of South America (e.g., Quito or French Guyana) will improve baseline accuracy by a factor of up to four for integrated doppler data, which is the data type which will be used exclusively for the next four years, and by a factor of over two for carrier range, which may be available beginning about 1969. These analyses also indicate that the establishment of a fiducial station in the southern part of South America (e.g., Santiago or Sao Paulo) provides essentially no improvement in accuracy for Caribbean baselines over that attainable using the North American POLARIS stations as a fiducial network. FIDUCIAL NETWORK CONCEPT Current plans call for deployment of GPS receivers in the Caribbean region by 1986 (Thornton et al. 1983). Preliminary tests of the envisioned measurement system have recently been conducted in California (Davidson et al. 1985). Further tests of the system are planned prior to the Caribbean measurements and may involve continued measurements in California in addition to occupation of sites on the Baja California penninsula and mainland Mexico. An important goal of all these initial deployments is to test the concept of a fiducial network. A fidu- cial network consists of three or more GPS receivers located at sites whose positions in an earth-fixed coordinate frame have been accurately determined by an independent technique such as VLBI or satellite laser ranging. During a baseline measurement, the receivers located at the fiducial sites and the receivers located at the poorly-known mobile sites simultaneously observe all visible GPS satel- lites. In the subsequent data analysis, measurements from the fiducial receivers allow accurate values of the NAVSTAR satellite orbits to be estimated along with the unknown station locations. Without the ability to estimate accurate GPS orbits through use of a fiducial network, centimeter level geodesy cannot be expected for baselines greater than 50 km in length given the present accuracy of the published ephemerides. In order for the fiducial network concept to provide the most accurate orbits possible, careful consideration must be given to the location of the fiducial sites. If they are too far from the primary observing area then data recording by the fiducial and mobile stations will be increasingly non-simultaneous and it is no longer possible to effectively remove station clock errors by generating differenced observables. As a consequence, baseline accuracy will be severely degraded. Since their locations must be known to within a few cm, practical considerations limit fiducial sites to locations which have had some history of VLBI or SLR occupations or at least have the facilities available for making these 448 # QUASAR • FIDUCIAL STATION o MOBILE STATION GPS SATELLITE Figure 1. Schematic diagram of the fiducial network concept for making baseline measurements with the GPS system. Data from the fiducial stations enables accurate orbit determination, which in turn enables accurate mobile baseline determination. VLBI observations from the fiducial sites (not necessarily simultaneous with the GPS observations) determine fiducial baselines, tie the GPS results into the inertical frame of the quasi-stellar radio sources and unify the VLBI and GPS geodetic coordinate systems. measurements. For this reason the fiducial network for geodesy in the Caribbean will initially be comprised of the Project POLARIS (Carter et al. 1984) VLBI sites at Ft. Davis, TX; Nestford, MA; and Richmond, FL, and perhaps an additional site in South America. A sufficiently long history of VLBI measurements between the radio telescopes located at the POLARIS sites can be expected to yield station locations accurate to a few cm or better. Because of the expense which would be incurred in establishing an additional fiducial station in South America, it should be clearly established that this additional "southerly" fiducial will add sufficient accuracy to the GPS baseline measurements to justify the ejipense. We have carried out several simulations of GPS baseline measurements to determine which of several possible South American sites would provide the greatest improve- ment in baseline accuracies. This analysis has been carried out for both the current integrated doppler data type and the unambiguous carrier range data type of the advanced receiver design. 449 ERROR MODEL Table 1 contains a summary of the major elements contained in the error model used to simulate the GPS baseline measurements for both the integrated doppler data type currently used, and the unambiguous carrier range data which is antici- pated for the advanced 1989 system. It is assumed that the measurements are "double differenced" to remove the effects of all receiver and satellite clock errors. The differencing scheme used involves a linear combination of the data via a Householder transformation (Wu 1984). Water vapor radiometers (WVR) were assumed for the wet troposphere calibration with corresponding uncertainties based upon known and expected performance of these instruments. A new water vapor radiometer recently developed by the CDP at JPL (Janssen 1985) should allow the extra signal path delay due to water vapor to be measured with an accuracy of 0.75 at zenith. Data noise and fiducial baseline accuracies were based on projected 1989 levels of performance. TABLE 1. Covariance Analysis Error Model Data Noise for Single Differenced Data Data Rate Adjusted Parameters: Range Bias Parameters NAVSTAR Position NAVSTAR Velocity Mobile Station Location Considered Parameters: Solar Radiation Pressure Geopotential GM Relative Position of Fiducial Stations Location of Geocenter Troposphere 1.0 cm 300 sec intervals a priori uncertainty 1000.0 m 10.0 m at ecoch in each comDonent (X, Y, Z) 0.1 cm/sec in each component — ^^^*^^^\ ^/RICHMOND I \ r^ ^'^^^^^y^* ^ SAN JUAN ^^^ / ^^7^ SANTO DOMINGO ^^ v^,^^^ CAYENNE QUITO \^ J ^ \ ^^' •20 — • FIDUCIAL STATION ^^ j O MOBILE STATION 1 / 1 ) SAO PAULO SANTIAGO \| / - / * ^^-^ 40 1 1 . 1 ( ■ ^ . 1 240 260 280 LONGITUDE (deg) 300 320 Figure 2. Location of fiducial and mobile sites considered in covariance analysis RESULTS Figures 3 and 4 show the uncertainties in the three baseline coordinates for two baselines common to all of the fiducial networks in our comparison. Figure 3 illustrates the accuracies for a baseline length of 370 km (San Juan/Santo Domingo) and Figure 4 shows the results for a 2714 km baseline (San Juan/West- ford). It is clear from these results that choice of a southerly fiducial station 452 BASELINE: SAN JUAN SANTO DOMINGO 369.5 km E < Z Q o o u ea Z >- »— z < DATA TYPE: CARRIER RANGE A. RICHMOND, FL B. CAYENNE, FR. GUYANA C. QUITOE, EQUADOR D. SAO PAULO, BRAZIL E. SANTIAGO, CHILE F. RICHMOND & QUITOE G. RICHMOND & CAYENNE + FT. DAVIS, TX & WESTFORD, MA irnTTh mriTh E •3- < z a o o u ea Z z 5 z 3 AB C DE FG EAST A B C DE F G NORTH A BC DE F G VERTICAL A BC DE F G TOTAL (RSS) ABC D E FG EAST A B C D E F G NORTH AB C D E F G VERTICAL A BC D E FG TOTAL (RSS) Figure 3. Results of covariance analysis for San Juan to Santo Domingo baseline 453 BASELINE: SAN JUAN WESTFORD 2713.6 km Z >- I— z < h- Oi liJ U z 1 10 UJ (— < z Q o o (/I < ^ 5 DATATYPE: CARRIER RANGE A. RICHMOND, FL B. CAYENNE, FR. GUYANA C. QUITOE, EQUADOR D. SAO PAULO, BRAZIL E. SANTIAGO, CHILE F. RICHMOND & QUITOE G. RICHMOND & CAYENNE + FT. DAVIS, TX & WESTFORD, MA I A B C D E F G EAST A B C D E F G NORTH A B C D E F G VERTICAL A B C D E F G TOTAL (RSS) 40 30 20 15 < Z Q oi o o u < Z < o z 3 10 DATA TYPE: INTEGRATED DOPPLER Di A BC D E F G EAST A B C D E F G NORTH A B C D E F G VERTICAL A B C D E FG TOTAL (RSS) Figure 4. Results of covariance analysis for San Juan to Westford baseline can have a significant effect on baseline accuracy especially for long baselines 454 and integrated doppler systems. The results obtained with Ecuador or French Guyana as the southern fiducial stations in conjunction with the POLARIS stations in North America show improvements in baseline accuracy by a factor of up to four over that attainable using the POLARIS stations alone. This improvement is especially pronounced for the case of integrated doppler as the data type. Qualitatively, this increased accuracy may be seen to arise from the improvement in fiducial network geometry that results when Ecuador or French Guyana are added (Fig. 2), conincident with minimal loss of mutual visability between the fiducial stations. The results obtained with Sao Paulo and Santiago as the southern fidu- cial station in conjuction with Westford and Ft. Davis show how loss of mutual visibility can adversely affect baseline accuracy. For these southernmost fiducial stations, the number of available double differenced measurements was decreased by approximately 20 % compared to the other fiducial networks. More- over, the geometry of these remaining mutual observations becomes extremely heterogeneous. This affects the accuracy with which the GPS orbits can be deter- mined, and hence the overall baseline accuracy is actually reduced by up to factor of three from what is attained using the POLARIS stations alone. Because of the greater geometric strength inherent in the carrier range data type, results obtained using it are less affected by the location of the southern fiducial station than are the integrated doppler results. This is evident from the results shown in Fig. 3 for the relatively short San Juan to Santo Domingo baseline. The baseline accuracies obtained with carrier range show virtually no change for the different southern fiducial stations. Longer baselines such as the San Juan to Westford baseline in Fig. 4 show a greater dependency on fiducial network for the carrier range results. Unfortunately, carrier range data will not be used before 1989. Further, since many of the most scientifically interesting baselines in this region are longer than 1000 km, establishment of a southern fiducial station at Quito or French Guyana would insure that the requisite accura- cies would be obtained even after 1989. In the case of the integrated doppler data, the geometry of the fiducial network is particularly important. It must provide a uniform distribution of all compo- nents of the satellite velocites in order to allow accurate determination of all baseline components. This presents some difficulty in the Caribbean region where the ground tracks of the GPS satellites are predominantly north to south with very small east-west components. This phenomenon is responsible for the typically poor determination of the east-west components for experiments utilizing the integrated doppler data type. The locations of Cayenne and Quito allow for better determina- tion of the east-west components of the GPS satellite orbits and hence provide a more accurate determination of the east baseline components when integrated doppler is used. For example, the addition of French Guyana to the POLARIS network reduces the east-west uncertainy in the San Juan/Westford baselines (2714 km) from 9 cm to 2 cm. Finally it should be mentioned that this analysis treats only one of many possible observing scenarios in the Caribbean region(Dixon 1984). Other scenarios might result in somewhat different conclusions as far as the relative merits of the fiducial networks treated here. This may be particularly true for baseline measurements in the extreme western Caribbean where a fiducial station at Quito would almost certainly provide better baseline accuracies than French Guyana. CONCLUSIONS Establishment of a third or fourth fiducial station in South America would in 455 general allow greater accuracies for baseline measurements in the Caribbean region. In the case of the integrated doppler data type, this would represent an improvement in accuracy of up to a factor of four for baselines longer than 1000 km. Our analysis indicates that location of a fiducial station near French Guyana would provide the greatest improvement in accuracy for baselines in the Caribbean region. This would be especially true if it is be used in conjunction with a fiducial station at Richmond, Florida as part of a four station network. In fact, such a system would enable 1-3 cm geodesy with an integrated doppler system for baselines almost up to 3000 km in length. ACKNOWLEDGMENTS The research described in this publication was carried out by the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. REFERENCES Carter, W. E. , Robertson, D. S., Pettey, J. E. , Tapley, B. D. , Schutz, B. E., Eanes, R. J., and Lufeng, M. , 1984: "Variations in the Rotation of the Earth", Science 224, 957-961. Christodoulidis, D. C. , Smith, D. E., Kolenkiewicz, R. , Klosko, S. M., Torrence, M. H. , Dunn, P. J., 1985: "Observing Tectonic Plate Motions and Deformation from Satellite Laser Ranging", to be published in J. Geophys. Res. Special Issue on Lageos . Clark, T. A., 1984: "Geodesy by Radio Interferometry: GAPE '84 Interim Report", Transactions, American Geophysical Union 65, 856. Davidson, J. M., Thornton, C. L., Vegos, C. J., Young, L. E. , and Yunck, T. P., 1985: "The March 1985 Demonstration of the Fiducial Network Concept for GPS Geodesy: A Preliminary Report", this issue. Davidson, J. M. and Trask, D. N., 1985: "Utilization of Mobile VLBI for Geodetic Measurements", submitted to IEEE Transactions on Remote Sensing and Geoscience, Special Issue on Geodynamics (in press). Dixon, T. H., 1984: "Caribbean Geodetic Measurements with GPS Receivers", Jet Propulsion Laboratory Document D-1485. Janssen, M. A., 1985: "A New Water Vapor Radiometer for Geodetic Applications", Transactions, American Geophysical Union 65, 854. NASA, 1982: "Application of Space Technology to Crustal Dynamics and Earthquake Research, Technical Paper 1464. Thornton, C. L. , Davidson, J. M., Beckman, B. C. , Young, L. E., Thomas, J. B., Dixon, T. H., Trask, D. W., 1983: "System Study for Global Positioning Satellite (GPS) Geodesy in the Caribbean", Jet Propulsion Laboratory Document D-941. Nu, J. T., 1984: "Elimination of Clock Errors in a GPS Based Tracking System", Proceedings of the AIAA/AAS Astrodynamics Conference, August 20-22, 1984, Seattle, Washington. 456 A SURVEY OF CIVIL NAVIGATION SATELLITE SYSTEM ALTERNATIVES, AND THEIR POTENTIAL FOR PRECISE POSITIONING Keith D. McDonald Federal Aviation Administration Washington, D.C. Richard L. Greenspan The Charles Stark Draper Laboratory, Inc. Cambridge , MA ABSTRACT, "fliis paper addresses the technical characteristics and implementation plans of a number of space-based radio navigation systems which have been either partially deployed or investigated recently for possible future implementation as civilian alterna- tives to the Global Positioning System (GPS) . These systems include the European Space Agency's NAVSAT, the Soviet Union's GLONASS, the Federal Republic of Germany's GRANAS, and several proposed domestic satellite-based systems which offer radio posi- tion determination services. The principal characteristics of the various alternative systems and GPS are presented. The influence of these factors on the exploitation of the capabilities of se- lected systems for precise terrestrial positioning is evaluated and system suitability criteria are developed. A preliminary assessment is provided of the precise positioning performance of the alternative systems using as a baseline the GPS demonstrated capabilities and operational parameters. INTRODUCTION The development of the GPS by the United States Department of Defense (DOD) has resulted in worldwide civil interest in the applications of navigation satel- lite systems to a variety of aeronautical, maritime, and terrestrial uses. An important application, and one which has received considerable interest and recent activity as GPS nears implementation, is that of precise positioning. T^e tech- nique normally employed involves the use of a set of stable satellite signals which are measured on an interferometric basis, tracking the radiofrequency car- rier phase of the signals. Relative positioning with accuracy in the decimeter range has been obtained with the GPS over baselines extending to thousands of kilometers. Although GPS may currently be the leading contender for use by the interna- tional community, several alternatives to the GPS have been configured and these systems have received substantial development effort. These include the Soviet GLONASS system which has six or more satellites deployed for test purposes, and which operates at the same orbital altitudes and at close to the same frequencies 457 as the GPS; the European Space Agency's NAVSAT system (ESA NAVSAT) which has received considerable study effort in the last 2 to 3 years; the Federal Republic of Germany's GRANAS system which appears to be in its initial study phases; and a number of other systems, both domestic and international, which provide position determination capabilities in addition to other functions, such as communications. OBJECTIVES It is not clear which of these systems beyond GPS will attain operational status; however, it appears that there will be other systems than GPS available for precise positioning in the future. The questions then arise as to what are the characteristics of these systems and what are their capabilities for precise positioning. We are not attempting to assess the viability or desirability of the various system alternatives or to judge the capabilities of the various systems in their normal operational modes. Ttie principal objectives of this paper are the following: 1 ) to identify the potential precise positioning satellite-based alternatives to the GPS and to describe the salient characteristics and technical features; 2) to analyze the fundamental system capabilities which influence pre- cise positioning performance and to develop system evaluation criteria for assess- ing precise positioning capabilities, and 3) to provide a preliminary evaluation of selected alternative precise positioning systems using GPS as a reference base- line. Organization To accomplish the first objective, charts are presented which identify and describe within a matrix format the GPS and a group of alternative systems. "Hie charts provide a summary of the characteristics and technical features of the selected alternatives along with the system performance data necessary to estab- lish their precise positioning capabilities. An analysis is then developed relat- ing the fundamental factors influencing precise position system performance to the characteristics of the alternative systems. General Evaluation criteria are formulated which are used to provide a preliminary assessment of the precise positioning capabilities of the selected satellite-based system alternatives. A brief summary and a set of conclusions are presented relating to the capabilities of the system alternatives considered and the factors involved in using satellite- based systems for precise positioning. SATELLITE-BASED PRECISE POSITION ALTERNATIVES SURVEY The alternative systems considered were selected on the basis of announced plans for achieving operational status, available information about the candidate system concepts which indicate promise of development in the future, or in a few cases, from the general or technical interest perspective. These systems include the GPS as a baseline, the ESA NAVSAT system, the Soviet Global Navigation Satel- lite System (GLONASS), the Federal Republic of Germany's Global Radio Navigation System (GRANAS), the United States' domestic systems currently in the develop- mental stages represented by Geostar, Mobilsat, Skylink, and possibly others providing the same type of service to small users. Additionally, the maritime INMARSAT system may provide multiple satellite coverage for oceanic areas, and other systems may be deployed which resemble some of the system configurations described. 458 Figures 1 and 2 are matrix charts which provide information on the general and technical operating characteristics for the GPS and the selected alterna- tives. The principal systems considered are identified by the column titles. "The row titles for these matrix charts describe the attributes relating to the selec- ted system alternatives. Figure 1 presents the general attributes such as system sponsor, status and schedule, and the technical characteristics including operat- ing modes, user measurements, accuracy, coverage, and orbital constellation con- figurations. Figure 2 covers the characteristics of the signal structure, modula- tion, operating frequencies, multiplexing techniques, power, error contributors, and system accuracies, "flie sources for this information are indicated on the fig- ures and cited in the references. System Comments The charts of Figures 1 and 2 provide the basic data associated with the GPS and the selected alternatives; however, a few comments relating to the systems appear appropriate. ■The GPS is a U.S. DOD system which has been developed to provide worldwide navigation and positioning services to equipped users on an unlimited (passive) basis. "The present plans call for an 18 satellite system constellation with three active spares in twelve-hour orbits with an orbit altitude of 10,900 nauti- cal miles. Eighteen Block II GPS satellites are planned to be in orbit by late 1988 or early 1989. Ihe system operates in the aeronautical L-band at 1575.42 MHz with a second frequency at 1227.6 MHz. Carriers of both frequencies are on simul- taneously from all satellites and pseudorandom noise (prn) code modulation is im- pressed upon the carriers using both 1.023 MHz and 10.23 MHz codes. A fifty bit- per-second data channel is incorporated in the signal structure which transmits ephemeris, satellite health, and other system information. A GPS test constella- tion currently consists of 6 satellites in 2 orbit planes inclined at 55 degrees. This provides coverage centered at the Yuma, Arizona, test range and is available for approximately 2 to 4 hours each day. A comprehensive test program of user equipment has recently been completed and a substantial buy of DOD user equipment, totalling many thousands of units, is currently in process. The ESA NAVSAT is a system currently being studied by the European Space Agency. The system would provide worldwide civil navigation satellite coverage on a passive basis to an unlimited number of users. Its satellite constellation de- sign is similar to an earlier GPS arrangement which incorporated 24 satellites. It departs from the GPS in its design in that no atomic clocks are employed in the satellites. The satellites consist of translating repeaters which relay time- division multiplexed ground station transmissions to the users. The ESA NAVSAT concept is directed toward economically providing service to low-cost user receiv- ers. The satellite transmissions include a combination of tone bursts and phase modulated pulsed signals for position determination and data transmission. The system development by ESA is intended to transition to an international civil en- tity of some type for implementation. Several comprehensive studies have been completed for this system. GLONASS is a Soviet worldwide satellite navigation system for aircraft cur- rently in the experimental stage. The International Telecommunications Union fil- ing (Ref. 2) indicates that the system uses nine to twelve satellites positioned into three orbit planes having inclinations of 63 degrees. The operating frequen- cies for GLONASS are approximately 25 MHz above those established for GPS. Little 459 -i-i b gW O ^ » «> < I- o lU O m < o -■ ^ ? o a «o o (0 5, < -• ^ « o z »> < 2 > 3 < z :» I- 5 3 » Z .J Ul < UK W w ^ >- 111 Ul B> W o in I ^^ 2tS o •> w ^ o >- o a. tt> 52 8 2S i-'H S" »l*s ^\^ S=^ H>1 et ^ 'SS - - = ^ ^5 i-=S y t- <-> « o ,•1 . .B. Joe ^u E !iS:93E NPdg sn 5ti iS ^ ■>= cox uJ O 0^ »• 3 z I— a S3xS 9 z z oe o .5 3 uj" - ; o •" y _"y 13 •S3: ''SS Si si i» u lU ui u. o a: 132 ft 55 ^r ifcpi^ 5P « ui5 Ui o =>o. ) cor^ ae as SPSS 5=^ 000- f- . >- => 5-JbJ O of O C3 U < UJ UJ •QCc^ 3 t^ s»- ^ .3^2 « CD Oi->0 UI S —I z3 o S Z S lis ^ g|58g (/^oto z o^z3o - x* ^1 Bfoe CD t— •— OUJ h- z o^- Ot-" Q.«- Q t- O o o as gf: St t— '^UJ UJ Sh- 2_iz CO %»- 0. O.S I CJ UJ^* CD -t = zcst: « z oe ujiot-« oQ Sz X z5 UJ •-•>oi-> D < *z agSP ^".32=. mo i-^a UI c33 z<3 o — w IE •-• O l/> •-« tf . < »--: €/) « Sin*-, t- Q. Z a. B£ X o yo ■—U. = >- Q •— < P a xuj P < UJ . ujPzujzxPe Oi/> — ■S' <~* S ^ UI Z3'CQ"- sz in O O Wl St3 - Z t— ro §<(=<>- oe UJ X to •— oc pe o a. uj LK :« oc P o P ■«U. 3 UJ UJ O • (/) Z3 .moc«c<— xu- 5_-" O =) •• (N J H O Q •■ UJ ■< u = Q f- H HO c/^ O tiJ H Dt (-•J O O ■« Q- f- to ■< O I O -J t- U U c 3^f- ViZ^ 1-00 ;i^< y ""• O 3 fega >-" X (Jl cs J g z'^'=^gs;;;— z . « oe UJ H-> •— _iuj (- o tn CO 00 — 5 zo coo g S B S< ^ S e UJ 3 oe 460 (0 Q if tt «^ o > •« z OS , J J -i-i UJ -J s o CO -J Ul SKYLINK: 821-825 MHz 866-870 MHz POSSIB. L-BAND BW: 5-10 KHz. ^•F:'i S:" 10 KHz POLLING CHANNE 400 - 10 KHz RETURN CHANNELS TONE CODE RANGING _ . . ACTIVE SYSTEM FOR POSITION SURVEILLANCE GROUND BASED CLOCKS: STABILITY IN SHORT TERM: REOMTS MODEST TROPOSPHERE IONOSPHERE MULTIPATH EPHEMERIDES RCVR NOISE TRANSPONDER DELAY CORRECTION TECH. DEVELOPED MOBILSAT: SURVEILUNCE SYSTEM: FIX ACCUR: 200 M. ACTIVE SYSTEM. Ii. 3 o <: Q- O 3 . ^gs^a ,: »; ,., oc < -USER) -2500 MH AT) 6.5 MHz TR.F.) MHz S 174.75 M UM SIGNA 0: 8.192 98,550 B N: 12 MS EC: 83 AL: VARI REC. TRANS. . ER.COR m tt: 3; D SYSTEM SYNCH 'D PULSE. USES PACKETS BPS ON A 5E0UENCE 1 FOR i/ElLLANC : LOCKS: SHORT MODEST (/I Q U. i o UJ O LINK(SAT : 2483.5 NK(USER S 1610-152 UPLINK(C 6533.25 DOWNLINK 5125.25-; READ SPECTR X-LENGTH SE ORT CYCLE: lAME DURATIO ;PETITIONS/S XESS INTERV ATA: 64 KBPS 16 KBPS ALF RATE FWD L __ EIRP: 53.6 d DOWN(SAT-USE C/N : 57.9dB USER SELECTS ACCESS BY PRN REPLY INBOUND LINK BURST DATA RATE: 15 K GOLD CODE ACTIVE SYSTE POSITION SUR GROUNDBASED STABILITY IN TERM: RF.QMTS TROPOSPHERE IONOSPHERE MULTIPATH EPHEMERIDES RECEIVER NOI TRANSPONDER DIFF. OPER. STATIONARY U 2-3 M. VEHICLES: 3-7 M. |'-gcSc|2 K ^ 0) < o i i O ^ £ NOWN INS (MAX dB dB NOWN 1 g mo - S z K — — e- N Z ^ 5 '^ '^ ^ UJ po < te (9 UJ S S ii ND F2 t lOH THER LABLE NOT ANT. : 15 : 15 NOT i^^ 5: u: si z -J MED T LAR T NFORM LABLE s: UJ £3 O o ^ '"' < " .. °5 &^ . u^ a! "o o ^ ^ So s: ^ ""* < o > O > (9 % u> u. u. u-m 2 «: "" " 2a.t- O _x ^ ?g g al 1 o ~ 5 o ooe 0) Q 2 O k- O TDMA FRAME DURATION: 1. T. SLOTS/FRAME: 10 SLOT DURATION: 14C SIGNAL BURST DURATI 120 MS DATA BIT TRANSMISSI CAPACIH: 26 BPS CHIP RATE: 4 MHz, .- K, u. 8 _ ^S rry a q: u « O o * UI K 1575 MHz 1228 MHz 1575 MHz W G. : 2200-22 SIGNAL BURS RATE: 4 HH : 39.9dBw PWR: 23dBM; SIGNALS SIG: C/No = DIVISION IPLE ACCESS OULED FOR PODAL SETS 20 SAT. TELLATION STATION CLO IDIUM): GTIME: +10-' RTTIME: +5x1 CLOCK (CRY GTIME: +10-7 o "+ E R CONTRIBUTO LAR TO THOSE NAVSAT. 2 F . FOR lONOSP DELAY POSSIB EQUIPPED USE O <0 F1: F2: TTC: EMER • o. EIRP TH. NAV. NAV TIME HUL1 SCHE ANTI FROC CONS GND. (RUB LON SMO SAT LON o ERRO SIMI ESA CORR GP. FOR g 5? LJ . .UJLO o .. Vl M g ™ .^sSd -^ s w Bw; 204w. (DOWN AND, C/No , C/No z AND, C/No < o ~ ~ 5 U- o . u- o l^.. >U NAD C-BAND 5.25 G N MULT ). ON: 1 E: 12 N: 13 IGNAL 1,071 M-SYN ESTER /FRAME , 2KHz TOTAL 20 MHz 5 ;iBPS S BW: CD 2 ^ o: t^ ^- o '7 ° ^1^ " => is o o CO o t o 2. OH 3.0M MODE LI T., DI .OM 1.5H : 0.9H 4.0M PPLER ONLY (CW MODE): TDMA BURST: 18 PAIRED TTDHA FR INTERFERCHETRIC ISM. UJ Ui 5 : 1556 MH (PROVISIO SC: WN i UP: 5.00- HE DIVISIO CESS (TBHA AME DURATI SLOTS /FRAM OT DURATIO VIGATION S LENGTH: 13 MOD: PRN, TA: HANCH ENCODED: 700 BITS 500 BAUD ECISE NAV, +10 MHz; IP RATE: PPLER HA7: TA REQUIRE +2 KHz. RP: 39.9dB . PWR: 23d V. SIGNALS LINK): NTROL: C-B = 79 dBHz TA: C-BAND = 32.5 dBh V SIG: L-B = 45 dBHz gs 1E DIVISIO LTIPLE ACC HEOULED FO TIPODAL SE OM 24 SAT. NSTELUTIO 9ID. STATION (RUBIDIUM): LONGTIME: t SHORTTIME: + SAT. CLOCK ( LONGTIME: +1 OP. REFR: NO. DEUY: CORR. BY KALMAN ES CORR. LTIPATH: 1 HEMERIDES: STEM CLOCK ;R NOISE: OO ■(/ a,n:rl UJ ui «0 w uT tg o. o o o uPz o o z Pisses p: o 3 a. >• (J OC g -^ — ^ ..,-«—. 5k. „S E (P ITIO OD. P URE. 1 MS EC.) G--Sm (P CODE) Y PRN P SIGNAL Y F GOLD o T 3°i .8 KP (LI) TO DRHS (RMS (0 2 Ji i^ ECIS QUIS ES H PSK. SEC TH: SK 30 S (DOD ATE: HBP MHz IVIL CHI MBPS MHz 2 g--5' • -7 ■ox:x t (n u a; o in EFR. P DE EAS. F. C SIM DIFF cyt/> _J TIME REQ TED (2 TIME % ^£y Q. gS°g-=' ci ,- oc Schgu O s UJ u, o (/> O ;j K UI ^r- CM^ L2 CO lERS. COARS ) PRN lERS FOR DE LE 6 WEE CODE CHAN BPS FRAM 1500 ^'S'-^S- -^ Csj .. .. .- .- O SATELLITE 2 CESIUM LONGTERM: SHORT TER ¥S^- =^~^° = -IU<^ — OUO. O O Q =e i 5. DC < pe o -r o o Q- »/) 1— O (/> o o TRO ION COR MOD MUL EPH S/C RCV o. o o 3 o 8 o o s U- g 5 g n 5 SIGNAL STRUCTURE IRANSHISSIOIIS WI USERS HODUUTION TYPE g i 5 CD □C §1 5 SATELLITE (P, EIRP) AT SURFACE (C/NO, SNR) X 5 /I i i IRAN SWISS ION SPACECRAFT OR GROUNDBASED CL CHARACTERISTIC ill 1 1 0) u & 461 information is available on the details of the system's signal structure or of the system deployment to date. However, there are indications that six or more GLONASS satellites have been launched. The relatively small number of satellites planned for the final deployment (twelve) indicates that the system (at least in its initial phase) may normally use some form of aiding, such as altimetry. Geostar is a civil satellite-based location and data link system currently in development and test by the Geostar Corporation of Princeton, New Jersey. The system employs three (or possibly two) geostationary spacecraft to provide cover- age to selected North American and adjacent oceanic areas. High accuracy position location capabilities are claimed for the system, and data link communications services are provided. The system is proposed as basically a position surveil- lance system in that the position of a user is determined from transmissions re- ceived at a ground computing center and the resulting positon and data link infor- mation is relayed back through the Geostar satellites to the user. The system em- ploys reasonably large spacecraft antennas to provide service to low-power and low-cost user equipment. The multiple ground stations would employ large redun- dant computers for the position computations and for reliability. The system is in the design and test stage, and frequency allocation is being pursued. The operational system date requested for Geostar is 1987, The Mobilsat system is primarily for communications and data link ser- vices. However, a two-satellite configuration does provide for position location accuracies of about 200 meters. The Mobilsat space segment consists of two sat- ellites in geostationary orbit over the continental United States, with coverage of the North American continent and adjacent areas. This positioning system is also basically a surveillance configuration in which the position location is de- termined from signals received at a ground station and the position and data link information is transmitted to the user by a voice or data communications link. This system also is in the design stage with frequency allocation being pursued. The planned operational system date is 3 to 4 years after grant of a construction permit. The Skylink system is in many respects similar to Mobilsat in that it plans for two spacecraft in geostationary orbit to cover selected North American and ad- jacent oceanic areas. This system again is primarily for voice and data communi- cation. However, it does provide means for surveillance position determination of equipped users. This system is in the design stage with frequency allocation be- ing pursued. Operational service is requested for about 1987. INMARSAT is the designation given the satellites deployed by the Interna- tional Maritime Satellite Organization, headquartered in London, The system cur- rently deployed over the Atlantic, Pacific, and Indian Oceans provides worldwide operational mobile satellite communications service by voice and data to ships and oil rig platforms. The INMARSAT organization consists of approximately forty mem- ber countries and approximately 2,500 ships are currently implemented. The space segment for INMARSAT currently consists of three geostationary satellites with a backup space segment planned to be on station by the mid-1 980' s. Ten ground sta- tions have been implemented worldwide with others planned. A second generation space segment is to begin service in about 1988 and will include the capability to provide aeronautical L-band service in the oceanic areas . 462 Although INMARSAT'S services are directed to the oceanic areas, it is included because the system may be of interest as a means for obtaining precise intercontinental measurements. INMARSAT'S operational characteristics are, in most respects, similar to those given for Mobilsat and Skylink and therefore the system is not shown on the matrix charts. PRECISE POSITIONING ANALYSIS Interest in the exploitation of signals broadcast by navigation satellites for purposes of precise positioning has accelerated since the deployment of a limited GPS constellation. Table 1 summarizes recent reports of accuracies in the subcentimeter range obtained for measurements of short baselines, and reports of accuracies that are limited by ephemeris errors for longer baselines and for point-pos i tioning . Table 1 . Precise positioning using GPS observations relative positioning. Baseline Length Vector Error (1-sigma) Dominant Error Mechanism Source < 1 .0 km < 1.0 cm Thermal Noise Greenspan, et al. , [1982] Goad S Remondi [1984] 10-40 km 1 part in 10^ Ephemeris Errors Goad S Remondi [1984] 2400 km 2 part in 10 Ephemeris Errors Bock, etal, , [1984] However, the acceptance of GPS by the international civilian navigation community is not certain. As noted earlier, several alternatives are currently being evaluated or are in the initial stages of implementation on both an interna- tional and domestic basis. In the balance of this paper, we analyze and evaluate whether some of these systems would be at least as suitable as GPS for precise positioning, and whether others are not suitable as currently conceived or imple- mented. In this section we identify and analyze the features of satellite-based radio-navigation systems that contribute to their exploitation for precise terres- trial positioning. The discussion is formulated in terms of relative positioning (baseline measurement) , with exceptions noted where requirements for point posi- tioning are different. The fundamental observable for relative positioning is the interferometric carrier phase difference. This is the difference between simultaneous observa- tions of the carrier phase of the signal transmitted by one satellite and received at each end of the baseline being measured. Each receiver estimates the phase of the incoming carrier signal relative to a locally generated reference frequency. The interferometric phase difference for observations of a satellite is denoted by 9. .(t), where antennas i and j define the unknown baseline B, .. We ID ID 463 assume that the transmitted satellite frequency is stable enough for receivers to maintain carrier phase lock. "Then the carrier phase of the satellite transmission cancels in the formation of the single-difference observable when these are inter- polated to a common epoch, (The ability to do point-positioning depends on the stability of the satellite oscillator.) We model 9ij(t) as the following function of p (t) , which is the slant range from antenna to satellite, and i(<(t), which is the phase of the reference oscillator at the receiver. e (t) = (p.(t) - p (t)) ^ + (i|; (t) - Ti> (t)) + N - ( .(t)-(j> . (t) is the phase measurement error attributable to receiver ' thermal noise, instrumentation, and multipath When the baseline length is small compared to the altitude of the satellite p.(t) - p. (t) « B, . . 1 (2) 3 1 ID s where ig is a unit vector in the direction of the satellite. Substituting Eq. (2) into Bq. (1) yields the final version of the measurement model for the single-differenced observable. 9 . .(t) = - B. . • i (t) +(!(;.( t) - ip. (t)) + N. . IT C IT s ^^1 ^x ^ n -(*e,j^^> -*e,i«^>l -(*n,j^^> " *n,i(^>) (3) In the following paragraphs we intercept each term of Bq. (3) to formulate requirements that must be satisfied if navigation satellite signals are to be useful to the precise positioning community. Signal-to-Noise Ratio The fundamental interferometric observable is the difference between pairs of carrier phase measurements. The signal-to-noise ratio (SNR) should exceed 15 dB to keep tracking loops in lock. However higher values of SNR are usually 464 desirable. For example, in an L-band sytem designed to measure baselines to subcentimeter accuracy the standard deviation of each phase measurement should be smaller than 0,03 radian (1 mm) to be small compared to measurement biases, "flie measurement signal-to-noise ratio should exceed 30 dB in the tracking loop band- width in order to satisfy this criterion. Satellite Visibility A precise, but ambiguous, baseline determination can be made by an independent-element interferometer from observations of four or more noncoplanar satellites. It is preferable, but not mandatory, that at least two satellites be visible simultaneously at each measurement epoch to obtain the greatest benefits of local oscillator drift suppression available from double-difference processing. The ambiguities are resolved by interpreting sequences of satellite obser- vations as the satellites move along their orbits. As a rule of thumb, the range of significant ambiguities is reduced to 1/a wavelengths if the satellites are observed across an arc of a radians. (For example, satellites in 12-hour orbits traverse about 0.5 radian in one hour). Satellite Ephemerides Radial errors in the predicted satellite position do not change the satel- lite direction vector i (t); therefore they have no effect on B • i (t). Along- s s track errors produce a fractional error in B on the order of the error in the satellite direction angle (radians) of i relative to the baseline. This error s is on the order of 1 part in 10^ for the orbit predictions currently broadcast by GPS satellites. When propagation corrections are available, the ephemeris errors at this level will dominate the errors in measuring baselines of about 100 km or longer. When propagation corrections are not available, these errors may equal or exceed ephemeris errors in the range of 100-2000 km. Reference Oscillator Stability The term (T|;j(t) - ipi(t) ) contributes the same error to simultaneous observations of two or more satellite signals in the same frequency band. There- fore, it cancels from a double-differenced observable formed by differencing simultaneous observations of 9ij(t) for two different satellites. We discuss the case in which there is a delay between observations of these two satellites in the next section. That analysis can also be interpreted to show that the phase stability of readily available oscillators is adequate to minimize the occurrence of cycle slips in the periodic tracking of any one satellite at intervals of a few seconds . Propagation Errors Propagation errors can be reduced, but may not be entirely eliminated except in special circumstances. For short baselines the propagation paths are close enough for propagation errors to be highly correlated. In that case their difference becomes negligible. In fact, one could argue that "short" baselines are those for which the propagation errors are correlated at the 90% level or higher. 465 As the baseline length increases, the propagation errors decorrelate. The distance at which this decorrelation occurs for tropospheric and ionospheric error components is not well characterized by observations at this time, and should be intensively investigated as the data base of interferometric observations becomes more extensive [Knowles, 1984]. When a two-frequency satellite transmission is available (as in GPS) then the component of phase delay attributable to the ionosphere can be accurately estimated at the cost of increasing the standard deviation of the background noise in phase measurements by a factor of about three. In one case, a 10-fold reduc- tion in post-fit residuals for a dual-frequency GPS observation along a 2000 km baseline was reported compared to single-frequency observation [Bock, et al. , 1984]. Figure 3 illustrates the hypothetical variation of baseline measurement errors with baseline length. For short baselines the errors are dominated by noise and instrximent effects that are independent of the baseline length, llie percentage error in baseline measurement attributable to uncompensated propagation errors increases with baseline length to a peak on the order of parts per million from about 50 km to about 1000 km. For larger baselines the dominant error mecha- nism will be ephemeris errors which are currently about 1 ppm for GPS orbit deter- mination, with efforts underway to reduce the uncertainty to about one part per 10 million [Bock, et al. , 1984]. THERMAL NOISE rss ERRORS CURRENT EPHEMERIDES ERRORS UNCOMPENSATED PROPAGATION DELAY FUTURE EPHEMERIDES ERRORS 8504J255-5 10 102 10^ 10^ BASELINE LENGTH (km) Figure 3. Hypothetical accuracy of baseline estimation. 466 Multipath and Instrumentation Bias Errors The effect of multipath errors can be reduced by antenna siting, antenna design, satellite selection, and perhaps by modeling. Instrument biases may be reduced by a combination of careful design and calibration. Note that the repeat- ability of a bias from one instrument to the next is a satisfactory design objec- tive because identical biases would be cancelled by interferometric processing. These error sources would have little efect on the selection of a satellite source for interferometric processing as long as good satellite visibility is maintained. In straimary the following features of satellite systems contribute to their success in precise 3-dimensional relative positioning: (1) An accurate ephemerides is essential. A 20 meter along track error in a satellite at 20 x lo^ meter altitude (e.g., GPS) produces baseline errors on the order of 1 part in 10^. (2) A measurement signal-to-noise ratio on the order of 20 dB or higher is necessary to keep thermal noise errors less than 0.1 radian. (3) Simultaneous visibility of two or more satellites at a time is desir- able to suppress receiver clock errors. (4) Visibility of four or more satellites (with double difference proc- essing) for a long enough time to resolve instantaneous phase ambi- guities is essential, itie more satellites that are simultaneously visible, the less time is required for ambiguity resolution. (5) Dual-frequency transmission is desirable but not essential, "flie significance of being able to suppress the ionospheric errors in a single-difference observable depends on the quality of ephemeris data and the receiver noise level, and the quality of tropospheric propa- gation delay estimates. (6) Satellite motion is essential to resolve ambiguities in the phase observables. SUITABILITY OF SATELLITE-BASED ALTERNATIVES FOR PRECISE POSITIONING Summary All navigation satellite systems being considered will provide worldwide visibility of three, four, or more satellites. The domestic position surveillance satellite systems provide regional visibility to two or three satellites. Signals from all satellites will be received at a C/Nq of about 35 dB-Hz or more, there- by guaranteeing that each carrier phase measurement will be very precise (Ta- ble 2). Mobilsat, Skylink, and Geostar are primarily surveillance systems which provide visibility of two or more satellites over limited regions. Although their signals are strong enough to permit precise carrier phase measurements, they would probably be useful only as supplementary sources. None of the systems being considered plans to disseminate ephemeris data as precise as will be needed to achieve the greatest accuracies desired by the pre- cise positioning community. "Bierefore, that community will be required to inde- pendently generate this data, much as is already anticipated for GPS. 467 Table 2. Predicted SNR for satellite transmissions. Satellite C/No dB Hz ESA NAVSAT 43 GRANAS 42 GPS/GLONASS 37-43 GEOSTAR 54 MOBILSAT 55 All of the GPS alternatives except GLONASS involve Time Division Multi- plexed (TDMA) satellite transmissions. Typical transmission formats involve 10-12 time slots in a 1-2 second frame, in which the satellites transmit bursts of about 25-133 ms duration per frame. This raises the question whether receiving system clock offsets can be adequately cancelled when satellite signals are not received simultaneously. The answer is yes, if the maximum delay between any pair of satellite observations will be less than 2 seconds. "Hie argument is based on the observation that quartz oscillators having a short term stability no worse than 5 parts in 10^^ over 10 seconds have been commercially available at under $2000 per unit for several years. This oscillator at 1.5 GHz would drift by no more than 5 degrees over a 2-second period. If the average frequency of the oscillator during each TDMA frame is measured, the first order effects of a linear drift on each double difference observable can be estimated leaving a residual error of 2.5° or less. In fact, the error may be as little as 1" or less because the time difference between adjacent satellite observations will usually be much less than the full TDMA frame, and the short term stability of selected commercial oscil- lators often exceeds their normal specifications. We conclude that the most probable TDMA formats would not impede the development of interferometer-based precise positioning equipment. Some improvement in performance may be achieved, with some added cost, if the satellite transmissions are phase-coherent from frame to frame. Only two of the alternative systems considered provide dual- frequency transmission, one continuously, and one on a time multiplexed basis. The signifi- cance of this capability depends on the particular precise positioning applica- tion. Figure 4 summarizes the findings for GPS and alternative system suita- bility. The figure illustrates the capabilities of the systems as a function of the performance conditions developed as evaluation criteria. •The systems we can rule out at this time as primary systems for precise positioning are GEOSTAR, MOBILSAT, SKYLINK, INMARSAT and similar geostationary satellites. They are rejected on the basis that they are comprised of geosta- tionary satellites, thereby failing to satisfy conditions 1 and 6 presented above. 468 8S04J255-6 LEGEND: Q Satisfies requirement Q Satisfactory performance with restrictions O Does not satisfy requirement Figure 4. Comparison of candidate satellite systems for precise positioning. Conclusions (1) GRANAS, ESA NAVSAT, and GLONASS would be suitable signal sources for precise relative positioning. (2) lAie geodetic community should be prepared to develop the observation- al and computational resources required to independently generate precise satellite ephemerides. (3) The civilian capability of GPS (the SPS service) remains as an at- tractive means for supporting precise positioning. (4) Precise positioning equipment should Include provisions to measure Ionospheric propagation delay If the full precision potential of a satellite-based system Is to be realized. For SPS, this measurement opportunity will be available as long as Identical signals are transmitted on the LI and L2 frequencies In the Precise Positioning Service. This remains valid even If the signals are encrypted, since the LI and L2 signals may be cross correlated to obtain the propagation group delay. 469 REFERENCES 1. Global Positioning System , 1984: papers published in Navigation , the Jour- nal of the Institute of Navigation , Vols. I and II, the Institute of Navi- gation, Washington, D.C.. 2. GPS Navstar User's Overview , September 1984: prepared by Deputy for Space Navigation Systems, Code yEE-82-009A, Navstar GPS Joint Program Office, Los Angeles, CA, Third Edition. 3. NAVSAT, A Worldwide Civil Satellite Navigation System , 1983: European Space Agency, Paris, France. 4. Diederich, P., R. A. Allan, S. G. Hazeltine, et al. , August 1984: A Study of the ESA-NAVSAT Control Segment , Final Report, Racal Satellite Systems Division, Racal-Decca Advanced Development, Ltd., Walton-on-Thames, Surrey, Kent. 5. GRANAS Global Radio Navigation System , 22 October 1984: submission by the Federal Republic of Germany for a World-Wide Satellite Navigation System to the Sub-Committee on Safety of Navigation - 30th session. International Maritime Organization (RTCM Paper 220-84/RPP-5B) , NAV30/INF.6. 6. GLONASS Network of the U.S.S.R. , 8 October 1982: Advanced Publication of Information on a Planned Satellite Network, Special Section No. AR11/A/3 annexed to I.F.R.B. Circular No. 1522, International Telecommunications Union. 7. Petition of Geostar Corporation for Issuance of a Notice of Proposed Rule- making to Allocate Spectrum for the Geostar Satellite System (RM-4426), 30 August 1983: to the U.S. Federal Communications Commission, by Counsel for Geostar Corporation, Princeton, N.J. 8. Additional Information on the Applications of Geostar Corporation , 27 Sep- tember 1984: to the U.S. Federal Communications Commission, by Counsel for Geostar Corporation, Princeton, N.J. 9. Application of Mobile Satellite Corporation for a Developmental Land Mobile Satellite Service , September 1983: to the U.S. Federal Communications Com- mission by Counsel for Mobile Satellite Corporation, King of Prussia, PA. 1 0. Application of Mobile Satellite Corporation for a Developmental Land Mobile Satellite Service , September 1983: to the U.S. Federal Communications Com- mission by Counsel for Skyline Satellite Corporation, Boulder, Colorado. 11. Future Navigation Technology , 10 December 1984: Interim Report (Draft) prepared by the Navigation Subgroup, Radio Technical Commission for Aero- nautics, Special Committee 155, Washington, D.C. 12. Bock, Y. , R. I. Abbott, C. C. Counselman, S. A. Gourevitch, R. W. King, A. R. Paradis, 1984: "Geodetic Accuracy of the Macrometer Model V-100," Bull. Geodesique, Vol. 58, No. 2, pp. 211-221. 470 13. Carr, J. T,, J. W, 0' Toole, 1982: "Point Positioning with the NAVSTAR Global Positioning System," Proc« IEEE Symposium on Position Location and Navigation , Atlantic City, N.J., pp. 166-170. 14. Goad, C. C, B, W. Remondi, 1984: "Initial Positioning Results using the Global Positioning System," Bull. Geodesique , Vol. 58, No. 2, pp. 193-210. 15. Greenspan, R. L., A. Y. Ng, J. M. Przyjemski, J, D. Veale, February 1982: "Accuracy of Relative Positioning by Interfereometry with Reconstructed Carrier GPS: Experimental Results," Proc. Third International Geodetic Symposium on Satellite Doppler Positioning , Las Cruces, NM, pp. 1177-1195. 16. Knowles, S.H., 27-29 November 1984: "Ionospheric Limitations to Time Transfer by Satellite," Proc. Sixteenth Annual Precise Time and Time Inter- val (PTTI) Applications Planning Meeting , Greenbelt, MD. To be published. 17. LaChapelle, G., N. Beck, P. Herorex, February 1982: "NAVSTAR/GPS Single Point Positioning Using Pseudo-Range and Coppler Observations," Proc. Third International Geodetic Symposium on Satellite Doppler Positioning , Las Cruces, NM, pp. 1079-1091. I 471 GPS ACCURACY WHILE SURVEYING ARRAYS OF DEEP OCEAN TRANSPONDERS Larry A. Anderson Pacific Missile Test Center Point Mugu, California 93042 ABSTRACT. This paper presents the observed accuracy of the Navstar GPS Global Positioning System when used with acoustic data to geodetically locate arrays of bottom-mounted ocean transponders. Two arrays were to be located, and each was surveyed on several separate occasions. In addition to GPS with dual frequency precise P-code, the arrays were located by using Argo, Syledis, Transit satellites, and by several other tracking methods. Because the array positions have been well deter- mined, the data is now able to reveal the absolute GPS fix error while at sea. For one survey, ground truth information from the Yuma GPS facility 263 nautical miles (487 km) away was used to reduce measurement bias. INTRODUCTION Arrays of bottom-mounted ocean transponders can be used for various appli- cations such as in the oil industry. A ship would activate the transponders so that they echo back acoustic replies. By using appropriate triangulation methods, the ship is then able to locate and track itself. Before an array can be used, its transponders must be geodetically surveyed as accurately as possible. A survey ship must move back and forth above the array while it records both its own geodetic ship fixes and also the in-water acoustic transit times between its pinger and the transponders. The relative positions of the transponders within the array are solved for by using the acoustic data by itself. The centroid of the array and its orientation to north are solved for by using the geodetic ship fixes together with the acoustic data. Two arrays of transponders were surveyed. Array A is a calibration array located 35 nautical miles (nmi) southwest of Point Mugu, California, between Santa Cruz Island and San Nicolas Island in waters 1900 meters deep. It was surveyed on three different occasions, using Navstar GPS as well as six other tracking methods. Array B is located elsewhere, and it was surveyed on two different occasions, once with GPS precise P-code. Array A is of more interest for this discussion because it was surveyed more often with more methods, and thus its geodetic location is well known. Also, Array A is 263 nmi (487 km) from the Inverted Range GPS facility at Yuma, Arizona, which allows one to attempt dif- ferential GPS methods by using Yuma's ground truth results. The location of Array A is quite well determined, based on the first two surveys: Its transponders have a one-sigma horizontal uncertainly of only 0.24 meter relatively, a depth uncertainty of 0.4 meter, a geodetic uncertainty of the array centroid of only 1.5 to 3 meters, and an orientation uncertainty to north of 0.008 . Now acoustic self-tracking will be used with Array A for the third survey, and by comparing the corresponding GPS fixes with it, one can learn how well GPS has performed. Error propagation shows the noise in this acoustic self- tracking to be about 1.0 meter; the bias is the above amount of 1.5 to 3 meters. Thus, acoustic self-track can yield "true" ship positions which are a standard of comparison against which ship fixes from GPS, etc., can be compared. 473 Usually, it is quite difficult to observe the error in GPS while at sea. One can try to use some geodetic tracking method such as Argo or Mini ranger for com- parisons, but these systems have their own biases and noise which tend to obscure the GPS error. Acoustic self-tracking with a well surveyed transponder array offers a unique opportunity. Because of the smoothness of acoustic self-tracking, one now has a standard of comparison at sea which is an order of magnitude better than what is being observed. SURVEYING WITH THE VARIOUS TRACKING SYSTEMS The GPS data was obtained by using a Texas Instruments TI-4100 user set, and it was unaided and independent from the other systems aboard the ship. Precise P-code was used, and only fixes from four satellites were used. The antenna was mounted near the rear of the ship, 18.0 meters behind the pinger. Thus a knowl- edge of the ship's heading is needed to transform fixes from the antenna to the pinger. In addition to GPS, the arrays were surveyed using Argo, Syledis, the Extended Area Test System (EATS), precision tracking radars, Loran-C, and Transit satellites. In figure 1 are shown various array centroid estimates for Array A. The table which follows shows the resulting centroid error and orientation error when each system was used. Also listed in the table are statistics obtained by comparing each system's ship fixes with acoustic self-track fixes. In figures 2 and 3 are shown the scatter plots of ship fix error for some of these cases. (X is positive east, and Y is positive north.) Argo is a radio navigation phase-measuring system which can detect changes in distance back to its several ground stations. It must be initialized by using an independent knowledge of position, and this was accomplished by using Syledis fixes when closer to shore. If Argo is carefully calibrated by methods such as baseline crossing tests, then it can provide highly repeatable results. It uses groundwaves which can reach relatively far before skywave interference renders the fixes unuseable. The main limitation of Argo is the uncertainty in its radio propagation velocity over long distances. Syledis is a radio navigation system which can directly measure distances back to its ground stations, and it does not have to be initialized or calibrated in the field. It is accurate closer to shore where line-of-sight transmission can be used, although its accuracy can often be maintained over the horizon where radio diffraction and scattering modes are needed. As with Argo, its accuracy is limited by uncertainty in the radio propagation velocity. EATS is an acronym for Extended Area Test System, which is a radiofrequency triangulation system in use by the Pacific Missile Test Center. Transponders are located at ground stations along the coast and on the offshore islands. Other transponders are placed on aircraft or ships to be tracked, and range measurements between transponders are then recorded. Precision tracking radars at Point Mugu and at San Nicolas Island were used for Array A. Only one radar was used at a time. Loran-C was used, but the receiver was not operating properly. The bias in the fixes would repeatedly shift from one value to another throughout each survey. Usually, Loran-C results can be expected to be somewhat noisy with a bias of perhaps a hundred meters or so. 474 1 id ,^^ . M > f CO 5 § > UI > 3 o « o ^ * (0 s >- •a: a: o Q I — I O UJ o o 00 00 Lul oo ID o I— I q:. C3 «jO O o 0£ O I— < 5» z UJ Of => to LOCATING THE ARRAY CENTROID ROTATION X.Y ERROR ERROR ? DO 1 DO OO 8 O 1 O § ? o o\ 1 O d t o O O ? o o ? o O O ? O o OO ? -» lA 1 o% o ? o ? 1 O O ? o o 1 -* UN rr\ o ? ■3- d 1 r>j O o ? o d O rM d 1 -» \0 rM 1 m rM O ? O O 1 o d 1 OO 1 -* o o ? IM 1 sO rr% 1 » o o ? 1 x> o OO o o ? o o o ? 1 o o d 1 -9 m -» IN O o ? d 1^ d o ? 1 1 1 1 m o o 1 tT\ DO d m rM d 1 o o^ rM O d CO rM IM § d J- d -* rM o o o o ir\ IN 1 DISTRIBUTION OF SHIP FIX ERROR NO. OF X.Y MEAN X.Y STO.OEV. FIXES (NETERS) (METERS) OO OO OO 1 r«i o ii\ ^0 a* vO OO O O -» 1 m o DO rM €N O O o -9 1 r- 1 IM OO en rM J- ^o 1 1 1 1 -» rr\ r- vO m -» OO t 1 1 O DO rM m OO m ON 1 o rrv IN o o o in o Ui o % o m t CI o O O OC < to a UJ > o > 1- Ui < UJ Ul Q. vl Z -J — tl -1 UJ -1 X 4/, J_ Ul — u tn a z «< < o Wl 1 — ec _J UJ -J x: UJ UJ tf l/> Ui — i/» in — z u « Ul OC OC K O- - (yi tn — UJ OC ts -1 UJ -I X UJ O. H UJ < W) 1- H- «« — O tn a z < < o a: OC 1- CD a: >- 3 « O Q X • o li% U. OC «/l UJ a. > u o V) '^ a: tn 3 >- o « X a <7I o ^^ a: l/l UJ o. > u o o >- X < a ~ X o - IN »/l CC ul UJ O- > U O if a: Wl H QC X o z lA 3 . O J DC Z. " 0. 3 13 >- 5 CD ■T z -^ o: o I/I z a. (9 a — o u OC O OC tn o UJ -1 >- tn a! =2 o- Ui o2 1 UJ Z -1 < CD OC O o o: -1 a. i/) — Ul DC _| UJ -1 X UJ a. »- UJ tn 1- »- < — o »n o z *I < o OC OC t~ ID • lA in — UJ OC ts ^ UJ -J X UJ O. h- UJ in H tn H «« — o in o z < < o OC a: H CD in UJ tn 1 — OC -1 UJ -i C UJ UJ 1- X < O. in UJ »- UJ — m in — z u < UJ DC OC 1- O- X z t- og z o in < UJ - 1- t- « — Z tn a: Z UJ «« H OC -J 1— < UJ a o «t * CL V^ Z Li 5o z a. i/i u 3 i/i .— K I/I D >- a « r a rM Ui • Z [7\ — - Z ae /I UJ k. > J o 55! « t/l < »>* - r>j - .. r<\ - tN 1^ - IM IN r. 1^ - ,. i»\ p^ r<\ 1 CO IN rM IM rM N 475 ; ! s ; .. .■■■i- • • ■ . ^' 'm • . *•*,'■' •" V • . '• y v|t»j . .:■■. iX'TkHk- ■-• • *• ■ '^Jiib^SM * " ' 'v^SKStx- ■ ■ ■■ •i^'/Mt^Kmit- •■ ■ '^u^^^^Ho*: .'.^j^^^^BF' •'• -. '^^i^HRv:''' • ■ ••■^•Risr':' . ■ . ■ ■ ♦*• '"'. . o at « at at < < o UJ at >■ > a a: • ■ m « • • • • • • • • • • • • • < • -» . i-* • • • • • • — • < CD o at >■ a < ec X at t- « 3 u. O ^~^ l/> UJ >- h- ui ut - > oc -1 at LjJ -J 3 UJ (/> 1— »- LlJ < o s z »- o "^ » m 9 m J » * 00 o Q. • iit- •*.*iA^^ ** * i^^^b^ * * • I^^^^^Bv** •.ME^^^^bl # >^^^^^^^^R^ ' ~ ^^^^^^^B ' * * * ^^^^^E * • •• ,v'*j:'>':<^-.-* • l/> u < Ui a: >- • a. « OO t!^ s: ►- « UJ H- -*}ii LT) «/> >- UJ >- 00 1- UJ - > -1 at o -J 3 z UJ »- < a 1-^ in z <_) «/i 1— z 00 ►- =3 O ►—1 oc . >■ Qi oe o at ll « u. q; O o >- d: UJ ai I— I CO a: ZD C3 476 o o ae »- ui ae > 3 oe o *»...; S:^ 73 ^■" W^-'^- ^: c >■ UJ > u o LU o + 1 cc CO I :> >» ■ iff^ at 3 O -C > O >- «/l UJ OS > 3 oe o I '^•^>, •2^::- •.-*\:i. ^ ;''^^^^ ;<^'^' 'W^ 477 < •» — ^ IK — oe ^ 1— < _I X O- v^ ^-^ UJ oe > 1- o: 3 O 10 Z 3 00 O- oe « CJ3 l*> 19 1 q: a. U- 13 Q UJ >• "^ q; - — in d; u z oe Cd i/i > a: 3 LlJ t- to oe X z 3 1 — 1 Ll. • X < Q_ >- • HH « Of Ol m oe ^- CO < u. • X • >- 3 UI oe 00 > »- oe uu 3 a q; l/» z 3 rD oe oe HH »0 13 U_ 1/) a. u Fixes from Transit satellites were used, and they were processed using both the broadcast ephemeris and the precise ephemeris. Only satellite passes which met customary quality criteria were used, and there was some effort to balance the number of northbound and southbound passes, and the number of eastward and west- ward passes. When using Transit fixes on land, one can locate oneself quite accurately if enough passes are used, since Transit fixes are noisy but are gen- erally unbiased. However, at sea the satellite fix calculations are sensitive to uncertainties in the ship's velocity. One needs to know the speed and heading of the ship during the satellite data collection in order to properly calculate the fix. Experience with these and other surveys has shown that the resulting centroid estimates are not unbiased. The ship did not have inertial navigation, and perhaps this would have helped during the data collection. But as often as not, the averaging of small numbers of Transit fixes led to relatively large array centroid errors. For the first and second surveys of Array A, four-satellite GPS fixes were collected for only 5.7 hours over four days, and 5.9 hours over two days, respec- tively. Even with such small amounts of data, they yielded adequate centroid estimates. For the third survey of Array A, there was a total of 20.1 hours of good data collected over six consecutive days. For 14.5 hours of this data, Yuma's ground truth information was available. For the second survey of Array B, there was 19.2 hours of good data collected over nine days. THE OBSERVED NOISE IN GPS FIXES It is unfortunate that the GPS antenna had been placed so far back of the ship's pinger, because then one needs to know the ship's orientation in order to transform fixes to the pinger's location. As will be seen, much of the noise observed in the GPS fixes may actually be caused by uncertainties in the ship's heading rather than in the GPS fixes themselves. However, the only places close to the pinger were high on masts; the rocking motion of the ship would then be magnified, and the apparent high antenna accelerations would keep the TI-41G0's Kalman filter from tracking properly. For the third survey of Array A, the ship's gyrocompass was unable to supply headings. As a substitute, the ship's direction of motion was obtained by using the velocity components output by the ship computer's Kalman filter. Once each minute, acoustic self-track fixes were input to this Kalman filter; with such a slow data rate, the filter's velocity estimates were too smoothed and not respon- sive enough, and the resulting direction of motion lagged behind the true direc- tion. (The "true" direction was calculated later by fitting each three consecu- tive acoustic self- track fixes with a quadratic curve and by taking the derivative of the curve at the middle fix.) When the ship is under power, the direction of motion (i.e., course-made- good) is a reasonable estimate of heading. But when the ship is dead in the water and drifting with the wind and current, one cannot validly estimate the heading. Because of this, 7.4 hours of good GPS fixes had to be discarded, leaving 20.1 hours of data to work with. It was found that the above-mentioned uncertainties in heading were directly causing much noise in the observed GPS fixes. The GPS-derived velocity outputs from the TI-4100 were then used instead, and the resulting heading was found to be superior. The TI-4100's Kalman filter was updated every three seconds, and so it 478 was more responsive and its results agreed better with the "true" headings. With the heading estimates based on GPS, the apparent noise in the GPS fixes was greatly reduced. Figure 4 shows plots of GPS fix noise for days 262 and 263 for the third survey of Array A (using GPS-derived heading). On day 262, the ship is turning often and the result is noisier fixes. On day 263, the ship is making periodic heading corrections so as to maintain a course due east or due west, and the resulting fix noise is less. Because the ship is moving east or west, the uncer- tainty in heading will show up mainly as Y error. Because figure 4 shows the X error to be about as large as the Y error, one can conclude that the plots are showing actual noise from the TI-4100 and not just the results of heading uncer- tainty. Much of the noise is probably caused by the ship's pitch, roll, and yaw being transformed into GPS antenna movement. COMPARING OBSERVED GPS FIX ERROR WITH YUMA'S GROUND TRUTH Figures 5 and 6 show plots of GPS fix error and Yuma's ground truth for days 262 and 263. Also shown are the geometric dilution of precision (GDOP), and the times the satellites were uploaded with ephemeris and clock corrections. At the U.S. Army Yuma Proving Grounds, the U.S. Air Force Space Division operates a sophisticated GPS set at a well-surveyed location and records the observed fix biases each day. The Yuma set is 263 nmi away, and so it sees almost the same biases in its fixes as does the ship. The satellite clock bias is the same for both locations. The satellite ephemeris error seen from the two sites is almost the same: At worst, the radial directions from the satellite to two sites 250 nmi apart are only 1.35 apart. When a satellite is close to the horizon, each set may correct somewhat differently for tropospheric refraction, and this might cause a small disagreement in bias. (For a site 250 nmi away, the horizon and zenith tilt by about 4.16 .) Also, two different types of sets may process their data in different ways, causing some difference. But the main reason why two sites 250 nmi apart may experience bias differences is differences in the ionosphere. With P-code, most of the effects of the ionosphere have been removed. However, a residual uncompensated error remains. If the ionosphere is roughly homogeneous between the two sites and the satellites, then there will be a high correlation in observed biases. But if the ionosphere is "stronger" over one site than over the other, then the correlation will be less. Yuma's ground truth was available for four of the six days, and figures 5 and 6 are typical of these four days. Notice that there is a definite correlation between the GPS fixes and Yuma's ground truth, but that at times they disagree. On some days, there seems to be a northward bias in the fixes relative to Yuma; this is probably due to chance however. Notice that the TI-4100 lags by up to half an hour in its altitude solutions after some uploads and constellation changes cause the altitude to change sharply. On the average, the use of Yuma's ground truth removes much of the bias and thus yields better survey results. Notice the two scatter plots in figure 3 which show the same 14.5 hours of fixes before and after ground truth has been used. The use of ground truth has made the scatter pattern become more compact, and it has reduced the error in the array centroid estimate from 5.16 meters to 2.06 meters. 479 CONCLUSION Navstar GPS is the ideal system for surveying transponder arrays at sea. Only GPS can avoid the weaknesses of Transit satellites and of radio navigation systems such as Argo and Syledis. The main weakness of Transit satellites is their sensitivity to uncertainties in ship velocity during a doppler interval; GPS does not have this problem because it uses triangulation instead. The main weak- ness of Argo is that the long over-water radio paths from ground stations suffer from an uncertainty in the radio propagation velocity; GPS does not have this problem because its signals come from above. With a second GPS receiver at a surveyed point on land, the biases in GPS fixes can be greatly reduced, resulting in survey accuracy as well as precision. From these tests, one can see that when P-code GPS data was recorded at a distance of 263 nmi from Yuma, the use of Yuma's ground truth has greatly reduced but not eliminated measurement bias. On other occasions, ionospheric conditions may reduce this correlation, however. Regardless of this, if GPS data is averaged over enough days, the result should be a survey of acceptable accuracy. DAY 262. SHIP HEADING 180 (DEG> 90 J ERROR 6flT , TinE isoor 19001 20001 ZlOOl 22001 23001 DAY 263- 360 270 SHIP HEADING ISO- (DEC) 90 J to ( ERROR V ERROR (n) -to 6nr TlflE ITOOl ^yi^w »%- v, V> ^V\^A ■ AA^Aft '^^^^^^ ' ^^l^^vA^.^^sM^^^^V >J ww/vs-vv>r^*^ »*i< ^ i \ * f < ^ ^ %. 18001 K- CHANCED CONSTELLATIONS 19001 20001 21001 "2200I FIGURE 4. GPS FIX NOISE, AS RELATED TO CHANGES IN SHIP HEADING. (FOR TWO DAYS.) 480 \ ( •h o o a. (9 C3 o C3 o o o £ s : c : o a: o oc 00 a. CD o >; LD Lul cc: C3 481 c 1— 3 =3 V S eo a. (9 =3 • i o ^- 1 a: *" 1 CD ~" tr> o oo o 00 vA < =) >- a. u • • 3 LU < ^ • a. — "^ — z: a» o o 00 o o o a: eo LU V0 X CD ' ■ ■ IM o • o >- v^ »- < ., "* O UJ =3 tr* CD 1— 1 % & »- Ll. 482 SLAC- PUB -3620 April 1985 (A) APPLICATION OF GPS IN A HIGH PRECISION ENGINEERING SURVEY NETWORK Robert Ruland* Stanford Linear Accelerator Center Stanford University, Stanford, California, 94305 ALFRED LEICK Air Force Geophysics Laboratory (AFGL/LWG) Hanscom AFB, MAO 1731. ABSTRACT. A GPS satellite survey was carried out with the Macrometer to sup- port construction at the Stanford Linear Accelerator Center (SLAC). The network consists of 16 stations of which 9 stations were part of the Macrometer network. The horizontal and vertical accuracy of the GPS survey is estimated to be 1-2 mm and 2-3 mm respectively. The horizontal accuracy of the terrestrial survey, consisting of angles and distances, equals that of the GPS survey only in the "loop" portion of the network. All stations are part of a precise level network. The ellipsoidal heights obtained from the GPS survey and the orthometric heights of the level network are used to compute geoid undulations. A geoid profile along the linac was computed by the National Geodetic Survey in 1963. This profile agreed with the observed geoid within the standard deviation of the GPS survey. Angles and distances were adjusted together (TERRA), and all terrestrial observations were combined with the GPS vector observations in a combination adjustment (COMB). A comparison of COMB and TERRA revealed systematic errors in the terrestrial solution. A scale factor of 1.5 ppm ± .8 ppm was estimated. This value is of the same magnitude as the over-all horizontal accuracy of both networks. * Work supported by the Department of Energy, contract DE-AC03-76SF00515. t NRC Research Associate (On Sabbatical from the University of Maine at Orono, Department of Civil Engineering, Orono, ME 04469) 483 INTRODUCTION At the Stanford Linear Accelerator Center a new project is under construction, the Stanford Linear Collider (SLC). The shape of the completed SLC will be like a tennis racket with the handle being the existing linac and the curved parts being the new North and South collider arcs. The diameter formed by the loop will be about 1 km. To position the approximately 1000 magnets in the arc tunnels, a network of nearby reference marks is necessary (Pietryka 1985). An error analysis has shown that a tunnel traverse cannot supply reference points with the required accuracy. Therefore, a control network with vertical penetrations will support the tunnel traverses. The required absolute positional accuracy of a control point is ± 2 mm (Friedsam 1984). This two-dimensional surface net must be oriented to the same datum as defined by the design coordinate system. This design coordinate system is used to express the theoretical positions of all beam guiding elements. Since this coordinate system defines the direction of the existing two mile long linear accelerator (linac) as its Z-axis, the SLC coordinate system must integrate points along the linac in order to pick up its direction. Therefore, three linac stations have been added to the SLC net. Figure 1 shows the resulting network configuration. ^10 19 42 500 lOOOM ^ 39 Figure 1 Network Configuration The disadvantageous configuration is obvious, especially since there is no intervisibility be- tween linac stations 1, 10 and 19 to stations other than to 42 and 20. To improve this configura- tion, one would have to add stations northerly and southerly of the linac. However, due to local topography, doing that would have tripled the survey costs. This was the situation when it was decided to try GPS technology, although it was at that time not yet proven that the required 2 mm standard deviation positional accuracy could be obtained. SURVEY DESIGN The horizontal control network consists of 16 stations, 12 in the 'loop', and 4 along the linac. Because of financial considerations, not all 16 stations have been included in the GPS survey. Only the 4 linac and 5 'loop' stations were occupied by the GPS survey. The intent was to determine the coordinates of the loop stations, including station 42, by conventional means, i.e. triangulation and trilateration, followed by an inner constraint adjustment. Then the GPS information would be used to orient the net to the direction of the linac (Ruland 1985) . Conventional Horizontal Net All monuments are equipped with forced centering systems and built either as massive concrete pillars or steel frame towers, both with independant observation platforms. The observation 484 schedule consists of directions and distances with standard deviations of 0.3 mgon and 2 mm, respectively. Conventional Vertical Net All 16 stations are part of a high precision level network. To minimize errors and simplify repeated leveling, both benchmarks and turning points are permanently monumented. Double- running the entire net requires about 700 setups. The standard deviation for a 1 km double-run line is 0.3 mm. GPS Survey The GPS survey, which utilized the five available satellites, was carried out in August 1984 by Geo-Hydro Inc. The whole observation window was used for each station. In general three Macrometers were put to use. Linac Laser Alignment System For the frequent realignment of the linear accelerator, the linac laser alignment system was designed and installed. This system is capable of determining positions perpendicular to the axis of the linac (X and Y) to better than ± .1 mm over the total length of 3050 m. To do so, a straight line is defined between a point source of light and a detector. At each of the 274 support points, a target is supported on a remotely actuated hinge. To check the alignment at a desired point, the target at that point is inserted into the lightbeam by actuating the hinge mechanism. The target is actually a rectangular Fresnel lens with the correct focal length so that an image of the light source is formed on the plane of the detector. This image is then scanned by the detector in both the vertical and the horizontal directions to determine the displacement of the target from the predetermined line. The targets are mounted in a 60 cm diameter aluminum pipe which is the basic support girder for the accelerator. The support girder is evacuated to about 10 {i of Hg to prevent air refraction effects from distorting or deflecting the alignment image (Hermannsfeldt 1965). Using this system it was possible to determine the X-coordinates of the four linac stations, independant of terrestrial or GPS survey techniques, to better than ± .1 mm. ANALYSIS OF LEVELING DATA To check for blunders, the L-1 norm adjustment technique was applied (FUCHS 1983). Several blunders have been identified and cleared. A L-2 norm adjustment was then carried out with CATGPS (Collins 1985) in a minimally constrained fashion by fixing the height of station 41 to its published value of 64.259m. The choice of this particular station as well as the specific numerical value is, of course arbitrary for the purpose of the adjustment. CATGPS is suitable for adjusting leveling data if the latitudes and longitudes of the stations are fixed. The results of the level adjustment are summarized in Table 1 (Column Level). ANALYSIS OF GPS DATA All GPS vectors and their respective (3x3) covariance matrices as received from Geo-Hydro were subjected to an inner constraint least squares solution for the purpose of blunder detection and to get an unconstraint estimate of the obtained accuracy. 485 SUMMARY of ADJUSTMENTS LEVEL GPS ANGLES DIST TERRA (A) TERRA (B) COMB Incl 1,10,19 YES YES NO NO NO YES YES Hz Angles Slant dist Leveled AH GPS Vectors 54 18 85 94 85 94 93 106 93 106 18 Observed h — — 12 12 12 15 15 Fixed Coordinates H41 { Z (m) B107A2 Figure 5 Linac Discrepancies parameter transformation after the ellipsoidal coordinates had been converted into cartesian co- ordinates. The results are shown in table 5. Looking at the (LINAC-COMB) column, the values of the differences are insignificant with respect to the standard deviations of the COMB-solution. In other words, the COMB-solution reflects the cor- rect geometry of the linac; whereas the significant differences in the (LINAC-TERRA) column indi- cate that the geometry of the stations in the sys- tems is not congruent. The column GPS-COMB shows only small dis- crepancies. The latitudinal differences are all smal- Table 5 Linac Comparison ler than 2 mm. The discrepancies in the east-west direction are somewhat larger. A proper interpretation of these discrepancies requires that one distinguish between the two coordinate systems involved. The combination solution COMB (as well as TERRA) refers to the terrestrial coordinate system (U). Because of the specific choice of the coordinates of the fixed station 41 and the fixed latitude of station 10, the terrestial coordinate system (U) and the satellite system (S) are parallel. This is confirmed by the estimates of the rotation angles listed in Table 1. However, the same table lists a scale of +1.5 ppm. Going back to the definition of these transformation paxameters it is seen that a positive scale estimate implies that the polyhedron determined by GPS observations (satellite system) is bigger than the one determined from the terrestrial observations. This is readily confirmed by comparing the longitudes of stations 1, 41, and 35 for the GPS and the COMB solutions in Table 4. The scale factor is, of course, also present in the latitudinal discrepancies, but to a lesser extent, because of the predominently east-west extension of the whole network. The longitudinal effect of the scale factor on station 1 relative to station 41 is 1.5 ppm • 3200 m = 5.4 mm. This is the value by which the longitudinal separation of stations 1 and 41 should be increased in COMB. In fact, the effect of the scale on the longitudes of all stations is computed as (-5,-3,-2,0,- ,-1,0, 1,2) in millimeters. Differencing these values with those listed in Table 4 under column "GPS-COMB" yields the discrepancies in which the effect of the scale is eliminated. The values are (0,0,-1,0,- ,-1,-1,0,-3) in millimeters. These values and those listed for the latitude are of the same size. They reflect 491 the "non-scale" discrepancies between the GPS solution and the combination solution. Their smallness reflects the dominance of the GPS vector observations in the combination solution. CONCLUSIONS The leveling data were used only to compute (interpolate) the geoid undulations. The accu- racy of these undulations depends directly on the accuracy of the leveling and the vertical com- ponents of the GPS survey. Processing the phase observations "line by line" yielded a completely acceptable accuracy for this project. Comparison with the terrestrial observations demonstrates that the GPS accuracy statements (standard deviations) are, indeed, meaningful and not too optimistic. Compared against the standard of the precise network and especially the linac laser alignment system measurements, it could be proven that the GPS technique in a close range application is capable of producing results with standard deviations in the range of 1-3 mm and, therefore, can be applied for engineering networks. The GPS survey has made it possible for the weak network of the linac (stations 1, 10, 19, 42) to be tied accurately to the loop network. The terrestrial observations did not control the latitudinal position of station 1 accurately. To determine station 1 accurately with terrestrial observations would have required the design of a "classical" network which would have been difficult and expensive because of the visibility constraints due to topography and buildings (which did not exist during the first survey for the linac). The GPS survey served as a standard of comparison for the terrestrial solution and revealed the existence of systematic errors in the latter solution even though a thorough analysis of the terrestrial observations did not reveal such errors. Since the estimated scale factor of 1.5 ppm ± .8 ppm is of the same magnitude as the over-all horizontal accuracy of both networks, no conclusion can be drawn as to internal scale problems of either the electronic distance mezisurement devices or the Macrometer. REFERENCES Baarda, W. (1976): Reliability and Precision of Networks, Presented Paper to the Vllth Interna- tional Course for Engineering Survey of High Precision, Darmstadt. Collins, J., Leick A. (1985): Analysis of Macrometer Network with Emphesis on the Montgomery (PA) County Survey, Presented Paper to the First International Symposium on Precise Position- ing with the Global Positioning System, Rockville. Fuchs, H. (1980): Untersuchungen zur Ausgleichung durch Minimieren der Absolutsumme der Verbesserungen, Dissertation, Technische Universitat Graz. Fuchs, H., Hofmann-Wellenhof, B., Schuh W.-D. (1983): Adjustment and Gross Error Detection of Leveling Networks, in: H. Pelzer and W. Niemeier (Editors): Precise Levelling, Dummler Verlag, Bonn, pp. 391 - 409. 492 Friedsam, H., Oren W., Pietryka M., Pitthan R., Ruland R. (1984): SLC- Alignment Handbook, in: Stanford Linear Collider Design Handbook, Stanford, pp. 8-3 - 8-85. Hermannsfeldt, W. (1965): Linac Alignment Techniques, Paper presented to the IEEE Particle Accelerator Conference, Washington D.C. Leick A. (1984): Macrometer Surveying, Journal of Surveying Engineering, Vol. 110, No. 2, August 1984. Pietryka, M., Friedsam H., Oren W., Pitthan R., Ruland R. (1985): The Alignment of Stanford's new Electron-Positron Collider, Presented Paper to the 45th ASP- AS CM Convention, Washington D.C. Rice, D. (1966): Vertical Alignment -Stanford Linear Accelerator-, in: Earth Movement Inves- tigations and Geodetic Control for Stanford Linear Accelerator Center, Aetron-Blume-Atkinson, Report No. ABA 106. Ruland, R., Leick, A. (1985): Usability of GPS in Engineering Surveys, Presented Paper to the 45th ASP-ASCM Convention, Washington D.C. 493 INTERFEROMETRIC PROCESSING OF NNSS DOPPLER OBSERVATIONS by Sz.Mihaly, T.Borza and I.Fejes Satellite Geodetic Observatory, Penc, Hungary /H-1373 Budapest Po Box 546/ ABSTRACT An interferometric approach has been proposed earlier to process Doppler observations of NNSS satellites. To check this approach test network measureitients have been carried out on high precision baselines of different length and adjusted by conventional and interferometric methods. Two sets of results have been compared to each other and to the precise survey data. A 10 cm accuracy of relative positions has been reliably demonstrated. This methodical investiga- tion may be usefull for further exploitation of NNSS as well as for utilization in GPS. 1. Introduction Earlier an interferometric approach was proposed to pro- cess the Doppler observations of NNSS satellites /Fejes, Mihaly 1980 and Brunell et al. 1982/. The proposal was followed by software development at the Satellite Geo- detic Observatory /SGO/, Penc, Hungary in different directions. All the preliminary investigations and developments have shown the interferometric approach as a promising method to utilize the Doppler observations to obtain high quality survey results in relative sense. As a consequence three types of special test network measurements have been carried out on high precision survey baselines of Presented at the First International Symposium on Precise Po- sitioning with the GPS. Rockville, Maryland, USA, 15-19 April 1985 495 different length with purpose to check the method in practice: - The Penc test with very short baselines / 29-210 m/ - The Doppler Baseline Interferometry test measurements /DBLI test/ with relatively long baselines / 40-800 km/ - The Finnish-Hungarian Doppler Observation Campaign /FHDOC/ on the High Precision Traverse of Finland with baselines of different length /Czobor et al. 1984/. The FHDOC has been carried out under the Scientific Agreement between the Finnish Geodetic Institute and the Hungarian Geodetic Survey / 20-200 km/. The paper presents a short concept of realization and some practical results obtained with the Penc test and the DBLI test. Interferometric processing of the FHDOC recently is in progress, therefor the results will be published only later. . The concept 2.1. Mathematical model A detailed description of the mathematical model is - given by Fejes, Mihaly 1983. Some m.ain features are described below. On Fig.l. let us consider two receivers A and B obser- ving strictly simultaneously the same orbit between points A B 1 and 2. In this case the N and N Doppler counts are obtained by receiver A and B, respectively. In the interferometric approach these Doppler counts will be used in a special way. The quantities T-, and Ty on Fig.l. are the time differences of arrival of the signals from a single source. Generally they are called as basic observables of interferometry. 496 Geometrically their difference can be expressed as follows c -(^2 - r^) = (IS2 - R^l - IS2-R^l)-(lS^-R^I-|S^-R^) = = 1^2-^2)- (^?---l) /^/ where c is the light velocity; S and R are geocentrical vectors and r i^ topocentrical vector with the respective indecis. The same difference c-('C2-^-,) can be expressed using the results of Doppler observations. In this case after con- sidering the other factors which exist in practice, the expression looks as follows -ih 'h) -% [NB^-N^-^f. ^t^]- T/.B .B\ ^.A .An-B - [(ff - i\)- c^r^] - A /2/ where fg is the satellite frequency, Af is the frequency difference of the two receivers^ A B At and at are the time intervals for which the Doppler A B counts N and N were obtained, A A B B ^2 / r^^ , r2 and r, are the receiver-to-satellite slant- ranges at epochs t^ and t, , respectively, • A •A.B B r2 t r,, ^2 and f, are the respective slant range rates. 497 _B V, is the receiver time delay at locking-on the k-th orbit for station B, AT is the del^y difference of the two receivers, A is the sum of different corrections^ A A tj and t, are the time epochs at satellite associated A with the beginning and the end of counting the N at receiver A. Eq.l.and Eq.2. are the basic expressions used in inter- ferometric processing of Doppler observations which we call interferometric fringe count equations. There are two crucial points in the model: the time delay difference A^ and the frequency difference Af of the two receivers. The accuracy requarements are less than +10 juis and +0.002 Hz in ^r and Af respectively. A special handling is necessary in the measurements and the processing. The other quantities in the above equations can be approxi- mated well enough. Summarizing all the error sources, the interferometrical model generally will be affected by an error less than 10 cm. 2. 2. Software developments Two version of software has been developed. The first developed by Mihaly utilizes features of the SADOSA program /Brunell et at. 1982, Mihaly 1983/. In this case so called initial value of the receiver delay difference should be measured at the beginning of the ob- servations. The subsequent del^ differences are tracked in the software using the Loiler 's-formula /Loiler 1980/. 498 The receiver frequency differences are computed by SADOSA in a translocation solution. The second heeds a little more detailed description. The PENCDIP software program package has been developed at the Satellite Geodetic Observatory, Penc, Hungary by Fejes and Borza. The purpose of PENCDIP is to process synchronously observed 2 station NNSS Doppler data for high precision interstation distance determination. The mathematical model is based on the interferometric fringe count processing suggested by Fejes and Mihaly /1983/. An other novel feature in the program is the dynamic integ- ration of the nominal 4.6 s intervallSo This yealds a more effecient use of raw Doppler data than the conventional 1/2 minutes integrations. As a result the processing of a small number of passes /4-10/ give equivalent or superior accuracy as compared with con- ventional programs. In the program structure three main program stage should be distinguished. The first in which one cassette of a single station is processed. The raw data from the cassette reader is input via the IBM XT RS2 32 port and stored on magnetic disk. A tape directory is generated which contains all necessary parameters of that particular cassette for further processing. The second stage selects and handles strictly synchronous station pair datac After dynamic integration the satellite positions are computed using the broadcast ephemerides. The observed fringe counts are also produced. A station pair directory is generated which contains the necessary para- 499 meters for the adjustment. This directory may contain the parameters of more than one cassette. In the third stage the baseline solution is computed by keeping one station fixed /station A/ and computing corrections to the second /station B/o Station A as the reference station should have a well established Doppler point position. This stage is interactive in the sense that the operator may select passes which are to be included in the solution. The package has been developed and presently running on a standard IBM XT personal computer with DOS 2.0. The programming language is the Microsoft Advanced Basic which is standard for the 1MB PC. The program accepts raw JMR data on cassette. Additional parameters which has to be messured on site /receiver frequency and clock differences as referen- ced to the UTC and meteorological data/ can be input via the keyboard. 500 3. Practical results 3.1. Penc test In 1982 a series of Doppler observations has been carried out on the test network of the SGO at Penc. This network is surveyed practically with no error. The distance between the test points varies from 29,77 m to 218.83 m. The purpose was to check the interferometric method on very short distances and to analyse the error bud- get. The detailed description and results are given by Fejes and Mihaly 1983. In this section only a summary is presented. The error budget investigation shows that a distance accuracy better than 10 cm can be achieved. It was concluded that the distance determination by in- terferometric method does not depend on the point separa- tion in case of very short distances. A baseline of 38.56 m length has been determined from twenty independent pairs of passes and then averaged. The averaged distance differs from the survey distance by -11 cm with rms +18 cm. 3.2. DBLI observations and results The observations were carried out during a four station campaign DBLI in cooperation with the Zent- ralinstitut fur Physik der Erde, Potsdam, GDR. The results of this campaign will be published elsewhere /Borza et al.l985/. 501 Here we report only the observations at station Penc and Baja both in the territory of Hungary. The baseline orien- tation wQs dominantly N-S. Approximate distance is 180 km. The two stations were occupied by JMR-IA type Doppler receivers from 8-to 12 October 19 84. As external reference oscillators rubidium standards have been connected to the receivers. During each pass the receiver clock and UTC differences were recorded with an accuracy of l/AS. Meteorological data were also recorded. Due to this observational setup the critical parameters for interferometric fringe count processing could be ob- tained with sufficient accuracy. The differential receiver frequency was known better than 1 mHz at 400 mHz and the differential delay was known better than 2 jus. The absolute receiver delays were computed with respect to the UTC and no satellite clock deviations from the UTC has been taken into account. The point position of the reference station /Station A: Baja/ has been computed by the SADOSA program System and held fixed in the following PENCDIP processing. In Table 1 the BAJA-PENC interstation distance solution results are presented. The data has been divided into groups of 4-5 passes and processed by the PENCDIP program. The selection criteria was E-W symmetry of at least 2 pairs of passes within one group. The 90 CA passes were con- sidered either E or W according to the selection require- ments . The average distance from, the 7 independent solutions gave 180102.12 m. The repeatebility RMS was 0.12 m. i02 i I In Table 2 the solutions from 4 larger groups /8-10 pas- ses/ are presented. The average computed distance was 180102 . 11 m. The repeatebility RI-IS was 10. 10 m. For comparison the whole set of data has been processed by the SADOSA program system /Brunell et.al. 19 82/. The interstation distance according to the SADOSA SSA solutions is: 180102.38 +20 cm. The comparisons are summarised in Table 3. Conclusions The concept of interferometric fringe count processing of NNSS data has been demonstrated on a medium, long N-S baseline /180 km/ and gave repeatebility BIAS oft0.12 m using only 4-5 passes in the adjustment. By including 8 or more passes the repeatebility improved to +0,10 m. The experiments showed that NNSS Doppler receivers with additional time and frequency reference can be applied to determ.ine distances on the 10 cir accuracy level wit- hout requiring interstation visibility from some hund- reds m up to 200 km. The necessary observing time is 6-12 hours. 503 References Borza T. - Dietrich R. - Fejes 1.1985: The Doppler Baseline Inter ferometry Experiment /DELI/ /Acta Geod. Geoph.et Mont., In preparation/ Brunell R.D. - Malla R. - Fejes I. - Mihaly Sz . 1982: Recent Satellite Processing Improvements at JMR. Proc. 3rd International Geodetic Symposium on Satellite Doppler Positioning, 8-12 Febr. 1982. Las Cruces, N.M. , USA. Czobor A. - Adam J. - Mihaly Sz . - Vass T. - Parm T. - Ollikainen M. 1984: Preliminary Results of Finnish- Hungarian Doppler Observation Campaign. Paper presented at the Intercosmos Scientific Conference, Section 4, Karlovy-Vary, Czechoslovakia. Fejes I. - Mihaly Sz. 1980: A suggestion to use Doppler receivers as VLBI terminals. Paper presented at the Intercosmos Scientific Conference, Section 6, Albena, Bulgaria. Fejes I. - Mihaly Sz. 1983: Inter ferometric Approach in the NNSS Data Processing. Paper presented at the 34. lAF Congress, Budapest, Hungary 10-15 October 1983. /Acta Astronautica 1985. in press./ Loiler R.D. 1980: JMR-IA Computed Lock-On Time Delay. JMR Memo Number RDL80046, JMR Instruments, Inc., Chatsworth, CA, USA. Mihaly Sz. 1983: SADOSA Program System /I.Matematical Description, II. Operators Manual, I I I. Programming Documentation/. Institut of Geodesy and Cartography, Satellite Geodetic Observatory, Budapest, Hungary. 504 Table 1 BAJA-PENC Interstation Distance Solutions by PENCDIP Selected synchronous passes k Group NO DATE SAT GEOM CA DATA DDEL DF/mHz / B /m/ 2820816 20 W 45° 16 80jlLS -0.6 1 2821010 13 E 68 13 68 -0.6 2822056 20 W 23 22 6 -0.6 2822112 13 E 27 15 -50 -0.6 180101^96 2830550 11 E 34 11 39 -0.6 2 2830738 11 W 68 11 -16 -0.6 2831122 48 W 81 21 25 -0.6 2831842 11 E 68 15 -15 -0.6 180102.29 28 30852 20 W 21 15 7 -0.6 2832150 48 E 40 20 29 -0.6 3 2832210 13 E 80 26 36 -0.6 2832338 48 W 63 15 47 -0.6 2832356 13 W 28 24 204 -0.6 180101.96 2840740 20 W 69 16 50 -0.6 4 2840910 48 E 21 17 21 -0.6 2841058 48 W 90 24 -14 -0.6 2841202 13 W 26 20 14 -OoO 180102.16 2841248 48 W 19 12 -0.6 2842120 13 E 31 13 -60 -0.6 5 2850558 11 E 46 24 -28 -0.6 2850632 20 E 58 21 33 -0.6 2850818 20 W 33 23 -15 -0.6 180102.13 2850924 13 E 39 15 -58 -0.6 6 2851112 13 W 59 17 -55 -0.6 2851226 48 W 26 13 14 -0.6 2851730 20 E 22 20 -27 -0.6 180102.20 2852252 48 W 90 26 -43 -0.6 7 2860004 13 W 22 22 -61 -0.6 2860044 48 W 19 16 -34 -0.6 2841838 20 E 69 18 20 -0.6 180102.13 Average 180102.12 +0.12 m ■^'OS Table 2 BAJA-PENC Interstation Distance Solutions by PENCDIP Selected synchronous passes Group NO DATE SAT GEOM CA DATA DDEL DF/mHz/ B fia/ 2820816 20 W 45*' 16 80>*5 -0.6 2821010 13 E 68 13 68 -0.6 2822056 20 W 23 22 6 -0.6 2822112 13 E 27 15 -50 -0.6 2822260 13 W 78 19 -19 -0.6 2830550 11 E 34 11 39 -0.6 2830738 11 W 68 11 -16 -0.6 2830852 20 W 21 15 7 -0.6 180102.24 2831122 48 W 81 21 25 -0.6 2831310 48 W 14 9 45 -0.6 2831842 11 E 68 15 -15 -0.6 2 2832030 11 W 25 17 -21 -0.6 2832150 48 E 40 20 29 -0.6 2832210 13 E 80 26 36 -0.6 2832338 48 W 63 15 47 -0,6 2832356 13 W 28 24 204 -0.6 2840740 20 W 69 16 50 -0.6 180102.01 2840910 48 E 21 17 21 -0.6 2841058 48 W 90 24 -14 -0.6 2841202 13 W 26 20 14 -0.6 3 2841248 48 W 19 12 -0.6 2842120 13 E 31 13 -60 -0.6 2850558 11 E 46 24 -28 -0,6 2850632 20 E 58 21 33 -0.6 2850818 20 W 33 23 -15 -0.6 180102.07 2850924 13 E 39 15 -58 -0.6 2851112 13 W 59 17 -55 -0.6 2851226 48 W 26 13 14 -0.6 2851730 20 E 22 20 -27 -0.6 2851914 20 W 81 23 -25 -0,6 4 2852040 11 W 19 17 -104 -0.6 2852252 48 W 90 26 -43 -0.6 2360004 13 W 22 22 -61 -0.6 2860044 48 W 19 16 -34 -0,6 2841838 20 E 69 18 20 -0.6 180102.12 Average 180102.11 +0.10 m 506 Table 3 Comparison between different group solutions Stations BAJA-PENC Program No of groups No of passes in the group Avg. distance RMS m m 180102.12 0.12 180102.11 0.10 180102.38 0.20 PENCDIP 7 PENCDIP 4 S ADOS A SSA 1 4-5 8-10 >40 X X = standard deviation obtained by SADOSA 507 Fig. i 508 ^ PENN STATE UNIVERSITY LIBRARIES ADQDD7D' bit