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, Journ. of the Inst. of Navigation, Vol. 49(1), 7-34, Spring 2002

INTRODUCTION The Global Positioning and GPS have had a synergistic rela- System Geodesy Odyssey tionship that began well before the first GPS was launched. Indeed, the roots of this relationship began before the first man-made satellite was orbited. (1) (2) Alan G. Evans, ed.; Robert W. Hill, ed.; Geodesy is the science concerned with the accu- Geoffrey Blewitt;(3) Everett R. Swift;(1) rate positioning of points on the surface of the , Thomas P. Yunck;(4) Ron Hatch;(5) and the determination of the size and shape of the Stephen M. Lichten;(4) Stephen Malys;(6) earth. It includes studying and determining varia- John Bossler;(7) and James P. Cunningham(1) tions in the earth’s , and applying these varia- tions to exact measurements on the earth [1]. Prior to the advent of , geodesists (and cer- 1. Naval Surface Warfare Center, Dahlgren tainly navigators of that era) concerned with measur- Division, Dahlgren, Virginia ing and mapping the earth’s surface usually 2. Applied Research Laboratories, University of conducted their analysis in two surface dimensions Texas, Austin, Texas rather than the three space dimensions. 3. Nevada Bureau of Mines and , and above the surface was included but treated separately Seismological Laboratory, University of Nevada, from horizontal positions. This does not mean the Reno, Nevada geodesists considered the earth to be flat; on the con- 4. Jet Propulsion Laboratory, California Institute of trary, usually points are projected onto a curved ref- Technology, Pasadena, California erence surface or . The third dimension of 5. NAVCOM Technology, Inc., Redondo Beach, above the reference surface, while small when California compared to the earth’s , could be projected 6. National Imagery and Mapping Agency, approximately onto the surface with acceptably small Bethesda, Maryland errors for short measurement baselines. However, as 7. Center for Mapping, The Ohio State University, measurement baselines became longer through stellar Columbus, Ohio and, more recently, satellite observations, it has be- come simpler to obtain acceptably small projection errors by considering the lines of observation in three ABSTRACT dimensions, and by performing computations and network adjustments in three dimensions [2].

Satellite geodesy can be considered to have mo- Fundamental to NAVSTAR Global Positioning tivated three-dimensional geodesy. In a proposal System (GPS) operation and application are the dated 13 April 1955, scientists at the Naval Research computational developments that have led to accu- Laboratory (NRL) proposed a scientific satellite pro- rate user positioning. This paper discusses some of gram that included, as one of its major items, the ap- these developments from a historical perspective. plication of satellite observations to the “field of The developmental odyssey begins with the events geodesy” [3]. In the proposal, the discrepancies leading to initial GPS operation. Early developments among reference ellipsoidal parameters, the problem in satellite geodesy, which led to the GPS constella- of not knowing the semimajor axis of the earth to bet- tion development, are briefly reviewed. A chronology ter than 300 m, and the procedures for determining of the incremental improvements in satellite de- the absolute positions of termination is presented. Contributions basic to GPS were detailed. The paper set the stage for satellite operation and accuracy, including coordinate frame geodesy, outlining both classic triangulation and what definition and software development for user abso- came to be known as dynamic satellite geodesy. lute and differential/kinematic positioning, are re- Soon after the first were in orbit, ge- viewed. Applications—including and odesists, by observing the perturbing effect on satel- mapping, , and spaceborne geodesy, lite motion, began to evaluate the earth’s which have motivated the most stringent accuracy gravitational field [4 – 6]. These determinations were requirements for GPS—are discussed. The paper followed by a rapid succession of more extensive and ends with a discussion of expected future geodetic accurate descriptions of the earth’s gravity field. capabilities and then a summary of the impact of Early was conducted primarily using GPS geodesy contributions to the user community. optical instruments (photographic processes) adapted

from earlier stellar systems. With the development of

the Navy Navigation Satellite System ()

1 Navigation, Journ. of the Inst. of Navigation, Vol. 49(1), 7-34, Spring 2002

[7], Doppler satellite geodesy became a cheaper, quality, and timeliness of the orbit computation and more rapid technique for space geodesy. prediction. One of the striking characteristics of space geod- Final introductory comments need to be made esy in the 1960s and 1970s was the almost complete with regard to GPS tracking equipment and receivers. separation between the optical school and the Dop- As noted previously, GPS geodesy is synergistically pler school. By 1965 a global gravity field dependent on accurate satellite ephemerides; every- (NWL 5E), comprising about 70 coefficients, had thing fails if the GPS receiver does not provide accu- been determined using Doppler satellite data [8]. In- rate measurements. Fortunately for geodesy, the GPS terestingly, the measured coordinates of ground sta- signal structure allows for very accurate measure- tions agreed with a precise survey to about 20 m, ments, positions, and times to be obtained. For more while between stations agreed with precise information on GPS signal structure, see [10, 11]. survey to about 10 m, leading the U.S. DoD to adopt Precision ephemerides for GPS have been computed the Doppler system as its primary space geodesy sys- using three generations of ground receivers. The pre- tem. Subsequent DoD World Geodetic Systems cise was and is computed combining data (WGS) were heavily influenced by Doppler satellite from the GPS operational tracking stations and the geodesy. The 1972 Defense Mapping Agency (DMA)—since October (WGS 72), considered to be the standard for about a 1996 the National Imagery and Mapping Agency decade, contained a gravity field represented by (NIMA)—tracking network. The first-generation re- about 450 coefficients and could demonstrate a sys- ceiver, termed the NAVSTAR Geodetic Receiver tem consistency of about 1 m, while the overall accu- System (NGRS), was based on a Stanford Telecom- racy for tracking station locations was estimated at munications model 5007 receiver. Of particular in- about 3 m. In the WGS 84, several thousand gravity terest was the full-cycle counter, which greatly coefficients were determined, and the separation be- enhanced the ability to measure accurately integrated tween “Optical” and “Doppler” satellite measure- Doppler phase counts over long (60 s) time intervals. ments was somewhat reduced; however, most major The STI 5007 receiver was designed to measure datum parameters were greatly influenced by Dop- range on the L1 frequency (1575.42 MHz) with a pler satellite measurements. Space geodesy computa- precision of 1 m. Its most important feature was its tions performed with WGS 84 demonstrate internal capability to measure phase counts on L1 and L2 consistency of several tens of centimeters, with an es- (1227.6 MHz) with a precision of 0.025 cycles, while timated accuracy of about 1 m. tracking both frequencies on a single satellite simul- The 1980s were transition years for space geod- taneously [12, 13]. The second generation of re- esy in that they represented the maximum use and ac- ceiver was based on the Texas Instruments model curacy of Doppler satellite techniques. Investigators TI4100. The TI4100 proved to be an extremely ca- routinely reported submeter accuracy for Doppler pable receiver system and for many years was used as surveys [9] and a few tens of centimeters for network a yardstick for judging less capable receivers. The adjustments. By the end of the decade, many geode- TI4100-based trackers multiplexed the tracking sists had made the transition to GPS. channels to provide simultaneous range and inte- The accuracy for dynamic geodesy and—to a grated range rate on both L-band GPS frequencies for large extent—all space geodesy, is dependent on ac- up to four satellites [14]. Significantly for geodesy, curate positioning of the satellite. In turn, satellite the pseudorange and integrated phase measurements orbit computation accuracy (and satellite ephemeris were synchronized to occur at specified GPS times. accuracy) is dependent on the accuracy of the space The third-generation GPS receivers used at the DMA geodesy. Satellite observations made from the monitor stations were based on the Ashtech Z/Y-12. ground can be used accurately only if the ground sta- In late 1994, the DMA Monitor stations were up- tion locations are known accurately, while the orbit graded by the Z/Y-12. These new DMA monitor sta- itself can be computed accurately only if all of the tions have proven to be accurate and reliable in forces governing the satellite motion are known. The tracking the GPS satellites, and provide range and early dynamic geodesists observed satellite prediction phase measurements on both frequencies for up to 12 errors and made bootstrap corrections to the gravity satellites in view [15]. Additional geodetic receiver models. GPS benefited greatly from the existing developments are discussed later in the paper. WGS gravity model. Techniques that eliminate Webster defines odyssey as “a long wandering common-mode errors among ground locations pro- usually marked by many changes of fortune.” In re- vide improved accuracy over limited distances, but viewing the following geodetic journey, readers must they still depend on satellite position accuracy. GPS evaluate its changes for themselves. However, the geodesy, like GPS navigation, relies on the accuracy, goal of the geodetic community has been focused and clear. The objective has continually been the im-

2 Navigation, Journ. of the Inst. of Navigation, Vol. 49(1), 7-34, Spring 2002 proved accuracy of GPS satellite orbit determination, both used in integrating the equations of motion for user positioning, and earth modeling. This paper re- each satellite. Weekly batch least-squares orbit fits views developments in these areas to help provide a were first performed using 15-min smoothed pseudo- background and understanding of the geodetic as- range data, with clock parameters estimated on a pects of GPS. pass-by-pass basis. The accuracy of these weekly fits was improved when a procedure was implemented in which successive pseudorange measurements were ORBIT DETERMINATION differenced to obtain range difference measurements. This time differencing removed the effects of clock Early estimation of GPS satellite and clock jumps and allowed better modeling of the remaining states was performed using a two-stage process in the stochastic clock effects. The MCS operational production of the broadcast navigation used the smoothed pseudorange measurements di- message. The early work was transitioned into the rectly because it included stochastic models for the GPS Operational Control System for real-time opera- clocks and had to predict satellite clock states in addi- tions and into precise orbit determination (POD) for tion to the orbits. meeting the high-accuracy goals of the geodetic In the early years of GPS orbit estimation and community. The following sections review these de- prediction, satellite-momentum dump thrusts caused velopments, including the corresponding reference considerable problems. Initial fit errors were on the frame definitions and the positioning of GPS tracking order of 20 m and initial orbit prediction error growth sites. rates were on the order of 100 m/day [18]. The orbit fitting and predicting errors were reduced in the early INITIAL OPERATION 1980s after a means was developed for dumping Estimating and predicting GPS satellite orbit and momentum magnetically. In about 1980, after analy- clock states in near real time and uploading the navi- sis led by personnel at the Aerospace Corporation, gation message information broadcast by the satel- the “y-bias” acceleration parameter was introduced lites has always been the responsibility of the U.S. into the fitting, predicting, and Kalman filtering pro- Air Force (USAF). This began with the launch of the cedures. The y-bias is an empirical parameter used to first Block I satellite in 1978. At that time, the USAF model accelerations of unknown cause along the so- had deployed a four-station North Pacific basin- lar panel axis. Orbit prediction error growth rates tracking network using Magnavox-developed four- were reduced to less than 10 m/day. Estimation of channel X-set receivers. This Initial Control System this y-bias parameter by the ICS dramatically im- (ICS), developed by the General Dynamics Corpora- proved the quality of the broadcast navigation mes- tion, consisted of four monitor stations located in sages. When the ICS was decommissioned in 1985, Hawaii, Guam, and Alaska; and a Master Control the broadcast user range error (URE) accuracy was Station (MCS) with a single-upload antenna located better than 5 m 1 σ [19]. at Vandenberg Air Force Base in California. With this four-station network, each Block I satellite could OPERATIONAL CONTROL SEGMENT (OCS) be tracked only about 50% of the time. The ICS was The OCS—developed by International Business optimized for validating the GPS navigation concept Machines/Federal Systems (now part of Lockheed and testing user equipment under development at the Martin Management and Data Systems)—began con- Yuma Proving Ground in Arizona and at other west- trol of the Block I satellites in July 1985. The OCS ern continental United States (CONUS) locations. consists of five globally distributed tracking sites in The original Block I constellation was designed so Colorado Springs, Ascension Island, Diego Garcia, that the satellites would cluster over the western Kwajalein, and Hawaii; three upload antennas collo- CONUS once per day. The satellites could be cated at Ascension, Diego Garcia, and Kwajalein, tracked for several hours and then uploaded prior to and an MCS at Colorado Springs. With these five their coming into view at Yuma. stations, each satellite can be tracked over 80% of the The Naval Surface Warfare Center, Dahlgren time. A complete description of the OCS is con- Division (NSWCDD) supported the ICS by produc- tained in [20]. A requirement was established for the ing long-term orbit predictions and partial derivatives OCS to provide a 1-σ URE of less than 6 m 10 hr af- that were used as reference trajectories in a Kalman ter upload. Initial ICS vs. OCS comparisons indi- filter run at the MCS [16]. This was initially con- cated that this could easily be met [19, 21]. The ducted on a weekly basis and was eventually per- Kalman filter used by the OCS can process up to six formed every other week. The WGS 72 gravity field satellites in a single partition and uses 15-min pseu- model truncated to degree and order 8 and the Rock- dorange measurements smoothed using carrier-phase well-formulated radiation pressure model [17] were data. Kalman filter estimates are used to generate

3 Navigation, Journ. of the Inst. of Navigation, Vol. 49(1), 7-34, Spring 2002 new predicted reference trajectories on a weekly ba- improvements in the quality of the broadcast naviga- sis. tion messages. This program [33] includes incorpo- Orbit estimation and prediction accuracies have rating tracking data from six globally distributed gradually improved over the years. A 30-day evalua- NIMA stations, single-partition processing in the tion of OCS accuracy for Block I satellites was con- OCS Kalman filter, and a new upload strategy. With ducted in 1986 with UREs of 3 to 5 m estimated these improvements, the expected URE delivered to independently by several organizations [22]. The navigation users will be below 1.3 m. Operational WGS 84 gravity field model replaced the WGS 72 implementation of the AII changes is planned for late model in 1987. The ROCK42 radiation pressure 2004 or early 2005. model was implemented for Block II satellite orbit estimation [23]. This model is still in use even PRECISE ORBIT AND CLOCK ESTIMATION though its limitations were discovered and evaluated The fitted portions of the four-station-based ref- in 1990 [24]. A discussion of the operational aspects erence trajectories generated for the ICS by of the OCS Kalman filter is given in [25]. An esti- NSWCDD were called “precise” ephemerides and mation procedure that eliminated the use of a master were provided to organizations such as DMA, NRL, clock was implemented in June 1990 [26]. and others from 1980 through 1985. In 1981 experi- Another comprehensive study of UREs con- ments were begun on improving the quality of the ducted in 1993 indicated a 3- to 4-m orbit accuracy precise orbits by including data from up to three addi- [27]. In 1994 the OCS evaluated and updated the tional tracking stations deployed by DMA to Austra- clock process noise statistics used for all satellites lia, Seychelles, and Argentina [34, 35]. These and stations [28]. The OCS continues to reevaluate stations used the early geodetic-quality receivers built and adjust these statistics on a routine basis. In early by Stanford Telecommunications, Inc. All of these 1997, the OCS implemented an ephemeris orbit fits were single-satellite solutions using time enhancement endeavor. This involved updated orbit differences of pseudorange measurements from the and radiation pressure/y-axis acceleration process USAF stations and integrated Doppler measurements noise levels [29]. This improved the orbit estimation from the DMA stations. and prediction accuracies further so that the broadcast The quality of the precise ephemerides was im- UREs were in the 2.0- to 2.5-m range [30]. With six proved in September 1985 when NSWCDD’s next Block IIR satellites now operating, the broadcast generation of estimation software, called OMNIS, re- UREs have been reduced to about 1.6 m. The URE placed the batch fit software [36, 37]. It used data accuracies will continue to improve as more Block from the five OCS stations and three of the DMA sta- IIR satellites replace Block II/IIA satellites. tions. This software implemented a multisatellite Kalman filter/smoother estimation algorithm using Operational Initiatives the 15-min smoothed pseudorange data directly, since The Space Segment is currently undertaking a the stochastic nature of the satellite and station clocks modernization program leading to GPS upgrades for could be accommodated as estimated states. Unmod- the replenishment satellites well into the 21st century. eled accelerations acting on the satellites could also These upgrades include (1) the addition of a new civil be accommodated. The multisatellite capability al- code signal on the L2 frequency (L2C) and the new lowed better separation of the satellite and station military (M-code) signal on the L1 and L2 frequen- clock variations from the orbits. By 1987, DMA had cies on the last 12 Block IIR satellites; (2) plans for deployed second-generation, geodetic-quality TI4100 similar upgrades to the Block IIF satellites, with the receivers to tracking sites in Australia, Argentina, addition of a third GPS civil signal at 1176.45 MHz England, Ecuador, and Bahrain. An evaluation con- (L5); and (3) planned GPS III satellites that are to ducted in 1987 indicated that radial orbit accuracy have the above capabilities plus increased power for was probably at the 1-m level, with horizontal errors the M-code signals. The nominal schedule for an Ini- at the 3-m level per component [38]. Also, in 1987 tial Operational Capability (IOC) of 18-satellite earth evidence that the Block I clocks were undergoing coverage of the M-code and L2C code is 2008. The large orbit period variations was believed to be due to planned L2C IOC is 2012. The planned high-power thermal cycling on the satellites [39]. Changes to the M-code IOC is 2016. The OCS will correspondingly clock estimation procedures were implemented at the be upgraded to support the modernization program. beginning of 1988 to handle these variations. A Further discussion on GPS modernization and its fu- solid-earth correction to station coordinates was ture expected performance is given in [31] and [32]. also added at this time. All of the DMA stations The USAF is also currently in the process of im- were updated to dual TI4100 configurations by De- plementing a program called the Accuracy Improve- cember 1989. ment Initiative (AII), which will lead to further

4 Navigation, Journ. of the Inst. of Navigation, Vol. 49(1), 7-34, Spring 2002

In July 1989, production of the precise tained by NIMA and used, along with data from the ephemerides for the Block I satellites was transi- USAF stations, in their precise orbit and clock esti- tioned to DMA in Bethesda, Maryland. Improve- mation. ments over the next few years included changes to Geodetic systems, such as WGS 84, include a the radiation pressure scale parameter designed to definition of the coordinate reference frame, parame- address estimate degradation during eclipse seasons ters of the , and associated - [40]. Starting in 1991, plate motion effects on the detic and geophysical constants. The process used in station coordinates (using the AM0-2 model), and developing such systems produces self-consistency more accurate earth’s orientation computation were between the reference frame and the coordinates of incorporated [41]. the stations used in the process. At the time of the In June 1993, production was moved from Be- WGS 84 development, its reference frame realization thesda to DMA facilities in St. Louis, Missouri. was defined by TRANSIT tracking stations; however, Ashtech Z-12 receivers replaced the T14100 receiv- to define the most accurate TRANSIT coordinates, ers at the DMA stations by December 1993. In Janu- external calibration was necessary. All radio fre- ary 1994, more accurate station coordinates were quency tracking systems (i.e., TRANSIT and GPS) introduced (see next subsection) and the NUVEL have a nearly -independent observation. NNR-1 plate motion model was implemented [42]. Within these tracking systems, absolute determina- During 1995, DMA deployed additional tracking sta- tion of station longitude is ambiguous. External tions at the U.S. Naval Observatory (USNO) in comparison and calibration is performed between sets Washington, DC, and Beijing, China, bringing the to- of station coordinates to allow for uniform systematic tal number of stations to 12. In early 1995, all station network adjustments. Ashtech receivers were upgraded to be Y-code capa- In 1983 the WGS 84 development committee ble. Tracking station antennas were upgraded in Au- adopted the Bureau International de l’Heure Terres- gust 1995 to reduce multipath effects. trial System (BTS) as the external comparison stan- With 12 stations in place, it was determined that dard for the WGS 84. The BTS, based on very long interferometric-type processing could be imple- baseline interferometry (VLBI) and other observa- mented to take advantage of the precise carrier-phase tions, was globally distributed and very accurate. data in addition to the smoothed pseudorange data. The WGS 84 TRANSIT tracking station coordinates These data and the new processing approach were were adjusted to match the BTS as well as possible. adopted by DMA in late September 1996 and modi- The preliminary WGS 84 coordinates of the fied in November to provide for better clock estima- USAF and DMA GPS tracking stations were ob- tion. Further NSWCDD analysis and the addition of tained by transformation from their WGS 72 coordi- better tropospheric refraction modeling resulted in nates. During 1985 and 1986, the WGS 84 another set of changes being adopted by the NIMA in coordinates were directly derived using Doppler late November 1997. These two sets of changes re- TRANSIT pointpositioning by DMA. This position- sulted in RMS UREs associated with the NIMA pre- ing technique used the recently calibrated WGS 84 cise ephemerides of better than 10 cm [43]. The Doppler station coordinates, Doppler observations recent addition of four more stations by NIMA has collected from TRANSIT satellites, and the WGS 84 resulted in this URE being reduced to about 5 cm. gravity model. The WGS 84 positions of the GPS tracking stations were defined by transferring Coordinate Frame Definition: World Geodetic WGS 84 positions of nearby collocated Doppler sta- System tions using terrestrial survey differences [45]. The global reference frame currently used by Uncertainties in these Doppler-derived WGS 84 DoD, the World Geodetic System 1984 (WGS 84), station coordinates were attributed principally to un- was defined by the DMA [44]. In addition to the im- compensated ionospheric effects on signal propaga- proved reference frame, the development of the tion and, to a smaller extent, the determination of the WGS 84 included estimating a refined electrical phase center of the antennas. TRANSIT, (gravity) model and determining coordinates for sat- like GPS, used dual-frequency observations to correct ellite tracking stations. This section addresses the for ionospheric effects. This correction’s residual er- development and continuing refinement of the opera- rors are inversely proportional to the satellite- tional WGS 84 reference frame, defined presently by transmitted frequencies. Ionospheric corrections for the coordinates of two DoD globally distributed net- the TRANSIT low-frequency observations contained works of GPS tracking stations. One network con- relatively large residual errors; these errors primarily sists of five USAF GPS tracking stations used in their corrupted the height of Doppler-derived coordinates. real-time computations of the GPS broadcast Smaller errors in the GPS station coordinates were ephemerides while the other station network is main- introduced by inaccurate definitions of the electrical

5 Navigation, Journ. of the Inst. of Navigation, Vol. 49(1), 7-34, Spring 2002 phase center of both the TRANSIT and GPS antennas Refinement of the WGS 84 reference frame con- used in the coordinate transfers. The combination of tinues, with future improvements to potentially yield these and other errors made the initial GPS station station coordinates accurate to a centimeter, or better, coordinates internally inconsistent and biased with per component of position. In addition, station ve- respect to the BTS. The largest bias, which was in locities, used to propagate the station coordinates to the GPS station , was estimated to be at the different epochs, will be estimated; consequently, the meter level. small inaccuracies associated with using worldwide Once the initial WGS 84 GPS stations were de- plate motion models will be eliminated. fined, tracking station coordinates could be devel- oped using GPS tracking data, and GPS precise Earth Orientation Prediction and Estimation clocks and orbits. However, successful redetermina- Earth orientation predictions for GPS have al- tion of WGS 84 station coordinates within the GPS ways been done on a weekly basis. For the ICS, system would be a measure of only internal GPS con- NSWCDD performed the predictions based on sistency. External comparison and calibration would USNO data [48] and the ICS updated these predic- still be needed to assure the best absolute position ac- tions in near real time using the tracking data from its curacy. four-station Pacific Basin network. With the imple- The Doppler-realized coordinates, discussed mentation of OCS, the prediction task was moved to above, were defined to be consistent with the BTS. DMA [49]. The OCS does not estimate any earth Over time, the BTS has been refined to the Interna- orientation parameters but the inertial orbit planes tional Terrestrial Reference Frame (ITRF) provided can rotate to accommodate slowly changing UT1- by the International Earth Rotation Service (IERS). UTC errors, where UTC is the Coordinated Universal To maintain consistency, the WGS 84 GPS station Time, and Universal Time 1 is a rotation about the coordinates have been tied to the ITRF. New coordi- pole representing the siderael rotation of the earth. nates for the operational USAF and DMA tracking In computing the precise ephemerides, the earth stations have been determined twice. Each set of co- orientation predictions generated by DMA/NIMA ini- ordinates showed improved accuracy over the previ- tially included constant offsets for the two pole coor- ous set. dinates and the UT1-UTC [50]. Starting in 1991, The first GPS derivation of WGS 84 coordinates solid-earth zonal tide effects on UT1-UTC were used data collected in 1992 from the ten USAF and added to the initial values, and pole coordinate rates DMA stations and from a set of globally distributed and a UT1-UTC acceleration parameter were also es- civilian stations defined in the ITRF [46]. A subset timated. of the ITRF stations, called fiducial sites, was held fixed, while simultaneously estimating GPS clocks, orbits, and the station coordinates of the USAF, POSITIONING DMA, and remaining ITRF sites. These WGS 84 co- ordinates of the DoD stations were improved over the ABSOLUTE POSITIONING Doppler-realized coordinates due primarily to elimi- The term absolute positioning, when used in the nation of the height bias (approximately 1.5 m in discipline of geodetic surveying, generally refers to a magnitude) and redefinition of longitude. The esti- process that establishes the earth-centered, earth- mated 1-σ accuracy of these GPS-realized WGS 84 fixed coordinates of a solitary station on the earth’s coordinates was 10 cm per component, an order of surface. Unlike relative positioning (differential po- magnitude better than the accuracy of the Doppler- sitioning), the absolute positioning process does not realized coordinates. These WGS 84 (G730) coordi- depend on use of a previously determined reference nates were adopted by DoD in 1994. station position. Instead, a set of satellite positions The DoD coordinates were rederived in 1996 for and clock states are obtained from an existing satel- the purpose of validation and also to improve the co- lite ephemeris. A position estimation algorithm is ordinates of two new DMA stations and two DMA employed that uses data collected at the solitary sta- stations relocated since the previous solution [47]. In tion over some period of time, typically at least a few this second GPS-based derivation, the DoD coordi- hours or more. nate solutions were tied to the ITRF by again holding fixed the coordinates of the fiducial stations, while Background solving simultaneously for GPS clocks, orbits, and While the commercial surveying community the station coordinates. The new DoD coordinates quickly developed and embraced the relative- are now estimated to have an accuracy of better than positioning capabilities that GPS offered, virtually all 5 cm per component, 1 σ. DoD adopted the im- commercial surveyors continue to rely on govern- proved WGS 84 (G873) coordinates. ment agencies, such as the National Geodetic Survey,

6 Navigation, Journ. of the Inst. of Navigation, Vol. 49(1), 7-34, Spring 2002 or similar agencies in other countries for absolute 1. The geometric range, which is the be- survey control points. The DoD relies on NIMA for tween the phase centers of the transmitting an- absolute survey control, while research institutions tenna on the satellite and the receiving antenna generally create their own control or rely on results employed by the user. This is the component of generated by other institutions in the international the pseudorange that is of primary interest to the scientific community. For these reasons, a small navigation user. number of geodetic organizations have concerned 2. The receiver clock time offset from GPS time. themselves with developing GPS geodetic absolute 3. The satellite clock time offset from GPS time. positioning capabilities. In the United States, these 4. Relativistic effects. organizations include NIMA, NSWCDD, The Uni- 5. Propagation delay/advance caused by tropo- versity of Texas at Austin, and NASA’s Jet Propul- spheric refraction. sion Laboratory (JPL). Outside of the United States, 6. Propagation delay caused by ionospheric refrac- researchers at the University of Calgary and a few tion. other research organizations have also developed al- 7. Multipath errors introduced by signal reflections gorithms and performed analysis in this area. from structures in the vicinity of the antennas. An application of absolute geodetic positioning 8. Receiver-dependent propagation delays such as is the estimation of transformations. the signal propagating through the preamplifier When a set of geodetic control points, established in and antenna cable. a local or regional horizontal geodetic datum, are po- 9. Receiver measurement biases. sitioned with an absolute GPS point-positioning 10. Satellite transmission biases among frequencies. technique, a set of similarity transformation parame- 11. Selective Availability (SA) effects, if present. ters can be determined. These parameters can then Intentional SA errors on GPS satellite timing and be used to convert , charts, or other geospatial ephemerides were turned off under a U.S. presi- data from a local or regional datum into a global ref- dential directive on 1 May 2000. erence frame such as WGS 84. Conversely, a GPS 12. Background wideband noise generated by the re- user’s navigation position can be converted from ceiver components. WGS 84 into a local or regional datum by application The phase observation can be considered to be a of these transformation parameters. NIMA maintains precise version of the pseudorange observation, with a large set of these transformations and makes them an additional unknown parameter attached: an inte- available for GPS receiver manufacturers and other ger wavelength bias. The receiver phase observation users. They can be found in TR8350.2 [45] or on the is a cycle count relative to an arbitrary receiver refer- World Wide Web at: ence epoch. There is no information in the phase http://www.nima.mil/GandG/pubs.html. measurement about satellite transmission time except Another application for geodetic point positions what is provided by the pseudorange. Ideally, the ar- lies in establishing geodetic control networks, which bitrary integer phase offset could be deduced by are needed for a variety of purposes, including high comparing the phase count with the pseudorange. resolution modeling. Other applications, such However, the inherent pseudorange noise is large as geodetic control of remotely sensed imagery and enough to make this process difficult even under the the metric evaluation of remotely sensed imagery, are best conditions. Also, the ionospheric refraction particularly important within DoD since they support component must be considered, because ionospheric the targeting processes for a number of modern refraction delays the pseudorange, but advances the weapons systems. Other military applications of phase. A discussion of the possibility of using pseu- geodetic point positions are discussed in [51]. dorange to determine the phase integer bias is given by [53]. Pseudorange Observation Equation: Relationship Except for the geometric range, all of the items to Absolute Positioning listed above can be considered to be sources of error. The pseudorange observation is the link between Fortunately, most can be accounted for and reduced the user and the satellites. It is instructive to decom- to an acceptable level. The goal for accurate absolute pose this observation into its various parts to estab- positioning is to faithfully separate the geometric lish where the sources of error lie. The observation is range from the propagation errors. Besides accurate a measurement, determined by the receiver, of the pseudorange observations, in order to perform the ab- time interval between the reception and transmission solute position solution, the satellite position is re- of an L-band signal. The pseudorange is this time in- quired at the time of transmission. A geometric terval multiplied by the speed of light in free space. range with zero error will still provide erroneous user [52] identified the following components in the pseu- position solutions if the satellite position is not pre- dorange observation. cisely known. Under most user conditions, in the ab-

7 Navigation, Journ. of the Inst. of Navigation, Vol. 49(1), 7-34, Spring 2002 sence of SA, the satellite ephemerides errors and Navigation technique [54], was developed specifi- clock offset errors are the largest sources of absolute cally for this purpose. positioning error. Exclusive use of the pseudorange may lead to so- lutions being strongly influenced by multipath effects GPS Absolute Positioning Algorithms if a hostile antenna environment is present. Smooth- In comparison to the number of GPS relative po- ing the pseudorange observations with phase meas- sitioning algorithms in existence at this time, the urements can reduce this effect and has been used number of absolute geodetic positioning algorithms is successfully in many applications. In order to exploit somewhat small. Prior to 1 May 2000, these algo- the lower noise phase observation, range differencing rithms could be categorized into two distinct catego- can be used. Since the unknown integer phase bias is ries: those developed by the DoD, for which the constant while the receiver tracks the satellite signal effects of SA are removed before the process takes (ignoring cycle slips), time differences of the phase place, and those developed by research groups or produce a range difference observation between adja- universities or implemented by manufacturers, for cent epochs. The range difference over a time inter- which the effects of SA are handled in other ways. val is akin to an average velocity measurement. At The distinction is no longer important now that SA least two epochs are required to construct the range has been set to zero. difference, though many observations at equal inter- The raw satellite observations generally consist vals are usually used. of the pseudorange and phase measurements de- Another technique used to construct an observ- scribed previously. Several different combinations of able for point positioning uses the ionospheric-free these data types are used for absolute point position- range difference from phase, along with the iono- ing, however, and each point-positioning algorithm spheric-free pseudorange, to transfer each pseudo- known to the authors’ forms a different combination range observation to a common epoch. At the of the raw data types to use as an observable in the common epoch, all of the transferred pseudoranges estimation process. While the scope of this paper are averaged to minimize the uncorrelated pseudo- will not allow a complete description of each of these range errors (measurement noise and some forms of combinations, a general outline of the observables multipath effects) that appear in each of the observa- and estimation algorithms will be provided. tions. This average pseudorange can then be trans- The simplest way to perform absolute position- ferred back to all observation epochs through the ing is with the epoch-by-epoch navigation solution. range difference observations. This technique is use- Though unsophisticated mathematically, this ap- ful if the phase integrity is such that cycle slips, and proach has several advantages. It solves for only four integer phase ambiguity resets are few. parameters: the three components of position and the A type of double differencing of the phase ob- local clock offset. Since there are only four un- servations has also been successful. For this double knowns, four satellite pseudoranges are enough for a differencing, the first difference is the between-epoch solution, though data from all satellites in view may range differences based on phase data, then the range be used in a least-squares algorithm. Since each ep- differences are differenced between satellites. The och is treated independently, the navigation solutions differencing between satellites removes effects that can be found with uniform accuracy regardless of the are common to all satellites, such as the receiver time user’s motion. If the receiver is stationary, the indi- offset. Multipath effects are reduced because only vidual position estimates can be averaged to reduce phase observations are used. However, the doubly the impact of random errors. Propagation effects— differenced observable requires very good geometri- such as tropospheric and ionospheric refraction— cal strength over several hours in order to produce a must be modeled if single-frequency observations are satisfactory position accuracy. used. When dual-frequency observations are avail- In the early 1990s, the routine absolute accuracy able, the ionospheric refraction can be computed and of geodetic point positioning was in the vicinity of essentially eliminated. The satellite positions and 1m (1 σ). Today (2002), with the precise epheme- clock offsets are obtained either from the broadcast rides and corresponding satellite clock states, 12 hr of satellite ephemerides or from a set of precise observations, plus recent improvements in several al- ephemerides and clock states if timeliness is not a gorithms known to the authors, absolute point concern. position accuracies at the 5-cm level have become If the broadcast navigation messages are used routine. For further details on several of the point and the tracking data are not retained, a user can still positioning algorithms discussed here, the reader can improve the accuracy of these navigation solutions by refer to: [55 – 64]. using precise ephemerides and clocks, if a record of the satellites tracked is kept. The Precise Absolute

8 Navigation, Journ. of the Inst. of Navigation, Vol. 49(1), 7-34, Spring 2002

DIFFERENTIAL POSITIONING economically attractive even while only a few GPS Differential positioning is not new. Prior naviga- satellites were in orbit—long before the system was tion systems—such as Omega, Loran C, and TRAN- declared operational. The most common use for SIT—were improved via differential implemen- static DGPS was in surveying. A monitor receiver tations. In each case, just as with GPS, the accuracy was placed at a known reference , and a sec- is improved by using a monitor receiver to measure ond receiver was placed at a site whose position was the errors at a reference site and to transmit correc- to be determined [65]. Measurement data were re- tions derived from those measurements to the differ- corded at both sites and then brought back to an of- ential user receiver. Because of the strong spatial fice for subsequent processing. The primary correlation of the errors, the accuracy of the user re- measurement data needed for survey quality results ceiver is substantially improved. The civil GPS user were the carrier-phase measurements. However, the was further motivated to develop differential posi- pseudorange (or code) measurements were often used tioning techniques with the advent of anti-spoofing to aid the processing. and, the now removed, selective availability, which intentionally degraded accuracy. This and later sec- Pseudorange Differences tions discuss some of these techniques. The pseudorange (or code) measurements were It is stated in almost all differential GPS (DGPS) used in many different ways in the early survey ap- descriptions that the position of the monitor receivers plications. Quite often the purpose was to measure must be determined by precise survey. However, this the vector difference between two surveyed points. is not necessarily the case. DGPS is fundamentally a In this relative positioning task, the location of the relative positioning system. The monitor receiver monitor receiver is not required to attain high accu- could be (and sometimes is) located on a moving ve- racy. Thus, the position of the monitor site was often hicle such as a ship, airplane, or satellite. In this computed using the undifferenced pseudorange case, the measurement corrections supplied to the measurements. This was followed in many process- user, who is positioned relative to that vehicle, are the ing programs by a preliminary differential pseudo- negative of the measurement residuals from the vehi- range solution. This first stage in computing the cle position computation. When multiple monitor re- vector difference between the monitor site and the ceivers are used they, of course, must be located user site used the double difference of the pseudo- accurately relative to one another. The requirement range measurements or some nearly equivalent proc- for accurate surveying of the monitor receiver posi- ess. tion arises only from the desire to transform the rela- Differencing the measurements allows the re- tive positioning accuracy into an absolute accuracy. moval of satellite and receiver clock errors. By tak- One can find in the literature descriptions of a ing the difference across satellites of the measure- GPS position differential technique often referred to ments taken at each site, one eliminates the common as “Relative GPS,” which makes use of corrections to effect of the receiver clock variation. By then differ- the position rather than corrections to the measure- encing these differences (double differencing) across ments used in computing the position. This requires sites, the variation in the satellite clocks is elimi- the user receiver to use measurements from exactly nated. An essentially equivalent process is to use the the same satellites (some of which may not be visible undifferenced measurements and to select either a to the user). The alternate way to implement DGPS satellite clock (preferable) or one of the receiver is to send corrections from the monitor receiver clocks as the standard clock and then to solve for rather than the raw pseudorange measurements. This clock differences as part of the solution process [66]. avoids sending the monitor receiver location (assum- ing the tropospheric refraction effects are removed at Carrier-Phase Differences the monitor receiver before generating the correc- The next stage in the process of computing the tions). vector difference between a monitor site and a user DGPS techniques can be used in both static and site is to use the more precise carrier-phase meas- kinematic applications and may involve either pseu- urements. The carrier-phase measurements are much dorange or carrier-phase measurements, or both. The more accurate than the pseudorange measurements static techniques are addressed first, then the kine- because they are much less affected by multipath (re- matic techniques. flection) effects [67]. However, they suffer a signifi- cant problem—specifically, they are ambiguous at Static Techniques the whole-cycle level (or half-cycle for early codeless Static DGPS positioning was probably the first receivers). One way of understanding this ambiguity commercial application of GPS. Because the appli- is to recognize that the phase measurement is the in- cation did not require continuous availability, it was tegral of the difference in phase of the signal received

9 Navigation, Journ. of the Inst. of Navigation, Vol. 49(1), 7-34, Spring 2002 and the phase of the local clock scaled to the trans- for resolving the whole-cycle ambiguities. One of mitted frequency. The fractional phase relationship the simplest for the static user, although not the most robust, is simply to round the values of the biases of this integral is well defined. However, the whole- computed in the prior solution (whether explicitly or cycle constant of integration is not. implicitly determined) to obtain a whole-cycle inte- The simplest way to overcome the whole-cycle ger value for each ambiguity. In some software, this ambiguity problem is to form “triple differences.” is accomplished by fixing one whole-cycle ambiguity The triple difference is obtained by differencing at a time and then recomputing the solution before measurements: (1) across user and monitor receivers, fixing the next one. (2) across satellites, and (3) across time. Note that It is not difficult, though the processing can be- the order of differencing (across receivers, across sat- come quite complex, to extend the single-monitor/ ellites, and across time) does not affect the final single-user scenario discussed above to the multiple- composite measurement. Because the whole-cycle monitor and/or multiple-user environment. ambiguity remains the same for all carrier-phase measurements to a given satellite, differencing se- Kinematic Techniques quential measurements (differencing across time) Differential code or pseudorange measurements cancels the whole-cycle ambiguity bias. Unfortu- are often used when the user receiver is no longer nately, this simple triple-difference solution is geo- static but moving (i.e., kinematic). As currently used metrically weaker than other alternatives. In fact, its in the literature, however, kinematic DGPS almost geometrical strength is a function of the time interval always refers to a moving user employing differential used in the differencing process. In spite of this carrier-phase measurements. Differential code tech- geometrical weakness, this triple-difference solution niques for the moving user are usually referred to as is generally significantly more accurate than the dif- either Local-Area Differential GPS or Wide-Area ferential code solution described above. It is also Differential GPS. The most common reference to ki- possible to form the single time difference and, as de- nematic carrier-phase techniques is real-time kine- scribed above, choose one of the clocks as the refer- matic GPS processing. The differential aspect is ence clock, and then solve for the clock differences simply implied by common usage. as part of the solution process. A solution stronger than the triple difference can Local-Area Differential GPS (LADGPS) be obtained for the vector difference between the two The U.S. Coast Guard has developed a number sites, still without resolving the whole-cycle ambigui- of LADGPS monitor sites that provide pseudorange ties. There are many ways to obtain this equivalent corrections for GPS users in the area adjacent to the solution. One of the simplest ways, although it monitor sites [68]. Local, in this context, can apply causes the number of solution parameters to increase to a radius of several hundred . These Coast significantly, is to avoid the time differencing of the Guard beacons provide code or pseudorange correc- measurements and instead include in the solution pa- tions in the standard RTCM format for each GPS sat- rameters an ambiguity bias parameter for each set of ellite on at least the L1, or primary, frequency. sequential carrier-phase measurements to each satel- Tropospheric refraction effects are generally com- lite. In using this approach, a new bias parameter is puted by the user for both the monitor and his own required any time continuous phase lock is not main- receiver using a mathematical model. Ionospheric re- tained. There are several other alternative ways of fraction effects are generally ignored because they obtaining a mathematically-equivalent solution. Per- are strongly correlated and, therefore, largely cancel haps the simplest of these alternatives is to form the over the local area distances involved. There are sequential time difference of the carrier-phase meas- many similar networks of LADGPS monitors around urements. However, during the processing of these the world. The primary users tend to be local marine measurements, the proper weight matrix is used to traffic, but farmers and other commercial users are account for the sequential measurement cross correla- becoming significant beneficiaries. tion (of –0.5) induced by that differencing. In this approach, the specific ambiguity bias parameters Wide-Area Differential GPS (WADGPS) need not be included in the solution, but they can be The U.S. Federal Aviation Administration found by taking the resultant position and computing (FAA) is developing a WADGPS system that is re- the range to the satellites in units of whole cycles. ferred to as the Wide-Area Augmentation System Finally, the strongest solution arises when the (WAAS). Japan is developing a similar system re- carrier-phase measurement ambiguities are specifi- ferred to as MSAS, and the European nations are de- cally determined to the correct whole-cycle value. A veloping a similar system referred to as EGNOS. A multitude of methods can be found in the literature number of commercial WADGPS systems have also

10 Navigation, Journ. of the Inst. of Navigation, Vol. 49(1), 7-34, Spring 2002 been developed by and for commercial applications. removed, and one can determine from the wide-lane, Typically, a WADGPS implementation will have whole-cycle solution the value of the narrow-lane (L1 between 10 and 50 monitor stations across a conti- nent-wide area. Generally, the monitor stations use or L2 or the average of L1 and L2), whole-cycle am- dual-frequency, L1 and L2, GPS receivers, even biguity. though the corrections they provide are usually for The second method is aided by the fact that the L1-only user receivers. In the WAAS, the dual- code measurements can be smoothed via the carrier- frequency monitor receivers are used to provide phase measurements. For single-frequency receivers, measurements of ionospheric refraction effects, this smoothing is limited by the ionospheric diver- which are then used to provide parameters to drive a gence of the code and carrier-phase measurements— model of the effects in the user receiver. In addition, i.e., the affects the code pseudorange the monitor station measurements are used to com- measurements opposite to the way it affects the car- pute orbital corrections, which are provided to the rier-phase measurements. However, a linear combi- user at a slow rate. Thus, the WAAS user is provided nation of the L1 and L2 carrier-phase measurements with three types of corrections: (1) a fast-rate clock can always be found that exactly matches the iono- correction, which removes the rapid (SA) distortions spheric refraction effects present in any specific lin- in the users’ L1 pseudorange measurements; (2) pa- ear combination of the L1 and L2 code measurements rameters used to compute an ionospheric refraction (and vice versa). This means that the pseudorange correction; and (3) slowly varying parameters to (code) measurements can be smoothed indefinitely to compute corrections to the GPS broadcast epheme- remove the multipath effects by using the matching rides. The WAAS users are responsible for comput- linear combination of the carrier-phase measure- ing their own tropospheric refraction effects with a ments. With this smoothing process, it does not take specified algorithm. The accuracy available from a long with a high-quality GPS receiver to obtain a well-designed WADGPS typically has a standard de- smoothed-code measurement (with ionospheric re- viation of about 1 m in each horizontal axis and about fraction matched to the wide-lane carrier-phase 2 or 3 m in the vertical axis. measurement) capable of resolving the proper whole In both the LADGPS and WADGPS implemen- cycle of the wide-lane carrier-phase measurement. tations, the GPS carrier-phase measurements play a Additionally, over short distances, as described subsidiary role. Specifically, they are used to above, this resolved wide-lane measurement can be smooth, and thereby remove, some of the multipath used to determine the whole-cycle ambiguity of the effects normally present in the code measurements narrow-lane measurements. [69]. For this second method, the whole-cycle ambi- guities can be verified when measurements to five or Real-Time Kinematic (RTK) Differential GPS more satellites have been obtained. If the whole cy- Navigation at the centimeter level is possible us- cles are correct, then the measurement residuals will ing differential carrier-phase techniques [70 – 76]. be small. If one or more have been resolved incor- As indicated above, this requires the resolution of the rectly, the measurement residuals will be much lar- whole-cycle ambiguities. There are two primary ger. In fact, one of the most significant benefits of methods to resolve the whole-cycle ambiguities [77]. the dual-frequency, code-assisted, whole-cycle ambi- Both are generally practical over distances of only 10 guity resolution is this simple residual verification to 20 km. The first method is to use a search proce- process. By contrast, since the search method uses dure in the position-solution domain. Generally, the the measurement residuals directly to find the best code measurements are used to aid this process by solution, it becomes more complicated to verify that determining the limits of the search. A wide variety it is the correct solution. Most implementations of of variations of this technique can be found in the lit- the ambiguity search process use the ratio between erature. the residuals of the best solution to the residuals of A second method is to use the code measure- the second-best solution as a measure of the confi- ments on a satellite-by-satellite basis to resolve the dence in the choice of the best solution. carrier-phase, whole-cycle ambiguity directly. This In any case, once the whole-cycle ambiguities technique becomes the preferred method if the user have been determined, the carrier-phase measure- has a dual-frequency receiver. The use of two fre- ments provide a navigation solution of about 1 cm in quencies allows the formation of a beat (difference) each axis of the horizontal position and about 2.5 cm frequency carrier-phase measurement with a substan- in the . This accuracy decreases tially longer wavelength, which is often referred to as slowly as the baseline separation distance increases the wide lane. Over distances of less than 10 to beyond about 10 km. But it is not the position accu- 20 km, the ionospheric refraction effects are largely racy that limits the technique. The limiting factor is

11 Navigation, Journ. of the Inst. of Navigation, Vol. 49(1), 7-34, Spring 2002 the ability to resolve the whole-cycle ambiguities as estimated simultaneously. The differential effect of the ionospheric refraction begins to affect the wide- the solid is also included. lane, whole-cycle resolved measurements differently For long baselines, the accuracy of the solution than it affects the narrow-lane, carrier-phase meas- is dependent on the number of satellites in common urements. view and the corresponding differential satellite ge- From the discussion above, it becomes clear that ometries between the dynamic user and reference RTK carrier-phase DGPS, using integer cycle resolu- sites or the differential position dilution of precision tion, can provide a solution that is more accurate than (PDOP). Since in long-range navigation it is neces- any other GPS navigation technique. However, the sary to solve for more parameters than just the coor- baseline separation distance over which the technique dinates of the moving antenna and receiver clock can be applied is generally limited to about 10 km error, at least five satellites in common view are [78]. Methods that incorporate a reference receiver needed. If the distribution of satellites allows, the network have been used to extend the distances to the cutoff of 17 degrees may be preferred to the roving user. Some approaches use the additional ref- usual 15 degrees to reduce the presence of multipath erence station measurements to improve the tropo- effects and cycle slips to which the long-range solu- spheric and ionospheric corrections and model the tions can be particularly sensitive. Further, a signifi- satellite ephemeris errors [79. Other approaches in- cant amount of processing time—over 20 min of data corporate the measurements into a single site [80] or collection—is required to accurately estimate the a virtual reference site that is generally placed near measurement and error biases, while simultaneously the roving user [81, 82]. These techniques extend by determining the dynamic user trajectory. a factor of 3 to 5 the baseline distance for reliable in- Test results using precise postfit satellite teger cycle resolution. ephemerides suggest that most of the time the kine- matic positions calculated with the long-range tech- Long Baseline, Multireference Kinematic DGPS niques were within 10 cm of the true positions, and There are a number of remote-sensing applica- that the RMS accuracy for baselines over 500 km was tions that require both precise positioning and long better than one part in 10 million of the baseline baselines. These applications include large area sur- length [84]. These results depend on having more veys in polar areas, , or other areas where than four satellites in view and on favorable geome- short-baselines are either difficult or costly to deploy. try (e.g., differential PDOP<8). Good results of Pseudorange-based WADGPS techniques are not suf- decimeter-level accuracy can be obtained with the ficiently accurate. Decimeter-level accuracy has broadcast ephemeris if readjusted as part of the ki- been demonstrated for long baselines (greater than nematic solution. Applications in real time and on a 1000 km) using a dual-frequency, carrier-phase global scale are discussed in a later section. measurement approach [83]. Here, pseudorange measurements are used only to provide initial esti- STATUS OF MAPPING AND SURVEYING AP- mates and assist with cycle slip detection and correc- PLICATIONS tion. Currently, the fields of surveying and mapping The approach uses an estimation procedure are being transformed by a number of new and inno- known as floating and positions the dynamic user vative technologies, including Geographic Informa- with respect to multiple accurately positioned refer- tion Systems (GIS), high-resolution , ence sites. The reference site absolute positions are and GPS. Of these, GPS has had the most important obtained to an accuracy of a few centimeters. This and immediate impact because of both cost savings allows the multiple sites to be used interchangeably and accuracy improvements over previous position- in the dynamic user solution and mitigates, to a de- ing technologies and techniques. The single most gree, the problem discussed earlier of the number of powerful feature related to GPS, which is not true of satellites in common view. With multiple reference traditional surveying techniques, is that its use does sites, especially if they are in various directions with not require a line of sight between adjacent surveyed respect to the dynamic user, the satellites in common points. This factor is very important in understanding view become more numerous at long baselines. the impact that GPS has had on the surveying, - Real-valued biases for the ionosphere-free combina- ping, and GIS communities. tion of L1 and L2 (or “L3”) double-differenced phase As previously stated, GPS has been used by the measurements are estimated in a joint solution with surveying and mapping community since the late the dynamic trajectory. Other biases due to the ef- 1970s when only a few hours of satellite coverage fects of reference station position errors, satellite or- were available. It was clear even then that centime- bit errors, and tropospheric refraction errors are also ter-level accuracy was obtainable over very long baselines (hundreds of kilometers). In the early

12 Navigation, Journ. of the Inst. of Navigation, Vol. 49(1), 7-34, Spring 2002

1980s, users of GPS faced several problems: the cost ronment to within ± 1.5 m (5 ft). Users now realize of GPS receivers; poor satellite coverage, which re- that if accuracies of ± 0.3 m (1 ft) can be obtained sulted in long lengths of time at each survey location; (and they can), the length of the guardrail, in addition and poor user-equipment interfaces. Today, instanta- to its location, can be obtained so that if the guardrail neous measurements with centimeter accuracy over needs to be upgraded or replaced, an accurate esti- tens of kilometers and with one part in 108 accuracy mate of the cost is available. This kind of application over nearly any distance greater than 10 km can be is growing rapidly because GPS’s accuracy and ca- made. The cost of “surveying and mapping-level” pability is becoming understood, and the technology receivers in 1999 ranged from $10,000 to $25,000, is being applied to various problems. Applications of and these costs are falling. Practitioners are develop- this kind are widespread and growing in the GIS ing numerous new applications in surveying, such as community. the use of GPS in a kinematic (real-time) mode to de- termine the elevation of prior to grading [85]. Geographical Information System (GIS) Applica- (See THE FUTURE section ) tions Traditional land surveying is increasingly being Today, in most developed countries, there exists accomplished using GPS because of the continuous a concept generally known as a National Spatial Data reduction in receiver costs, combined with an in- Infrastructure (NSDI) or simply a Spatial Data Infra- crease in user friendliness. This trend towards the structure (SDI). As defined by the [86], the NSDI is use of GPS for surveying and mapping has enhanced a process that includes spatial data collection, man- the volume of survey receiver sales. (Land surveyors agement, and distribution. Obviously, the location of outnumber control surveyors by at least one order of points of interest is central to this process. GPS, in magnitude.) This usage has also increased the accu- many of its modes of operation satisfies nearly all the racy and accuracy requirements of surveying in gen- positional requirements of an SDI. In this context, eral. The fact that accuracy requirements have the classical definitions of mapping should probably increased comes from the phenomenon that accuracy be expanded because of the many applications that do requirements tend to increase as the availability of not require high or even moderate accuracy. These better accuracy increases. applications are sometimes known as “GIS projects” The standard surveying and mapping activities and are usually focused on environmental, taxation, that are enhanced by GPS include surveying for sub- natural resource planning, and civil infrastructure (fa- divisions, highways, planned communities, etc. To cilities management) issues. Many demographic date, GPS has not been used widely for single-lot or studies that require approximate positioning are eas- mortgage surveys. This is because the accuracy im- ily satisfied by GPS. provement is marginal for distances of 30 m or fewer, Accuracy requirements for surveying, mapping, there may be problems with foliage attenuation, and and GIS applications are generally satisfied at this the cost of close-range GPS operations is still slightly time. The quest for better and better accuracy will higher than traditional techniques. However, it is continue, but any reasonable distance can currently likely that in the future GPS will be used for such ac- be measured, with significant care, to one part in 108. tivities. As noted above, GIS applications are fully satisfied. In general, the availability of higher GPS accu- racy has influenced various mapping and surveying requirements for three reasons: (1) people want the GEODYNAMICS state of the art; (2) past requirements were in some cases dictated by the cost of acquisition; and (3) if Everyone knows that the earth is rotating, but higher accuracy can be obtained, multiple purposes how many are aware that the earth’s pole moves a can be satisfied. As an example of requirements few centimeters per day, or that the state of Nevada is changing as a function of new capability, consider a stretching by several millimeters per year? Far from problem [85] of facilities management, which deals being trivial, this type of information has practical with the inventory of transportation features such as and societal use, whether it is navigating interplane- the location and attributes (type, condition, and so tary using NASA’s Deep Space Network, forth) of a guardrail along a highway. Previously, the or identifying areas at risk of having large earth- location was “required” by transportation depart- quakes. Geodynamics is the study of processes in- ments to be accurate to ± 6 m (20 ft), which is gener- volved in the rotation and deformation of the earth. ally the best that is possible from scaling or plotting Geodesy has, in a real way, been reinvented to meet on a 1/24,000 United States Geological Survey quad- the extraordinary accuracy requirements of geody- rangle. Using differential techniques, a GPS position namics. This has not only benefited geodesy, but the can easily be obtained in a real-time, dynamic envi-

13 Navigation, Journ. of the Inst. of Navigation, Vol. 49(1), 7-34, Spring 2002 technology has spun off into various aspects of posi- tioning and navigation. GPS GEODESY’S GEODYNAMICS HERITAGE This section does not focus on specific geody- From a historical perspective, GPS geodesy is namics investigations using GPS. Rather, it empha- very different than, say, GPS navigation, or other sizes (1) the principles of geodynamics and global branches of GPS positioning. GPS geodesy devel- geodesy and their close relationship as scientific dis- opment drew greatly from the fields of physics, as- ciplines, and (2) some of the historical and technical tronomy, and spacecraft navigation. GPS geodesy developments that have allowed GPS to become a can be considered a blend of two earlier space geo- valuable tool for geodynamics. For examples of geo- detic techniques: Very Long Baseline Interferometry dynamics applications of GPS and recent results, the (VLBI) and (SLR). Early reader is referred to the University NAVSTAR Con- developers of geodetic VLBI demonstrated centime- sortium’s (UNAVCO’s) online brochure: ter-level precision in the late 1970s [88]. Geodetic http://www.unavco.ucar.edu/community/brochure VLBI and SLR were developed through the 1980s as and the review paper by Segall and Davis [87]. Geo- part of the NASA Crustal Dynamics Project, specifi- dynamics is literally the study of forces that govern cally for geodynamics investigations. GPS was the motion of the earth’s components. Although the viewed by NASA and other federal agencies as an emphasis is on the solid earth, interactions with all economical alternative to VLBI and SLR, and thus the earth’s “” must be taken into account. It is provided funds to develop geodetic receivers and the goal of geodynamics to understand the earth’s software. rheology, structure, driving forces, and resistive The VLBI technique, similar to GPS geodesy, forces; as well as the interaction among the solid measures the relative time of arrival of radio waves earth , oceans, and ice sheets. propagating from a source in space to at least two in- Geodesy is commonly defined as the study of the struments on the ground. Models for signal propaga- shape of the earth and its gravity field, and is there- tion, including geometry, relativistic effects, and fore intrinsically connected to geodynamics. This is tropospheric refraction of the VLBI signal, were ini- even more so for space geodetic techniques, such as tially implemented by GPS geodetic software. De- GPS, which can be used to observe the earth on a velopments in tropospheric propagation for either global scale. technique have generally benefited the other (see GPS contributes to geodynamics through com- POSITIONING section). paring the observed and modeled motion of the However, the VLBI sources are not satellites, but earth’s surface. Since the observed motion of the quasars, effectively at infinite distance. Thus the di- earth’s surface will represent the sum of the various rections to them can, in principle, be determined with effects, it is clear that geodynamics must be modeled far greater precision than to the GPS satellites, with as a whole, even when investigating a specific prob- their more complicated dynamics. On the other hand, lem. This creates a rich area of interdisciplinary re- orbit models are a function of the earth’s gravity search. field; hence GPS stations, unlike VLBI stations, can As the precision and coverage of GPS stations be positioned relative to the center of mass of the has improved over the last two decades, the depth earth (see ORBIT DETERMINATION section). and breadth of GPS geodesy’s application to geody- As VLBI is a radio technique, VLBI technology namics has increased correspondingly. It has now was adopted in NASA’s earliest GPS geodetic re- matured to the point that it is viewed as an important ceivers. The SERIES receiver, developed by Mac- and often primary tool for understanding the mechan- Doran at the JPL in 1979, pointed at one source at a ics of earth processes. time using a directional antenna [89]. Many key Conversely, geodynamics models are essential to principles of the modern GPS geodesy were based on GPS geodesy; as such, models are embedded in the the omnidirectional instrument, MITES, proposed by reference systems we use to define high-accuracy po- Counselman and Shapiro in 1979 [90]. This was de- sitions. For example, if the reference system did not veloped by the Massachusetts Institute of Technology account for the tidal deformation of the solid earth, (MIT) group into the Macrometer, which proved cen- the coordinates of some stations could vary as much timeter-level accuracy using the innovative double- as ~10 cm in the time frame of several hours. There- difference method (see POSITIONING section) for fore, reference systems to enable high accuracy geo- eliminating clock bias [91]. An interesting historical detic positioning have developed in parallel with point is that the double-difference method has its ori- progress in geodynamics, which in turn depends on gins in a method also proposed by Counselman for geodetic positioning. This relationship is inextrica- of the Apollo mission [92]. ble. Global geodesy is just as essential for geody- In parallel, JPL developed an equivalent ap- namics as the converse. proach, known as white-noise clock elimina-

14 Navigation, Journ. of the Inst. of Navigation, Vol. 49(1), 7-34, Spring 2002 tion/estimation, based on the Householder transfor- portant developments during these years include am- mation [93]. This also has its pre-GPS origins as a biguity resolution over long distances [102 – 104], method of bias elimination for NASA’s spacecraft POD (see ORBIT DETERMINATION section), and navigation. GPS textbooks typically ignore white- troposphere modeling (see POSITIONING section). noise clock estimation, yet it has increasing relevance Developments towards high precision in the to the timing community. 1990s include (1) truly global GPS solutions (dis- Contrary to initial skepticism, the GPS orbits cussed below) made possible by the completion of eventually proved to be no more problematic than the Block II GPS constellation and, simultaneously, SLR, despite additional modeling problems. This is installation of the International GPS Service (IGS) because GPS geodesy uses far more stations and sat- for Geodynamics global network in 1994; (2) global- ellites than SLR, and can derive geodetic quality po- scale ambiguity resolution [105]; (3) further refine- sitions using orbit arcs, which are much shorter ment to tropospheric modeling [106] and the inclu- (24 hr) than for SLR (several days or weeks). sion of tropospheric gradient parameters [107, 108]; GPS geodesy also benefited from earlier work on (4) adoption of dual-frequency code receivers, as op- reference system conventions already established posed to the squaring receivers of the 1980s [109]; through a combination of astronomical observation, (5) adoption of the low-multipath choke-ring antenna VLBI and SLR observation, and geodynamics model- developed at JPL as the standard [109]; (6) improved ing. In general, earth models such as tidal deforma- orbit models, particularly with regard to GPS satellite tion are required by all global geodetic techniques, so attitude, and the tuning of stochastic models for solar GPS geodesy was in a position to exploit what had radiation pressure (see ORBIT DETERMINATION already been learned. section); (7) improved reference system conventions The space geodetic pioneers of VLBI and SLR [110]; and (8) solution combination analysis for or- deserve credit from the developers of GPS geodesy bits [111] and station positions [112]. for much of the initial technology [94]. Even so, some of the inherited ideas from VLBI and SLR re- GPS INFRASTRUCTURE AND COOPERA- quired some rethinking if GPS were to achieve its full TION potential. Infrastructure development and tremendous in- ternational cooperation characterized the 1990s. GPS HIGH PRECISION FOR GEODYNAMICS operations moved away from the campaigns, back to GPS geodesy as a tool for geodynamics requires the model of permanent stations, familiar to VLBI (1) subcentimeter positioning precision to detect geo- and SLR. As the prototype receivers developed by physical motion which, in turn, requires (2) a global research groups in the 1980s had become commer- network of stations to enable POD. Broadly speak- cialized, the cost of installing a GPS station in the ing, the 1980s developed the technology required for 1990s had fallen to ~$25K, in contrast to the millions (1), and the 1990s developed the infrastructure and of dollars required for VLBI/SLR. Thus the long- global cooperation required for (2). range goal of the federal funding agencies was real- The development of geodetic GPS during the ized: dozens of GPS stations could be installed for 1980s was characterized by intensive hardware and the price of one VLBI station. software development with the goal of subcentimeter With the cooperation of ~100 research institu- positioning accuracy, over increasingly long dis- tions around the world under the umbrella of the IGS, tances. Several high-precision geodetic software a global GPS network (GGN) (now at ~200 stations) packages that were developed around this time are with a full geodetic analysis system came into full still in use and far exceed the capabilities of commer- operation in 1994 [113]. This backbone, together cial packages. These include the BERNESE devel- with the regional stations located in areas of tectonic oped at the University of Berne [95], GAMIT activity, such as Japan and California, form a global- developed at MIT [96], and GIPSY/OASIS devel- scale instrument capable of resolving global plate tec- oped at JPL [97]. tonic motions [114, 115] and regional phenomena The first geodynamics experiments using GPS such as earthquake displacement [116, 117]. As a re- were carried out during the second half of the 1980s sult of this international cooperation, a culture of data using survey campaigns in areas of tectonic interest sharing has developed, with data freely available for [99 – 101]. These campaigns were to be repeated in research purposes via the Internet from IGS Global later years, during which time the effects of geody- Data Centers. Establishment of the Receiver Inde- namics would be revealed. Such experiments spurred pendent Exchange (RINEX) GPS standard measure- the development of analysis techniques to improve ment format [118] initiated this extensive inter- precision at the level required by geodynamics. Im- national data sharing in 1989 [119].

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While the IGS does not specifically carry out trasts with coordinates, which are frame dependent, geodynamics investigations, it does provide an essen- and therefore have secondary status. tial service without which geodynamics investiga- Since GPS orbits (see ORBIT DETERMINA- tions would be very costly and difficult to carry out. TION section) can be well modeled over an arc The 1990s has seen the development of collabora- length of a day (two complete orbits), we have access tions with specific geodynamics goals. Groups such to an instantaneous inertial frame (called an inertial as WEGENER [120, 121], UNAVCO, and the frame of date), which by definition, is the frame in Southern California Integrated GPS Network which Newton’s laws appear to be obeyed. Using (SCIGN) provide an umbrella for geoscientists using such an inertial frame, the system can therefore de- GPS geodesy as a tool. Such groups depend on IGS termine the direction of the instantaneous spin axis of for their success; conversely, IGS depends on such the earth (called the Celestial Ephemeris Pole (CEP)) users to justify its existence. with respect to the polyhedron. The direction of the The infrastructure has indeed become quite com- CEP, relative to the global station network, wanders plex, yet cooperative, and often with an efficient di- from one day to the next—a phenomenon known as vision between geodetic operations and geodynamics . Moreover, the rate of spin of the earth investigations. As a more recent example of how in- about its CEP can also be estimated. frastructure is developing, solutions are being ex- Finally, as discussed earlier, GPS is sensitive to changed in a standard Software Independent the location of the earth’s center of mass within the Exchange (SINEX) format to enable the construction geometrical figure of the polyhedron [127]. The of combined network solutions [122] and, therefore, earth’s center of mass is the dynamical origin of the combined global solutions for earth surface kinemat- force models used to compute the GPS satellite orbits ics [112]. Combination solutions have the advantage (see ORBIT DETERMINATION section). GPS geo- that (1) the processing burden is distributed among centric positioning is currently being used to correct many groups who can check each other’s solutions; records for land movement, so that long- (2) noise and errors are reduced through increased term -level change can be referenced to the earth’s redundancy and quality control procedures; (3) cov- center of mass [128]. erage and density are increased; and (4) regional In practice, residual station motions are esti- geodynamics can be interpreted in a self-consistent mated in a “free network” adjustment [124, 125], and global context. It appears that this decade (2000s) are then Helmert-transformed to a conventional will be focused on developing such combination so- frame [129]. For example, it is quite typical for lutions, and on the inversion of these solutions to in- global GPS results to be quoted with respect to the fer geophysical parameters [123]. ITRF [130]. In turn, ITRF depends on SLR to align its coordinate origin with the earth’s center of mass. GPS GLOBAL GEODESY—A MODERN Note that WGS 84, and hence the coordinate origin, PARADIGM has in recent years become aligned to ITRF (see OR- During the 1990s, a modern way of thinking BIT DETERMINATION section). In summary, GPS about GPS global geodesy [124, 125] has emerged global geodesy can well determine the shape and out of necessity, to assist a more confident interpreta- change in shape of the earth, as represented by a tion of geophysical signals [126]. From this view- global network of stations. It can also resolve polar point, we consider the GPS geodetic measurement in motion, rate of rotation, and to a lesser extent, the terms of the fundamental information content it can center of mass of the earth. These sensitivities pro- provide on global geodynamics, such as earth rota- vide the basis for GPS geodesy as a tool for various tion, earth center of mass, and deformation of the geodynamics investigations. The more predictable earth’s crust. aspects of earth motion—such as precession, nuta- Consider a network of GPS stations, tracking all tion, solid-earth , and the rigid-plate component the GPS satellites. Using the GPS data, we can esti- of plate tectonic movement—are often specified by a mate the geometrical figure defined by the stations conventional reference system, which can be further and the satellite orbits. That is, GPS provides infor- refined through observations using GPS and other mation on internal geometry—including the distances space geodetic techniques. between stations and the angles between baselines— and how these parameters vary in time. The elegant aspect of this geometrical picture is that it more SPACEBORNE GPS GEODESY closely relates to quantities that can actually be measured in principle, such as the time it takes for The first spaceborne GPS receiver system, called light to travel from one station to another. This con- the GPS Package [131], GPSPAC, was launched in July 1982 on the LANDSAT 4 satellite. Three more

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GPSPAC units were successfully launched: one on prove, in 1991 an international science panel LANDSAT 5 in March 1984 and two on DoD host recommended the pursuit of “technology develop- vehicle satellites in 1983 and 1984. While these units ments that lead to orbits of altimetric satellites with performed exceptionally well, geodetic applications no more than 1-cm RMS error” [135]. were limited due to the small number of GPS satel- lites in orbit at the time [132]. Spaceborne GPS ge- The first descriptions of POD at a level of deci- odesy started in earnest later in the 1980s. During meters or better by GPS were [136, 137], who exam- this period, the GPS techniques being devised for ined several DGPS tracking techniques. Since then, centimeter-level geodesy were adapted to provide refinements have been introduced that better exploit subdecimeter orbit accuracy for virtually any low sat- the unique signals and observing strength of GPS, ellite [133, 134]. Spaceborne geodesy is now grow- pushing POD performance close to 1 cm. The basic ing rapidly as more geodetic GPS receivers reach techniques are summarized briefly below. orbit. Here, we describe developments in four sub- categories, including POD, measurement of the Classical Dynamic Orbit Determination earth’s gravity field, ionospheric imaging, and indi- Conventional ground-based tracking systems rect enhancements to global geodesy and remote seldom provide coverage from more than one direc- sensing. tion at a time, and often provide no coverage. To supply the missing information for orbit determina- PRECISE ORBIT DETERMINATION (POD) tion, an orbit model must be fit to the tracking data. AND SPACE ALTIMETRY The most precise orbit estimation strategies employ Since the 1960s, the needs of earth remote sens- orbit models derived from detailed models of the ing, and in particular of space-based altimetry to forces acting on the satellite, a technique known as study circulation, have stimulated advances in dynamic orbit determination. POD. Examples of ocean altimetric satellites over The technique begins with a set of tracking the years include the U.S. (1978) and measurements along with models of the forces and (1985–1990); the European Remote Sensing satellites satellite mass. Those models yield a model of satel- (1991–); the U.S.-French TOPEX/Poseidon (1992–); lite acceleration over time, from which, by double in- and the French-U.S. Jason-1 mission, launched in tegration, a nominal or a priori trajectory is formed. December 2001. To produce the orbit solution, the two constants of in- The essential observable of space-based altim- tegration—the initial position and velocity—also etry is the height of the ocean surface, averaged over known as the epoch state, are estimated. the footprint, relative to the reference ellipsoid. Of principal interest are the systematic departures of Kinematic Orbit Estimation With GPS the ocean surface from the geoid—the surface of Continuous three-dimensional coverage from constant at —caused GPS allows us to discard detailed force models in a by the forces that drive ocean circulation. This sea- kinematic orbit solution. Force model errors yield surface , which consists of a quasi- distinct postfit residuals—that is, discrepancies be- permanent component reflecting the steady-state cir- tween the actual measurements and theoretical meas- culation and a variable component reflecting the urements based on the dynamic solution. Continuous time-varying circulation, is exquisitely subtle, with data from multiple GPS satellites permit us to con- typical amplitudes of less than a meter stretched over struct at every time point a full three-dimensional re- wavelengths of hundreds of kilometers. Modern sat- sidual vector between the dynamic solution and a ellite radar can measure the instantaneous position estimate based only on the measurements. height of the sea surface with respect to the We can thus assemble a complete observed trajec- with a precision of better than 2 cm, averaged over a tory, geometrically, from a dynamic solution and its footprint of several kilometers. But the height of the postfit residuals [138]. altimeter itself can vary by hundreds of meters around its orbit, confounding the translation of the al- Reduced Dynamic Orbit Estimation timeter range measurement to absolute sea surface In general, the kinematic solution is suboptimal. height. To extract the most from the altimetric data, We can often benefit by placing constraints on the es- we must therefore track the satellite’s absolute geo- timated corrections, consistent with the force model centric altitude continuously to a few centimeters as errors. And if the model errors are correlated be- well. Since orbit error is a limiting factor in ocean al- tween time points, we can benefit further by repre- timetry, and altimeter precision will continue to im- senting that correlation in the stochastic adjustment.

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More generally, we can model the force corrections solutions. Rapid-service IGS orbits are now avail- as colored (correlated) noise with a variance that re- able within hours of real time, permitting comparably flects the expected force model errors. If the variance fast, precise LEO solutions. JPL now distributes pre- and correlation model are chosen carefully, we can cise GPS orbits and clocks on an experimental basis fully exploit the dynamic information, while mini- over the Internet in real time. These are also avail- mizing the consequences of dynamic model error. able worldwide through Inmarsat. While these are at This reduced dynamic solution will, in general, yield present several times less accurate than IGS final or- the lowest overall error. Both versions effectively bits (1- to 2-week delay), they are adequate for deci- remove another altimetric bugaboo: geographically meter-level real-time POD [141]. As more real-time correlated orbit error, or error that is consistently ground sites are added, this will improve further. greater over regions (often the oceans) where the dy- Within years, a LEO satellite will be able to compute namic models are biased [139]. onboard a true real-time orbit with subdecimeter ac- curacy. GPS Orbit Improvement and TOPEX/Poseidon When users determine their positions from GPS Bistatic GPS Altimetry data collected by their own receivers, GPS ephemeris Spaceborne GPS receivers may one day perform and clock errors can enter at a level of several meters. altimetry directly by sensing GPS signals reflected In the early days of GPS POD by the scientific com- off the oceans and ice sheets, a technique known as munity (c. 1992–1996), this was dealt with by adopt- bistatic altimetry. Reflections received from low or- ing a global differential technique. A small global bit are weaker than direct signals by typically network of ground receivers, some at well-known lo- 40-50 dB. A spaceborne receiver with a high-gain cations, continuously tracks the GPS satellites. Data antenna can acquire reflected pseudorange data with from the orbiter and ground are then combined in a a precision of several decimeters after a few seconds grand solution for GPS and user orbits, some or all of averaging. (Ocean surface roughness generally ground positions, phase biases, receiver and satellite prevents the use of phase data.) While this is far clocks, and atmospheric delays. All positions are re- worse than the 2 cm of conventional altimeters, a covered in a consistent frame, and GPS orbits and single orbiter can observe up to a dozen reflections at clocks are removed as a direct source of error. As we once. A small constellation can cover the globe in a shall see later, the flight GPS data, in addition to pro- few hours, and in a few days can collect enough data viding the host satellite orbit solution, can considera- to average the height error to a few centimeters, with bly improve the solutions for the GPS orbits as well. a resolution of a few hundred kilometers, or several This grand solution technique was first demon- times better than TOPEX/Poseidon over ten days at strated in the early 1990s on TOPEX/Poseidon, the . This would make possible, for the first which carried a six-channel dual-frequency receiver. time, the detection and continuous observation of Because the kinematic solution eliminates dynamic eddy-scale circulation. error, it is independent of gravity model error. The Analysis has been performed recently at JPL of dynamic solution depends strongly on the gravity GPS reflections observed fortuitously by the Shuttle model and becomes limited by data noise and other Radar Lab-2 in 1995. This may be the founding errors only when gravity and other dynamic errors event of space-based bistatic GPS altimetry: the first are small. The reduced dynamic strategy offers op- carefully observed ocean reflection received from timum performance. The estimated actual RMS alti- space [142, 143]. The reflected signal provides a tude error achieved with GPS over the first year of measure of the range and of the scattering about the the mission fell to about 2.5 cm when the gravity specular point, which provides information on sur- model was tuned with GPS flight data at the Univer- face roughness and other quantities. To obtain ocean sity of Texas [140]. The error from gravity modeling height from reflected pseudorange, we must accu- on TOPEX/Poseidon is now believed to be well un- rately model the positions of the transmitter and re- der 2 cm. ceiver, and the effective reflection point [144]. Today, with the astonishing accuracy of the GPS orbit and clock solutions distributed by the IGS, this THE GEOID AND GRAVITY ESTIMATION grand solution strategy is no longer needed. IGS so- There is a second element to confound ocean al- lutions can be adopted without adjustment and pre- timetry: the geoid. Undulations of the geoid with re- cise low-earth orbit (LEO) satellite orbits can be spect to an ideal ellipsoid are on the order of 100 m, computed directly from the flight data alone, with lit- or 100 times those of the . Ac- tle or no performance penalty, vastly speeding POD curate knowledge of the geoid is therefore essential

18 Navigation, Journ. of the Inst. of Navigation, Vol. 49(1), 7-34, Spring 2002 to expose the permanent component of ocean circula- strategies were the rule in GPS geodesy, it is less so tion. Since the time of the first earth satellites, ob- today when high-quality IGS orbits are continuously servations of deviations in a satellite orbit from an available, and fewer users compute their own. It is ideal have been used to elaborate our models likely, however, that the IGS orbits, particularly the of the gravity field [145 – 147]. The more precisely rapid and real-time products, will improve further we can observe those variations, the more precisely when high-quality GPS data from multiple low orbit- we can reconstruct the field. It is the nature of the ers are routinely included in the solutions. gravitational potential that precise knowledge of the Apart from the indirect benefit of improved GPS gravitational signal for one orbit geometry does not orbits, spaceborne GPS provides unique value in de- termining the geocenter. Note that any earth satellite imply comparable knowledge for other geometries. follows a nominally-elliptical orbit with one focus at We therefore require tracking data from a variety of the geocenter. At present, the z component of the orbits to recover a general model of the global field. geocenter (the component along the spin axis) is less New satellites, including the U.S.-German Gravity well determined by ground-based GPS than the x and Recovery and Climate Experiment (GRACE) twin y components because the x-y solution is strongly spacecraft mission, carrying advanced GPS receivers aided by the earth’s rotation, while z must be inferred will permit useful improvement of current gravity only from the distant, slowly moving GPS satellites models. inclined at 55°. Data from swiftly moving low orbit- ers in highly inclined orbits will strengthen the z so- IONOSPHERIC IMAGING lution and help close the accuracy gap with x and y. Among the most anticipated ancillary benefits of spaceborne GPS is comprehensive three-dimensional imaging of the earth’s ionosphere. Apart from its in- THE FUTURE: GLOBAL, REAL- herent scientific interest, the ionosphere is of concern TIME, HIGH-PRECISION, GPS-BASED as an error source for single-frequency altimeters and POSITIONING SYSTEMS GPS users, and as a potentially disruptive influence on radio communications. Today’s two-dimensional GPS is now used extensively for orbit determina- global ionospheric maps derived from upward- tion by scientific and other earth satellites, and for looking, dual-frequency GPS ground data [148], many other science, government, and commercial while they have revolutionized ionospheric imaging, purposes around the world. GPS currently provides provide little useful information on the vertical struc- RTK positioning at the level of several meters, with ture. In contrast, spaceborne receivers directed to- the accuracy depending primarily on the accuracy of wards the earth’s limb will provide copious the broadcast GPS ephemerides and clocks, and on horizontal cuts, tracing out the vertical electron den- the quality of the observables in the user’s receiver. sity in surpassing detail. The combined space and The majority of GPS users will be well served by the ground GPS observations will provide enveloping present system, or by widely available commercial coverage [149, 150]. DGPS systems, which can provide moderate im- provements in real-time accuracy over prescribed lo- ANCILLARY BENEFITS FOR GPS GEODESY cal regions, perhaps to the level of one to a few Spaceborne data can provide other enhancements meters. However, a subset of users will continue to for GPS geodesy. Studies in the 1980s revealed that seek something more, both in geographical coverage data from a low orbiter could improve solutions for and in positioning accuracy. GPS orbits, ground positions (particularly the vertical The worldwide (global) commercial market for component), and the geocenter [151, 152]. Since precise real-time location devices, such as handheld ground receivers move at a rather stately pace with or in moving vehicles, is enormous. A triagency ef- respect to the GPS satellites, many hours (typically fort—involving NASA, NOAA, and DoD—to de- 24) of data are needed to compute GPS orbits of the velop a new generation of operational weather first quality. A low orbiter, by contrast, moves satellites is considering instruments that will require swiftly, with revealing dynamics, often seeing all real-time position knowledge to a few decimeters. In GPS satellites in less than 2 hr. These dynamically addition, various proposed free-flying space mis- and geometrically powerful data can sharply reduce sions—including microwave and laser altimeters, the time needed to obtain quality GPS orbits and im- synthetic aperture radar (SAR) mappers, and multis- prove their accuracy, with consequent benefits to de- pectral imagers—are seeking orbit accuracies ranging rived geodetic products. While this was of much from centimeters to one meter. While for many this interest at a time when grand, full-orbit solution performance is not needed in real time, the ability to

19 Navigation, Journ. of the Inst. of Navigation, Vol. 49(1), 7-34, Spring 2002 achieve such accuracy autonomously onboard could WADGPS—is moving towards initial operation to save greatly in the cost of ground operations. support a several-meter level of accuracy for general Many GPS science applications utilize terrestrial aviation navigation over the United States [153]. vehicles rather than earth orbiters. SAR imaging, to- Similar efforts are being planned in Europe, Asia, pographic mapping, , and other forms of and other locations. As noted above, a class of pro- remote and in situ sensing are carried out with bal- spective users—from satellites to aircraft to surface loons, aircraft, ships, buoys, and other vehicles. One vehicles—is emerging that will benefit from real- of the most stringent goals comes from airborne SAR time positioning accuracies, well surpassing what to- investigators, who wish to control aircraft flight paths day’s systems can deliver. This is an opportune time in real time to at least a meter, and eventually to a to evaluate future interests in precise real-time orbit few centimeters. Comparable goals apply to RTK determination and positioning, taking into account geodesy, which could be much simplified and readily the diversity of applications, performance require- extended to remote locations with global subdecime- ments, utility of current systems, alternative design ter positioning. A variety of mobile science instru- options, and relevant technologies that can now be ments worldwide could generate finished products in brought to bear. real time, ready for interpretation, with significant savings in data transmission and analysis costs. The scientific appeal of seamless worldwide positioning POTENTIAL OF GLOBAL WADGPS offering precise postprocessing performance in real Many GPS users require global coverage and the time can hardly be overstated. highest possible accuracy. Single frequency Table 1 lists some key categories of performance WADGPS systems do not meet these requirements. for real-time positioning with GPS. This discussion In contrast, with a dual frequency system, greater focuses on submeter positioning. The essential ele- accuracy is achievable and fewer reference sites are ments of a global-precision WADGPS are first dis- needed [154, 155]. This section discusses the issues cussed. The remainder of the paper then explores of accuracy and global coverage. means for obtaining the precise WADGPS perform- To provide global coverage, experiments were ance globally in real time, and without differential designed to take advantage of NASA’s GGN, which corrections, from a proposed extended global real- is operated and maintained by JPL. The GGN con- time GPS tracking system. sists of approximately 50 sites that are mostly oper- ated in batch mode over the Internet Table 1. GPS Performance Requirements (http://igscb.jpl.nasa.gov). To return data in real time a new software set called Real-Time Net Transfer Accuracy Technique Users and Applications was developed [156]. One-Hz phase and range ob- required, servables are returned over the open Internet using real-time User Datagram Protocol. More than 98% of the data 10 m — GPS, post- Satellite routine naviga- is returned in less than 2 s. Currently 18 global sites 1000 m processed, tion and stationkeeping are returning data in real time to JPL. Additional predicted to sites are being added. These new sites will increase real time the accuracy of the orbits and clocks, and also system 1 m — 5 m RTK; GPS; Precise satellite naviga- reliability by having redundant receivers in the refer- WADGPS tion; surveys; ence network. To address the issue of accuracy, the aircraft navigation; mili- system has been optimized for dual-frequency users. tary Both range and phase dual-frequency observables are < 10 cm Precision High-precision satellite used from geodetic reference receivers. The user’s global navigation; geodesy; software uses the phase observable, not to smooth the WADGPS high-precision surveys; range data, but as a basic data type in the user’s posi- aircraft takeoff and land- tioning filter, whose states include, along with the ing navigation; SAR, user’s position and clock, the necessary phase biases and precise earth map- and an optional slowly varying zenith troposphere pa- ping rameter. (Also see POSITIONING section) Tests in early 2000 of user positions show real-time, 8-cm RMS accuracy in the horizontal component and 20- WADGPS PERFORMANCE cm RMS accuracy in the vertical component [156]. Commercial WADGPS systems are now provid- These test results are for kinematic real-time user po- ing services nearly worldwide. Meanwhile, the U.S. sitioning on the ground. The user could be in princi- WAAS —a particularly ambitious example of ple moving on the ground or airborne, and the

20 Navigation, Journ. of the Inst. of Navigation, Vol. 49(1), 7-34, Spring 2002 accuracy should be similar (an airborne user might vances in global WADGPS. This accuracy experience a small improvement in accuracy from improvement will soon change the entire character of elimination of some tropospheric effects) virtually GPS applications, ranging from commercial, to scien- anywhere in the world. To achieve these break- tific, to military. It is only fitting that this remarkable through results, GPS orbits had to be generated in change in the GPS landscape was achieved for the real time, accurate to 30–40 cm. Such positioning re- first time using the Internet, which has itself often sults are about an order of magnitude better than been blamed for the apparent acceleration of the pace typically available from either the broadcast ephem- of life in general and of data communications, result- eris or from commercial DGPS providers. ing in a sort of compression of the world. Real-time In order to achieve GPS-based, high-accuracy user positioning on the ground and in space will (10-cm level) positioning in real time for terrestrial probably be ultimately limited by GPS signal noise, users that are situated below the atmosphere, one user equipment noise, and multipath. For orbiting must develop a methodology for determining tropo- users, the quality of dynamic models and multipath path delays to the 1-cm level. This, in fact, are likely to limit the accuracies achievable. Obvi- has now been demonstrated [156, 157], which places ously, dynamic models are worse for lower , the responsibility for exploiting this rich data set but at this time, it is not clear where these errors will firmly in the hands of the meteorologists. The ad- eventually cause performance to bottom out. It is vancement of large-scale dense networks of GPS re- possible that within the coming decade, ground, air- ceivers—including several that are operating in borne, and space users will routinely have knowledge Japan, SCIGN and, most recently, Suominet—has the of position to several centimeters in real time. One potential to significantly augment existing sparse ra- thing has been clear: based on past history, GPS re- diosonde networks and provide meteorologists with searchers can be expected to continue to surpass even enhanced observations of atmospheric the most aggressive future projections for accuracy [158, 159] to improve weather forecasting and enable and performance. detailed studies of climate and hydrology. The de- velopment and deployment of such networks of re- ceivers contributing to these applications is a CONCLUSION dramatic example of enabling science through tech- nology advances. Developments in GPS geodesy have been fun- For real-time onboard positioning and orbit de- damental to many of the improvements in GPS over termination a satellite would require flight software the past decades. Geodesy has set the highest accu- with the necessary orbit models, estimator, and racy requirements and has motivated many of the en- propagator. A version of such software can be em- hancements to both equipment and software. These bedded in an onboard GPS receiver or processor to improvements allowed the GPS user to enjoy the ad- support this capability. For high-precision, real- vantages of more accurate measurements and proc- time positioning in space, the availability of a global essing, orbit determination, tracking site positioning, DGPS system is essential, as the spaceborne user re- and WGS 84 reference frame definition. quires global coverage. Local or regional systems Three generations of improved geodetic receiv- (such as WAAS or various commercial systems) do ers provided the basic tools to allow GPS geodesy not provide global coverage. and software developments to flourish. In addition to A new era of GPS-based positioning for high- the standard pseudorange measurement, dual- precision GPS users has been entered, either in LEO frequency receivers provided the very accurate inte- or in near-earth and/or ground applications. As dis- grated carrier-phase measurement, with all measure- cussed above, a demonstration has shown that ground ments synchronized to occur at prescribed GPS user positioning can potentially be achieved with a times. These measurements were applied through global wide-area differential system at the level of sophisticated techniques to achieve positioning accu- 8 cm (horizontal) to 20 cm (vertical) in real time. For racy well beyond the capabilities of the pre-GPS era. this demonstration, inexpensive Internet links were Improved positioning and timing accuracy was used for data communications. In earth orbit, such accomplished incrementally. Concurrent to equip- kinematic capability would translate into 5-cm accu- ment improvement was a better understanding of the racy for real-time orbit accuracies at 1300-km alti- measurements and their associated errors. Initial ca- tude, and about 10-cm orbit accuracies (real time) at pabilities for short-baseline static and kinematic sur- 500-km altitude, for which Kalman filtering can be veying were extended to long baselines and then employed. global networks. Simultaneously, orbit determination Real-time GPS accuracy is catching up to non- continuously improved, reducing satellite position er- real time GPS accuracy through recent dramatic ad- rors several orders of magnitude from the early years.

21 Navigation, Journ. of the Inst. of Navigation, Vol. 49(1), 7-34, Spring 2002

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