high-precision, kinematic positioning with a single gps receiver

INTRODUCTION

A primary application of GPS is the precise (fewcentimeter– to few decimeter– level) positioning ofa myriad of differing user platforms over a broadspectrum of environments, on and above the earth’ssurface. Current processing techniques rely on rela-tive positioning between receivers, carrier-phaseambiguity resolution, differential receiver correc-tions, or spatial interpolation of receiver networkinformation, implemented in dynamics-tuned filter-ing schemes, to greatly improve position accuracyover that provided by the GPS Standard PositioningService.

The potential of point positioning is that it caneliminate these cumbersome aspects of GPS position-ing for many applications. We have devised a novelpostprocessing approach that obviates the need forthese techniques by using data from only the usergeodetic-grade (dual-frequency) GPS receiver andproducts of the International GPS Service (IGS). Thisapproach is not adversely affected by the decorrela-tion of biases in relative or differential positioning,unresolved phase ambiguities, spatial interpolationerrors, or assumptions regarding platform dynamics,and requires only the tacit assumption of sufficientGPS signals for positioning.

In the following sections, point positioning andpseudorange and carrier-phase processing are dis-cussed. Our single-receiver, platform-independentprocessing strategy is then described. A number oftests with terrestrial, airborne, and spaceborne dataare discussed, conclusions are given, and plans forfuture research are described.

POINT POSITIONING

The original intent for GPS usage was single-receiver, real-time, pseudorange-based positioning. Asis well known, this original design has been alteredand enhanced by the use of carrier-phase observables,relative positioning, and differential positioning onlocal and wide-area scales. In recent years, someresearchers have once again turned their attention topoint positioning. With the proliferation of regionaland global networks of geodetic-grade GPS receivers,such as the IGS network (see, e.g., [1]), precise GPSsatellite orbits, and in some cases precise satelliteclock offset estimates, derived from such networkshave been used to produce precise positioning resultswith a single receiver. Mathematically, the GPS satel-lite ephemeris and clock parameter errors can bemodeled from these estimates and the associatedorbit and clock terms eliminated from the positioningfunctional model.

Work in this area first centered on pseudorange-based positioning (e.g., [2, 3]), and more recently has

161

High-Precision, Kinematic Positioning witha Single GPS Receiver

SUNIL B. BISNATH and RICHARD B. LANGLEYUniversity of New Brunswick, Fredericton, New Brunswick, Canada

Received September 2001; Revised November 2002

ABSTRACT: The goal of the research described in this paper is the design of a GPS data processing techniquecapable of producing high-precision positioning results, regardless of platform dynamics, utilizing only a single,high-quality receiver. This goal is accomplished by combining two processing philosophies: point positioning, whichmakes use of precise GPS constellation ephemeris and clock offset information to estimate a single receiver’s state;and carrier-phase– filtered pseudorange processing, in which pseudorange-based positioning is supplementedwith carrier-based position-change information. Results derived with the developed software indicate that near-decimeter-level positioning accuracy is attainable for a variety of platforms, ranging from static, terrestrial refer-ence stations, to aircraft, to satellites. A number of modeling improvements can be applied to the existing software,and testing in the real-time environment is planned.

NAVIGATION: Journal of The Institute of NavigationVol. 49, No. 3, Fall 2002Printed in the U.S.A.

focused on pseudorange and carrier-phase process-ing (e.g., [4–6]). The carrier-phase strategies haveinvolved estimation of the receiver state, undiffer-enced phase ambiguities, and other parameters.

In our approach, we have avoided the ambiguityestimation process by utilizing adjacent-in-time dif-ferenced phase measurements. That is, the phaseobservable used represents the present epoch’sphase measurement minus the previous epoch’sphase measurement for each GPS satellite. Thisapproach represents a form of phase-smoothedpseudorange positioning. The rationale for such aformulation, as will be seen, is to eliminate the needfor dynamic modeling of the platform.

CARRIER-PHASE–FILTERED PSEUDORANGEPROCESSING

A number of researchers have proposed and/ordeveloped such carrier-phase–filtered pseudorangeprocessing techniques. The basic form of these tech-niques can be attributed to the seminal work of [7].The crux of carrier and pseudorange combination isthe use of averaged noisy code-phase range meas-urements to estimate the ambiguity term in the pre-cise carrier-phase range measurements. The longerthe pseudorange averaging, the better the carrier-phase ambiguity estimate will be. By performing thefiltering in the positioning domain rather than inthe measurement domain, changes to the trackedsatellite constellation have little effect as long as acontinuous filtered solution is possible. In essence,the pseudoranges provide coarse position estimates,and the relative carrier-phase measurements pro-vide precise position change estimates. The positionchange estimates are used to map all of the positionestimates to one epoch for averaging.

Similar processing filters with a relative positioningformulation have been described by several authors.In [8], the technique is developed for marine applica-tions utilizing the double-differenced pseudorangeand carrier-phase observables and the GPS broadcastephemerides in a sequential, least-squares processor.In [9], this type of filter is proposed for the purpose ofgeometric GPS-based low earth orbiter (LEO) orbitdetermination. However, this strategy was abandonedfor other methods, since at the time a global array ofterrestrial GPS reference stations did not yet exist toprovide sufficiently precise GPS ephemerides andclock estimates. A Kalman filter–based version of thisalgorithm is developed in [10].

PHASE-CONNECTED, POINT POSITIONINGFILTER DESIGN

We have proposed this form of dynamics-freeprocessing for single-receiver processing, utilizingonly readily available IGS data products and mobile

receiver measurements [11]. The term “dynamics-free” is used to indicate that no modeling of vehicledynamics is performed other than the measuring ofmotion with the precise change-in-phase observable.This approach provides for highly efficient, straight-forward processing and takes full advantage of theprecise, three-dimensional, and continuous natureof GPS measurements, as well as the existing GPSdata infrastructure.

The processing flow of the strategy is shown inFigure 1. The input pseudorange and carrier-phasedata are preprocessed to detect outliers, cycle slips,and so on, and then used to form the processingobservables. The mobile receiver position is thenestimated with the filter described in the followingsection. If necessary, an accurate interpolation pro-cedure can be applied to provide the mobile receiverstate estimates at non–GPS-measurement epochs.

The observables fed to the filter are the ionosphere-free, undifferenced pseudorange and the ionosphere-free, time-differenced carrier phase. These linearcombinations of the dual-frequency pseudorange andcarrier-phase observables remove the vast majority ofionospheric delay/advance while marginally increas-ing the combination noise. For point positioning,a number of additional modeling considerations must be taken into account above and beyond those required for relative positioning (see, e.g., [4, 6]).These considerations include the relativistic GPSsatellite clock correction due to the eccentricity in thesatellite orbits, GPS satellite antenna phase center tocenter of mass offset, GPS satellite phase wind-up dueto the relative rotation of the satellites with respect tothe receiver, subdiurnal variations in the earth’s rota-tion, solid earth tides, ocean loading, and consistencybetween the models used in generating the preciseGPS orbits and clocks and those used in the pointpositioning processing.

FILTER MODELS AND SOLUTION

The linearized filter observation model in matrixform is

� Pt � Pt0

��t � ��t0� � � 0

� At�1

At

At��xt�1

�xt� � � et

�t�1,t�;

162 Navigation Fall 2002

Fig. 1–Data Processing Flowchart of Strategy

(1)

where Pt and are the pseudorange measurementand predicted value, respectively; ��t and arethe time-differenced carrier-phase measurement andpredicted value, respectively; �xt�1 and �xt are theestimated corrections to the receiver position andclock at epochs t � 1 and t, respectively; At�1 and At

are the measurement partial derivatives with respectto the receiver position and clock estimates for epochst � 1 and t, respectively; et and �t�1 are the measure-ment errors associated with Pt and ��t, respectively;and and are the covariance matrices for Pt

and ��t, respectively. Note that the pseudorange andcarrier-phase measurements are in units of meters,and at present are assumed uncorrelated betweenobservables and between observations.

Since the troposphere is a significant contributorto the GPS error budget for platforms within thetroposphere, the UNB3 tropospheric predictionmodel [12] is used. The omission of residual zenithdelay estimation causes, on average, approximatelyfew centimeter– level biases in the position esti-mates. Improved positioning results will be obtainedwith such estimation.

Another error source not explicitly accounted for inour model is pseudorange multipath. To mitigate theeffect of this phenomenon (see [13]), a variant of thepseudorange minus carrier-phase linear combinationis used to estimate the pseudorange multipath plusnoise variance. These variances are used to constructmore realistic pseudorange stochastic models.

The best solution for equation (1), in a least-squares sense, is

(2)

where (the estimate is equal to theapproximate initially assumed value plus the esti-mated correction); wP and w�� are the misclosure(prefit residual) vectors for the pseudoranges andtime-differenced carrier phases, respectively; and

is the receiver position and clock covariancebased on the last epoch’s observations.

As can be seen, the position estimate at the pre-vious epoch, t�1, is used to estimate the position atepoch t and so on for the moving platform. Equa-tion (2) represents a kinematic, sequential least-squares filter. This filter is a special case of theKalman filter. Simply put, from equation (1) thepseudorange measurement contribution

(3)

can be extracted along with the carrier-phase meas-urement contribution

CPt

Pt � Pt0 � At�xt�et;

Cxt � 1

x̂ � x0��x

�� ATt�1C�1

��tw��

A"t C�1

PtwP�AtC�1

��tw��

��x̂t�1

x̂t��x̂0

t�1

xt0 ��AT

t�1C�1��t

At�1�C�1xt�1

� ATt C�1

��tAt�1

�ATt�1C�1

��tAt

AtT(C�1

pt�C�1

��t)At

��1

C��tCPt

��t0

Pt0

CPt, C��t

(4)

The terms in equation (3) can be mapped directlyto those of the Kalman filter measurement model,and with some rearrangement, the terms in equa-tion (4) can be effectively related to those of theKalman dynamic model. That is, the kinematic,sequential least-squares tracking filter behaves likea Kalman filter because the carrier-phase measure-ments represent its dynamic model. The filterprocess is illustrated in Figure 2.

Finally, since this tracking strategy is carried outafter the fact and not in real time, data smoothingcan be performed. That is, the data arc can beprocessed in the forward and backward directions,and the results can be optimally combined. Thesmoothed solution is

(5)

where is the smoothed parameter estimate, isthe forward filter parameter covariance, is the for-ward filter parameter estimate, is the backwardfilter parameter covariance, and is the backwardfilter parameter estimate [14]. This is a fixed-intervalsmoother in which the trace of the smoothed param-eter covariance matrix is smaller than the trace of thecovariance matrices of either filter.

DATA TESTING AND ANALYSIS

To validate the viability and performance of thisstrategy, a number of tests were conducted using thelatest version of the developed processing software.This software is based on the University of New

x̂bt

Cbt

x̂ft

Cftx̂st

x̂st� C�1

ftx̂ft

�C�1bt

x̂bt

C��t

��t��0t � �At�1�xt�1�At�xt�#t�1,t;

Vol. 49, No. 3 Bisnath et al.: High-Precision, Kinematic Positioning with a Single GPS Receiver 163

Fig. 2 – Combination of Pseudorange and Carrier-PhaseObservations in the Kinematic, Sequential Least-Squares Filter

Brunswick’s scientific GPS processing packageDIPOP [15] and implemented in the form of acompiled preprocessor and main processor. Eventhough the code was not designed to be optimal interms of processing speed, all of the results presentedhere were generated in minutes. Where applicable,mention is made of additional processing or modelingthat, with future development, can improve the accu-racy of the results.

To illustrate the platform-independent nature ofthe technique, three widely varying types of datawere processed: terrestrial, airborne, and space-borne. The only common (and required) characteris-tic of these datasets is that they were collected withgeodetic-grade receivers — that is, the receiverswere capable of measuring high-quality pseudo-range and carrier-phase dual-frequency observ-ables. The only other data used in the processingwere the requisite IGS precise GPS constellationorbit and high-rate GPS constellation clock offsetproducts. No alterations were made to the mainprocessor code to favor any one data type; the pro-cessing was of a completely generic nature.

Static, Terrestrial Data Testing

The objective of the testing with static terrestrialdata was to investigate the repeatability of positioncomputations with the technique and to test the per-formance of the technique against positioning resultsderived from the highest-quality geodetic techniques.The data used for this testing were collected over a1 day period on February 5, 2001, at NaturalResources Canada (NRCan) station Algonquin (IGSstation identifier ALGO) in Algonquin Park, Ontario,Canada (latitude 46° N, longitude 78° W). Note thatthe dataset was chosen at random. The NRCan pre-processed TurboRogue BenchMark receiver outputcontains measurements with a 30 s sampling intervaland a 10 deg elevation mask angle.

As mentioned previously, the currently unesti-mated residual tropospheric delay could cause fewcentimeter– level errors in the position domain. Thereceiver position and clock were estimated at thedata sampling interval, and the result was a satel-lite clock modeling error—a few centimeters at themost—arising from interpolating the 300 s intervalIGS satellite clock product. Finally, neither varia-tions in earth orientation nor carrier-phase wind-upwas accounted for. These components can also pro-duce centimeter-level errors in position, and will bemodeled in the near future.

Since this technique relies solely on GPS observa-tions, the first aspect of the processing to be analyzedwas the geometric strength of the measurementsused. Figure 3 shows the number of satellites trackedand the position dilution of precision (PDOP). As canbe seen, there are always at least 5 satellites being

tracked in this dataset and on occasion up to 10. Theaverage number for the processed data is 7.3. ThePDOP typically remains between 1.5 and 3, but a fewspikes exist where the PDOP reaches approximately4.5 and 6. The average PDOP is 2.2. Given that thereis a 10 deg elevation mask angle, these values arereasonable and represent geometrically strong mea-surements. However, given the complete reliance onmeasurements, low-elevation-angle data, e.g., downto 5 deg, would have aided in the improved accuracyof the position results.

The results of the processing are presented inFigure 4. The error values are computed by differ-encing the estimated position from the benchmarkInternational Earth Rotation Service (IERS), epoch-of-date, International Terrestrial Reference Frame1997 (ITRF97) coordinates. These benchmark coor-dinates are known to better than 1 cm [1]. As can beseen, the error in each component reaches a maxi-mum of 50 cm. The error fluctuates the most in thevertical component. This is expected, given the factthat the residual tropospheric delay was not esti-mated, as well as the inherent limitation due to theGPS constellation geometry.


Fig. 3–Number of Space Vehicles (SVs) and Position Dilution ofPrecision (PDOP) for Static, Terrestrial Dataset

Fig. 4–Component Errors in Smoothed Position Estimates forStatic, Terrestrial Dataset

Summary statistics for this dataset are given inTable 1. The root mean square (RMS) of thesmoothed solution is 15 cm in each horizontal com-ponent and 20 cm in the vertical component. Thesmoothed total displacement RMS is just under30 cm. Also of note are the few-centimeter– levelbiases that exist in the horizontal components.Given that the residual tropospheric delay and thesubdaily earth rotation variations were not appliedand that the GPS satellite orbits and clocks wereinterpolated to 30 s, these results compare favorablywith other published single-receiver processingresults (e.g., [6]), which show high accuracies. Wepoint this out since such other published techniquesinclude dynamic information to constrain the solu-tion space—in the case of [6], process noise valuesindicating stationary position.

The forward filter residuals (observations minusmodeled values), along with the associated GPSsatellite elevation angles, are shown in Figure 5.The large initial ionosphere-free, time-differencedphase values are due to filter initialization. Theionosphere-free pseudorange RMS is 66 cm withpeak-to-peak variations of 10 m, and the phaseobservable RMS is 2 cm with peak-to-peak varia-tions of 15 cm, aside from the initialization period,which is typically less than 20–30 min. These val-ues appear to be reasonable for the particular linearcombinations of the pseudorange and carrier-phasecombinations they represent.

Airborne Data Testing

The next test illustrates the performance of theprocessing technique for a receiver on a kinematicplatform—a small airplane in level flight in the vicin-ity of Sendai Airport, Japan, on December 5, 2000.Figure 6 depicts the complete trajectory for theapproximately 2 h flight. The cross pattern ofthe flight path indicates that the aircraft reached amaximum horizontal distance of over 50 km from thecross-over area (Sendai Airport), at which is located areference receiver that was used for conventionalkinematic, relative carrier-phase processing. The con-ventional solution was obtained with commercial soft-ware, using automatic processing parameter settings.

Measurement interruption is a casualty of suchlevel, straight flights with banking turns. As can beseen in Figure 7, the number of tracked satellites isreduced to five or four when the aircraft banks. Theactual number can be lower, but data when fewerthan four SVs are being tracked are not displayed inFigure 7. The average number of tracked SVs duringthe flight was 6.7. The associated spikes in the PDOPare more acute in this case, since not only is thenumber of SVs reduced, but their sky distribution isnot uniform. Hence, even though the mean PDOP is


Table 1—Summary Statistics (in cm) ofComponent Errors in Smoothed PositionEstimates for Static, Terrestrial Dataset

Component Bias Std. Dev. RMS

North 4.4 13.9 14.5East �4.3 14.2 14.8Up 0.6 19.8 19.83-D 6.2 28.0 28.7

Fig. 5–Forward Filter Observable Residuals and AssociatedSatellite Elevation Angles for Static, Terrestrial Dataset

Fig. 6–Airborne Dataset Trajectory

Fig. 7–Number of SVs and PDOP for Airborne Dataset

a respectable 2.4, there are PDOP spikes over 4during nearly every turn the aircraft makes. Thishas a significant effect on both the reference double-differenced solution and our single-receiver solution.

Figure 8 shows the differences between the twosolutions for one straight-line section of the flight.Table 2 contains summary statistics on the componentdifferences between the two solutions for this period.The horizontal components show 50 and 70 cm biasesin the north and east components, respectively, withstandard deviations of 5 cm or less. The up componenthas a nearly 1 m drift, causing a 30 cm standard devi-ation but very little bias. One possible explanation forthe biases and drift is the use of incorrect double-differenced ambiguities in the commercial softwaresolution. This appears to be a strong possibility for anumber of reasons. First, incorrect ambiguities canproduce such offsets and drifts. Second, offsets anddrifts were observed between the commercial solutionused and another commercial result. And third, suchlarge biases have not been observed with any otherdataset processed with our technique. These resultsindicate another possible use for this technique—theavoidance of incorrectly determined phase ambigui-ties for long-baseline kinematic datasets.

Spaceborne Data Testing

Spaceborne data is unique for a number of rea-sons. The very high velocity and upper atmospheretrajectory of the platform carrying the receiver

means that the tracked GPS satellites change con-stantly; there is no tropospheric delay on thereceived signals; high-fidelity dynamic models aretypically required for accurate position and orbitdetermination (especially for LEOs); and if preciseGPS/dynamic orbits have been determined for thesatellite, this data type provides an excellent oppor-tunity for evaluation of mobile receiver positioningalgorithms.

The spaceborne GPS dataset processed here con-sists of 3 h of data [16] from the CHAllengingMinisatellite Payload (CHAMP), collected onJanuary 5, 2002. This LEO initially orbited at anominal altitude of 450 km with an approximateperiod of 90 min, and provides dual-frequencypseudorange and carrier-phase data from a JetPropulsion Laboratory (JPL) BlackJack receiver.Figure 9 shows a typical ground track of the near-polar orbiting spacecraft.

The data provided by the CHAMP Data Centerare unprocessed and provided at 10 s intervals.During initial operation of the CHAMP receiver, noelevation mask angle appears to have been applied,as angles as low as �10 deg were observed. Thesevery low-elevation-angle measurements also havevery low signal-to-noise ratio (SNR) values (inBlackJack SNR units). It was found that using thesemeasurements produced large phase residuals, andan SNR rather than an elevation angle cutoff wasapplied in our data preprocessing in an attempt toremedy the situation. The cutoff used in this pro-cessing was 10 units. Processing of such an initialdataset resulted in solutions with significant gapsand spikes due to the lack of quality phase meas-urements [17]. Similar results were obtained by theUniversity of Berne using a comparable pseudo-range/changing-in-phase, point positioning process-ing approach [18].

Fortunately, this low-elevation-angle data waspresent in the 2001 datasets and not the 2002datasets. Apparent changes to the BlackJack GPSsatellite tracking algorithm have meant that thereceiver no longer tracks to such low elevationangles, increasing the amount of high-quality,


Fig. 8–Component Differences in Smoothed Position Estimatesfor Airborne Dataset

Table 2—Summary Statistics (in cm)of Component Differences in SmoothedPosition Estimates for Airborne Dataset

Component Bias Std. Dev. RMS

North 50.3 5.7 50.1East 69.1 3.0 69.3Up 7.4 33.4 34.83-D 85.8 34.0 92.3

Fig. 9–Ground Track of CHAMP Dataset

higher-elevation data that can be logged with theavailable tracking channels. This situation greatlyimproves the quality and availability of GPS-only–based orbit solutions.

The purpose of processing these test data was toinvestigate the geometric strength of the spacebornemeasurements and to assess the practicality andperformance of the technique against high-qualityCHAMP orbits. Figure 10 shows that the geometricstrength of the available observations is somewhatlower than that of the terrestrial dataset weanalyzed. This occurs even though the BlackJackreceiver can track up to eight GPS satellites fororbit determination, but data editing removes a por-tion of these measurements. The average number oftracked satellites is seven. However, the distributionof these tracked satellites causes occasional signifi-cant degradation of measurement strength. Themean PDOP is 2.6, or almost 20 percent larger thanthat for the terrestrial dataset we processed. It mustbe noted that a relatively good dataset is presentedhere, and periods of sparser data exist in the post-edited 2002 measurement files.

Figure 11 shows the orbit position componentdifferences of our smoothed pseudorange/carrier-

phase solution compared with the GPS-based JPLreduced dynamic orbit. Of the three position compo-nent differences, the radial contains the greatestvariation. For CHAMP, the radial component repre-sents the vertical direction, and as with all GPSstand-alone positioning techniques, the verticalcomponent is resolved at a lower resolution becauseof the GPS constellation geometry. Table 3 containssummary statistics for the comparison. Note thatthe bias between solutions is quite small—a fewcentimeters; the along-track and cross-track compo-nents have been resolved to the decimeter level; andthe radial component has been resolved to the 20 cmlevel. These difference statistics are judged to bevery good, considering that the position accuracy ofthe reduced dynamic orbit is on the order of 5 to10 cm for each component [19]. That is, the phase-connected point positioning results have an RMSalmost as low as that of the benchmark solution.

Figure 12 depicts the forward filter observableresiduals and associated GPS satellite elevationangles. The ionosphere-free pseudorange RMS is 54cm, and the ionosphere-free, time-differenced phaseRMS is 1.2 cm. These results compare favorablywith those from the terrestrial dataset, indicatinghigh-quality observations that fit well with themathematical and stochastic models. The spikes inthe phase residuals represent remaining measure-ment outliers and filter reinitialization events due


Fig. 10–Number of SVs and PDOP for CHAMP Dataset

Fig. 11–Component Errors in Smoothed Position Estimatesfor CHAMP Dataset

Table 3—Summary Statistics (in cm)of Component Differences in SmoothedPosition Estimates for CHAMP Dataset

Component Max. Bias RMS

Radial 61.8 3.3 21.9Along 34.5 �1.7 12.8Cross 29.4 �2.6 9.9Norm 63.8 24.3 27.2

Fig. 12–Forward Filter Observable Residuals and AssociatedSatellite Elevation Angles for CHAMP Dataset

to insufficient numbers of change-in-phase mea-surements. The fact that the RMS values are lowerfor the spaceborne than for the terrestrial data isindicative of the precision of the BlackJack observ-ables and the lack of observed tropospheric delay inthe CHAMP environment.

CONCLUSIONS

A postprocessing, platform-independent, single-receiver positioning strategy based solely on GPSmeasurements has been devised that is straightfor-ward, efficient, and fast. The strategy incorporates akinematic, sequential, least-squares filter/smootherthat utilizes the full potential of the GPS measure-ments and makes use of readily available GPS dataproducts. As a by-product of the technique’s design,its dynamics-free nature allows it to be applied toany platform where sufficient GPS measurementsare available.

Static, terrestrial testing results indicate thatnear decimeter-level position component RMS andfew centimeter-level position component bias areattainable. These results are seen as promising asthere are a number of improvements that have yetto be made in our software. Airborne results arefavorable as well, and perhaps indicate possiblerisks in long-baseline kinematic phase processing.The spaceborne data testing also indicates neardecimeter-level position component RMS. Given allof our test results to date, the goal of decimeter-levelposition component accuracy is seen as attainable.

FURTHER RESEARCH

A number of additional processing and modelingcapabilities are required to refine the present strat-egy and allow for the most accurate position esti-mates: modeling of subdaily earth rotation, phasewind-up, and residual tropospheric delay estima-tion. In terms of data processing, more datasetsneed to be processed to examine the repeatability ofthese results and expand the processing capabili-ties of this technique. Finally, predicted IGS GPSorbits and clocks could be used to attempt real-timeprecise point positioning. It should be noted thatJPL has developed such a real-time capability withits variant of precise point positioning [20], and acommercial service implementation of thisapproach is presently being offered by NavComTechnologies, Inc. [21].

ACKNOWLEDGMENTS

This research was conducted under a grant fromthe Natural Sciences and Engineering ResearchCouncil of Canada. The authors would like to thankthe International GPS Service (IGS) for providing

the Algonquin Park dataset and all of the preciseGPS satellite ephemerides and clock offset files; theElectronic Navigation Research Institute, Japan, forproviding the airborne dataset; the CHAMP DataCenter, GeoForschungsZentrum, Germany, forproviding the spaceborne dataset; and the JetPropulsion Laboratory, California, for providing thebenchmark spaceborne data orbits.

Based on a paper presented at The Institute ofNavigation’s ION GPS-2001, Salt Lake City, Utah,September 2001.

Sunil Bisnath is now at The University of SouthernMississippi, Stennis Space Center, Mississippi.

REFERENCES

1. Neilan, R. E., J. F. Zumberge, G. Beutler, and J. Kouba,The International GPS Service: A Global Resource forGPS Applications and Research, Proceedings of TheInstitute of Navigation’s ION GPS-97, Kansas City,MO, September 16–19, 1997, pp. 883–89.

2. Héroux, P. and J. Kouba, GPS Precise PointPositioning with a Difference, Presented at Geomatics’95, Ottawa, Ontario, June 13–15, 1995.

3. Gao, Y., J. F. McLellan, and M. A. Abousalem, Single-Point GPS Accuracy Using Precise GPS Data, TheAustralian Surveyor, Vol. 42, No. 4, 1997, pp. 185–92.

4. Zumberge, J. F., M. B. Heflin, D. C. Jefferson,M. M. Watkins, and F. H. Webb, Precise PointPositioning for the Efficient and Robust Analysis ofGPS Data from Large Networks, Journal ofGeophysical Research, Vol. 102, No. B3, 1997, pp.5005–17.

5. Han, S.-C., J. H. Kwon, and C. Jekeli, AccurateAbsolute GPS Positioning Through Satellite ClockError Estimation, Journal of Geodesy, Vol. 75, No. 1,2001, pp. 33–43.

6. Kouba, J. and P. Héroux, Precise Point PositioningUsing IGS Orbit and Clock Products, GPS Solutions,Vol. 5, No. 2, 2001, pp. 12–28.

7. Hatch, R., The Synergism of GPS Code and CarrierMeasurements, Proceedings of the Third InternationalGeodetic Symposium on Satellite Doppler Positioning,February 8–12, Las Cruces, NM, 1982, pp. 1213–32.

8. Kleusberg, A., Kinematic Relative Positioning UsingGPS Code and Carrier Beat Phase Observations,Marine Geodesy, Vol. 10, No. 3/4, 1986, pp. 257–74.

9. Yunck, T. P., S.-C. Wu, and J.-T. Wu, Strategies for Sub-Decimeter Satellite Tracking with GPS, Proceedings ofIEEE Position, Location, and Navigation Symposium1986, Las Vegas, NV, November 4–7, 1986, pp. 122–28.

10. Quiles-Blanco, A. and M. Martin-Neira, PerformanceComparison Between a Dynamic-Free Navigation Filterand the Carrier Smoothing Algorithm, Proceedings ofThe Institute of Navigation’s ION GPS-99, Nashville,TN, September 14–17, 1999, pp. 1597–1607.

11. Bisnath, S. B. and R. B. Langley, Precise OrbitDetermination of Low Earth Orbiters with GPS PointPositioning, Proceedings of The Institute ofNavigation’s National Technical Meeting, LongBeach, CA, January 22–24, 2001, pp. 725–33.


12. Collins, J. P., Assessment and Development of aTropospheric Delay Model for Aircraft Users of theGlobal Positioning System, M.Sc.E. Thesis, Departmentof Geodesy and Geomatics Engineering, TechnicalReport No. 203, University of New Brunswick,Fredericton, New Brunswick, 1999.

13. Bisnath, S. B. and R. B. Langley, PseudorangeMultipath Mitigation by Means of MultipathMonitoring and De-Weighting, Proceedings of theInternational Symposium on Kinematic Systems inGeodesy, Geomatics and Navigation 2001, Banff,Alberta, Canada, June 5–8, 2001, pp. 392–400.

14. Gelb, A. (ed.), Applied Optimal Estimation, Mas-sachusetts Institute of Technology Press, Cambridge,MA, 1974.

15. Kleusberg, A., Y. Georgiadou, F. van den Heuvel, andP. Héroux, GPS Data Preprocessing with DIPOP 3.0,internal technical memorandum, Department ofSurveying Engineering (now Department of Geodesyand Geomatics Engineering), University of NewBrunswick, Fredericton, 1993.

16. GFZ, CHAMP Home Page, http://op.gfzpotsdam.de/champ/index_CHAMP.html, accessed January 2001.

17. Bisnath, S. B. and R. B. Langley, High-PrecisionPlatform Positioning with a Single GPS Receiver,Proceedings of The Institute of Navigation’s IONGPS-2001, Salt Lake City, UT, September 11–14,2001, pp. 2585–93.

18. Bock, H., G. Beutler, and U. Hugentobler, KinematicOrbit Determination for Low Earth Orbiters (LEOs),Proceedings of the International Association ofGeodesy 2001 Scientific Assembly, Budapest Hungary,2001.

19. Kuang, D., personal communication, Jet PropulsionLaboratory, Pasadena, CA, January 2002.

20. Muellerschoen, R. J., A. Reichert, D. Kuang, M. Heflin,W. Bertiger, and Y. Bar-Sever, Orbit Determinationwith NASA’s High Accuracy Real-Time GlobalDifferential GPS System, Proceedings of The Instituteof Navigation’s ION GPS-2001, Salt Lake City, UT,September 11–14, 2001, pp. 2294–303.

21. NavCom Technologies, Inc., StarFire Network GlobalDGPS Service, http://www.navcomtech.com/prod-

Vol. 49, No. 3 Bisnath et.al: High-Precision, Kinematic Positioning with a Single GPS Receiver 169

high-precision, kinematic positioning with a single gps receiver

Documents