TECHNICAL PAPERS
Nov 1, 1998

Stochastic Modeling for Static GPS Baseline Data Processing

Publication: Journal of Surveying Engineering
Volume 124, Issue 4

Abstract

In global positioning system (GPS) data processing, incorrect stochastic models for double-differenced measurements will result in unreliable statistics for ambiguity search and biased positioning results. In the commonly used stochastic model, it is usually assumed that all the raw GPS measurements are independent and that they have the same variance. In fact, these assumptions are not realistic. Measurements obtained from different satellites cannot have the same accuracy due to varying noise levels. In this paper, a new method based on modern statistical theory is proposed to directly estimate the covariance matrix for double-differenced GPS measurements. Three different stochastic models have been tested and analyzed. Test results indicate that by using the proposed stochastic models the volume of ambiguity search space can be reduced and the reliability of the ambiguity resolution is improved. Also, the statistics of the baseline components estimated with the proposed stochastic models are more efficient.

Get full access to this article

View all available purchase options and get full access to this article.

References

1.
Ananga, N., Coleman, R., and Rizos, C.(1994). “Variance-covariance estimation of GPS networks.”Bull. Geod., Berlin, Germany, 68(1), 77–87.
2.
Bloomfield, P., and Watson, G. S.(1975). “The inefficiency of least squares.”Biometrika, 62(1), 121–128.
3.
Bock, Y., Abbot, R. I., Counselman, C. C., Gourevitch, S. A., and King, R. W.(1986). “Interferometric analysis of GPS phase observations.”Manuscripta Geodaetica, Berlin, Germany, 11(3), 282–288.
4.
Chen, Y. Q., Chrzanowski, A., and Kavouras, M.(1990). “Assessment of observations using minimum norm quadratic unbiased estimation (MINQUE).”CISM J. of ACSGS, Ottawa, Canada, 44(4), 39–46.
5.
Euler, H., and Goad, C. C.(1991). “On optimal filtering of GPS dual-frequency observations without using orbit information.”Bull. Geod., Berlin, Germany, 65(2), 130–143.
6.
Gerdan, G. P.(1995). “A comparison of four methods of weighting double-difference pseudo-range measurements.”Trans. Tasman Surveyor, Canberra, Australia, 1(1), 60–66.
7.
Giannou, M.(1995). “Quality analysis of the GPS observations for rapid-static and on-the-fly applications: Problems and solutions.”J. for Satellite-Based Positioning, Navigation and Communication (SPN), Wichmann Verlag, Karlsruhe, Germany, 20(4), 138–146.
8.
Goad, C. C.(1987). “Precise positioning with the GPS.”Applied Geodesy, Lecture Notes in Earth Sciences, S. Turner, ed., Springer-Verlag, 12, 17–30.
9.
Gokalp, E. (1991). “Evaluation of GPS measurements by MINQUE and integration of GPS and levelling in subsidence monitoring,”MEng Report, Dept. of Surveying Engineering, University of New Brunswick, Fredericton, NB, Canada.
10.
Grafarend, E., Kleusberg, A., and Schaffrin, B.(1980). “An introduction to the variance-covariance components estimation of Helmert type.”Zeitschrift für Vermessungswesen, Konrad Wittwer GmbH, Stuttgart, Germany, 105(2), 129–137.
11.
Han, S.(1997). “Quality control issues relating to instantaneous ambiguity resolution for real-time GPS kinematic positioning.”J. of Geodesy, Berlin, Germany, 71(7), 351–361.
12.
Jin, X. (1996). “Theory of carrier adjusted DGPS positioning approach and some experimental results,” PhD thesis, Delft University Press, The Netherlands.
13.
Koch, K. R. (1988). Parameter estimation and hypothesis testing in linear models. Springer-Verlag, Berlin, Germany.
14.
Kuang, S. L.(1993). “Evaluating the accuracy of GPS baseline measurements using minimum norm quadratic unbiased estimation.”Surveying and Land Information Systems, 53(2), 103–110.
15.
Landau, H., Euler, H.-J. (1992). “On-the-fly ambiguity resolution for precision differential positioning.”Proc., ION GPS-92, Albuquerque, New Mexico, U.S. Inst. of Navigation, Alexandria, Va., 607–613.
16.
Leick, A. (1995). GPS satellite surveying. John Wiley and Sons, Inc., New York.
17.
Rao, C. R.(1970). “Estimation of heterogeneous variances in linear models.”J. Am. Statistical Assoc., 65, 161–172.
18.
Rao, C. R.(1971). “Estimation of variance and covariance components—MINQUE.”J. Multivariate Anal., 1, 257–275.
19.
Rao, C. R. (1979). “MINQUE theory and its relation to ML and MML estimation of variance components.”Sankhya, Calcutta, India, 41, Series B, 138–153.
20.
Rao, C. R., and Kleffe, J. (1988). Estimation of variance components and applications. North-Holland Press, Amsterdam, Holland.
21.
Sahin, M., Cross, P. A., and Sellers, P. C.(1992). “Variance component estimation applied to satellite laser ranging.”Bull. Geod., Berlin, Germany, 66, 284–295.
22.
Schaffrin, B. (1983). “Varianz-kovarianz-komponenten-schatzung bei der Ausgleichung heterogener wiederholungsmessungen.”Deutsche Geodätische Kommission, Reihe C, Munich, Germany, Heft 282.
23.
Teunissen, P. J. G.(1997). “A canonical theory for short GPS baselines Part IV: Precision and reliability.”J. Geodesy, Berlin, Germany, 71, 513–525.
24.
Wang, J., and Stewart, M. (1996). “Stochastic assessment of the double differenced GPS observations.” paper presented at the annual research seminar, School of Geomatic Engineering, The University of New South Wales, November, 11–14.
25.
Welsch, W. M. (1981). “Estimation of variances and covariances of geodetic observations.”Australian J. Geodesy, Photogrammetry and Surveying, Canberra, Australia, No. 34, 1–14.

Information & Authors

Information

Published In

Go to Journal of Surveying Engineering
Journal of Surveying Engineering
Volume 124Issue 4November 1998
Pages: 171 - 181

History

Published online: Nov 1, 1998
Published in print: Nov 1998

Permissions

Request permissions for this article.

Authors

Affiliations

Jinling Wang
PhD Candidate, School of Spatial Sciences, Curtin Univ. of Technol., GPO Box U1987, Perth, WA 6845, Australia. E-mail: [email protected]
Mike P. Stewart
PhD and Sr. Lect., School of Spatial Sciences, Curtin Univ. of Technol., GPO Box U1987, Perth, WA 6845, Australia. E-mail: [email protected]
Maria Tsakiri
PhD and Lect., School of Spatial Sciences, Curtin Univ. of Technol., GPO Box U1987, Perth, WA 6845, Australia. E-mail: [email protected]

Metrics & Citations

Metrics

Citations

Download citation

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

Cited by

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share