Skip to main content
Earth, Planets and Space
Download PDF

Volume 57 Supplement 4

Special Issue: Special Section for the 2004 off the Kii peninsula earthquakes (2)

An improvement of GPS height estimations: stochastic modeling

Earth, Planets and Space volume 57, pages 253–259 (2005)Cite this article

Abstract

The results of GPS positioning depend on both functional and stochastic models. In most of the current GPS processing programs, however, the stochastic model that describes the statistical properties of GPS observations is usually assumed that all GPS measurements have the same accuracy and are statistically independent. Such assumptions are unrealistic. Although there were only a few studies modeling the effects on the GPS relative positioning, they are restricted to short baselines and short session lengths. In this paper, the stochastic modeling for IGS long-baseline positioning (with 24-hour session) is analyzed in the GAMIT software by modified stochastic models. Results show that any mis-specifications of stochastic model result in unreliable GPS baseline results, and the deviation of baseline estimations reaches as much as 2 cm in the height component. Using the stochastic model of satellite elevation angle-based cosine function, the precision of GPS baseline estimations can be improved, and the GPS baseline component is closest to the reference values, especially GPS height.

References

  • Barnes, J. B., N. Ackroyd, and P. Cross, Stochastic modeling for very high precision real-time kinematic GPS in an engineering environment. XXI International Congress of FIG, Brighton, UK, 19–25 July, 1998.

    Google Scholar 

  • Blewitt, G., GPS Data Processing Methodology: From Theory to Applications, in GPS for Geodesy, edited by P. J. G. Teunissen and A. Kleusberg, p. 231–270, Springer-Verlag, Berlin, 1998.

    Chapter  Google Scholar 

  • Bona, P., Precision, cross correlation, and time correlation of GPS phase and code observations, GPS Solutions, 4(2), 3–13, 2000.

    Article  Google Scholar 

  • Brunner, F. K., H. Hartinger, and L. Troyer, GPS Signal Diffraction Modelling: The Stochastic SIGMA-Δ Model, Journal of Geodesy, 73, 259–267, 1999.

    Article  Google Scholar 

  • El-Rabbany AE-S, The effect of physical correlations on the ambiguity resolution and accuracy estimation in GPS differential positioning. Tech Rep 170, Department of Geodesy and Geomatics Engineering, University of New Brunswick, 1994.

    Google Scholar 

  • Han, S. and C. Rizos, Standardization of the variance-covariance matrix for GPS rapid static positioning, Geomat. Res. Aust., 62, 37–54, 1995.

    Google Scholar 

  • Hopfield, H. S., Two-quartic tropospheric refractivity profile for correcting satellite data, J. Geophys. Res., 74(18), 4487–4499, 1969.

    Article  Google Scholar 

  • Hugentobler, U., S. Schaer, and P. Fridez, BERNESE GPS Software Version 4.2, Astronomical Institute, University of Bern, 2001.

    Google Scholar 

  • Jin, S. and J. Wang, Impacts of stochastic models on GPS-derived ZTD estimations. 17th Int. Tech. Meeting of the Satellite Division of the U.S. Institute of Navigation, Long Beach, California, 21–24 September, 2004.

    Google Scholar 

  • Jin, X. and C. D. de Jong, Relationship between satellite elevation and precision of GPS code observations, The Journal of Navigation, 49, 253–265, 1996.

    Article  Google Scholar 

  • King, R. W. and Y. Bock, Documentation for the GAMIT GPS Analysis Software, Mass. Inst. of Technol., Cambridge Mass, 1999.

    Google Scholar 

  • Rizos, C., Principles and Practice of GPS Surveying Monograph 17, School of Geomatic Engineering, the University of New South Wales, 555 pp., 1997.

    Google Scholar 

  • Saastamoinent, J., Contribution to the theory of atmospheric refraction, Bulletin Geodesique, 107, 13–34, 1973.

    Article  Google Scholar 

  • Satirapod, C., J. Wang, and C. Rizos, Modelling Residual Systematic Errors in GPS Positioning: Methodologies and Comparative Studies, In Vistas for Geodesy in the New Millennium, edited by J. Adams and K. P. Schwarz, IAG Symp. Vol. 125, pp. 410–414, Springer-Verlag, ISBN 3-540-43454-2, 2002.

    Article  Google Scholar 

  • Satirapod, C., J. Wang, and C. Rizos, Comparing different GPS data processing techniques for modelling residual systematic errors, J. Surv. Eng., 129(4), 129–135, 2003.

    Article  Google Scholar 

  • Tiberius, C. and F. Kenselaar, Variance component estimation and precise GPS positioning: case study, J. Surv. Eng., 129(1), 11–18, 2003.

    Article  Google Scholar 

  • Wang, J., Stochastic Assessment of GPS Measurements for Precise Positioning, 11th Int. Tech. Meeting of the Satellite Division of the U.S. Inst. of Navigation, Nashville, Tennessee, 15–18 September, 81–98, 1998a.

    Google Scholar 

  • Wang, J., M. Stewart, and M. Tsakiri, Stochastic modeling for static GPS baseline data processing, J. Surv. Eng., 124(4), 171–181, 1998b.

    Article  Google Scholar 

  • Wang, J., C. Satirapod, and C. Rizos, Stochastic assessment of GPS carrier phase measurements for precise static relative positioning, Journal of Geodesy, 76(2), 95–104, 2002.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Space Geodesy Research Group, Korea Astronomy and Space Science Institute, Daejeon, 305-348, South Korea

    Shuanggen Jin & Pil-Ho Park

  2. School of Surveying and Spatial Information Systems, University of New South Wales, Sydney, NSW, 2052, Australia

    Shuanggen Jin & J. Wang

  3. Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai, 200030, China

    Shuanggen Jin

Authors
  1. Shuanggen Jin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Pil-Ho Park
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shuanggen Jin.

Rights and permissions

Open Access  This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.

The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Jin, S., Wang, J. & Park, PH. An improvement of GPS height estimations: stochastic modeling. Earth Planet Sp 57, 253–259 (2005). https://doi.org/10.1186/BF03352561

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1186/BF03352561

Key words

  • Stochastic modeling
  • GPS
  • IGS
  • height