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Volume 52 Supplement 10

Special Issue: Application of GPS and other space geodetic techniques to Earth Sciences (1)

  • Letter
  • Published:

Probabilistic properties of GNSS integer ambiguity estimation

Abstract

Successful integer estimation of carrier phase ambiguities of Global Navigation Satellite Systems (GNSS) is the key to many high precision positioning applications. In order to describe the quality of the positioning results rigorously, one needs to know the probabilistic properties of both the integer and noninteger parameters in the GNSS model. In this contribution these probability distributions are presented and discussed. The probability mass function of the integer ambiguities is needed to evaluate the ambiguity success rate and the distribution of the GNSS baseline is needed to evaluate the relevant confidence regions for positioning.

References

  • Boon, F. and B. Ambrosius, Results of real-time applications of the LAMBDA method in GPS based aircraft landings, Proceedings KIS97, pp. 339–345, 1997.

  • Boon, F., P. J. de Jonge, and C. C. J. M. Tiberius, Precise aircraft positioning by fast ambiguity resolution using improved troposphere modelling, Proceedings ION GPS-97, Vol. 2, pp. 1877–1884, 1997.

    Google Scholar 

  • Chmielewsky, M. A., Elliptically symmetric distributions: A review and bibliography, Internat. Statist. Rev., 49, 67–74, 1981.

    Article  Google Scholar 

  • de Jonge, P. J. and C. C. J. M. Tiberius, The LAMBDA Method for Integer Ambiguity Estimation: Implementation Aspects, Delft Geodetic Computing Centre, LGR Series, No. 12, 45 pp., Delft University of Technology, 1996a.

    Book  Google Scholar 

  • deJ onge, P. J. and C. C. J. M. Tiberius, Integer estimation with the LAMBDA method, Proceedings IAG Symposium No. 115, ‘GPS trends interrestrial, airborne and spaceborne applications’, edited by G. Beutler et al., pp. 280–284, Springer Verlag, 1996b.

    Chapter  Google Scholar 

  • de Jonge, P. J., C. C. J. M. Tiberius, and P. J. G. Teunissen, Computational aspects of the LAMBDA method for GPS ambiguity resolution, Proceedings ION GPS-96, pp. 935–944, 1996.

    Google Scholar 

  • Han, S., Ambiguity resolution techniques using integer least-squares estimation for rapid static or kinematic positioning, Symposium Satellite Navigation Technology: 1995 and beyond, 10 p., Brisbane, Australia, 1995.

    Google Scholar 

  • Hassibi, A. and S. Boyd, Integer parameter estimation in linear models with applications to GPS, IEEE Trans. Signal Processing, Nov. 1998, 46(11), 2938–2952, 1998.

    Article  Google Scholar 

  • Hofmann-Wellenhof, B., H. Lichtenegger, and J. Collins, Global Positioning System: Theory and Practice, fourth edition, Springer Verlag, 1997.

  • Jonkman, N. F., Integer GPS-Ambiguity Estimation without the Receiver-Satellite Geometry, Delft Geodetic Computing Centre, LGR Series, No. 18, 95 pp., Delft University of Technology, 1998.

    Google Scholar 

  • Leick, A., GPS Satellite Surveying, 2nd edition, John Wiley & Sons, 560 pp., New York, 1995.

  • Parkinson, B. and J. J. Spilker (eds.), GPS: Theory and Applications, Vols. 1 and 2, AIAA, Washington D.C., 1995.

    Google Scholar 

  • Strang, G. and K. Borre, Linear Algebra, Geodesy and GPS, 624 pp., Wellesley-Cambridge Press, 1997.

  • Teunissen, P. J. G., Least-squares estimation of the integer GPS ambiguities, Invited Lecture, Section IV Theory and Methodology, IAG General Meeting, Beijing, China, August 1993. Also in: LGR Series, No. 6, Delft Geodetic Computing Centre, 1993.

  • Teunissen, P. J. G., The invertible GPS ambiguity transformations, Man. Geod., 20, 489–497, 1995.

    Google Scholar 

  • Teunissen, P. J. G., Some remarks on GPS ambiguity resolution, Artificial Satellites, 32(3), 119–130, 1997.

    Google Scholar 

  • Teunissen, P. J. G., A class of unbiased integer GPS ambiguity estimators, Artificial Satellites, 33(1), 3–10, 1998a.

    Google Scholar 

  • Teunissen, P. J. G., On the integer normal distribution of the GPS ambiguities, Artificial Satellites, 33(2), 49–64, 1998b.

    Google Scholar 

  • Teunissen, P. J. G., A theorem on maximizing the probability of correct integer estimation, Artificial Satellites, 34(1), 3–10, 1999.

    Google Scholar 

  • Teunissen, P. J. G. and A. Kleusberg (eds.), GPS for Geodesy, 2nd enlarged edition, 650 pp., Springer Verlag, 1998.

  • Tiberius, C. C. J. M. and P. J. de Jonge, Fast positioning using the LAMBDA method, Proceedings DSNS-95, Paper 80, 8 p., 1995.

  • Tiberius, C. C. J. M., P. J. G. Teunissen, and P. J. de Jonge, Kinematic GPS: performance and quality control, Proceedings KIS97, pp. 289–299, 1997.

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Teunissen, P.J.G. Probabilistic properties of GNSS integer ambiguity estimation. Earth Planet Sp 52, 801–805 (2000). https://doi.org/10.1186/BF03352285

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  • DOI: https://doi.org/10.1186/BF03352285

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