Integer Ambiguity Resolution with Nonlinear Geometrical Constraints

  • G. Giorgi
  • P. J. G. Teunissen
  • S. Verhagen
  • P. J. Buist
Conference paper
Part of the International Association of Geodesy Symposia book series (IAG SYMPOSIA, volume 137)

Abstract

Integer ambiguity resolution is the key to obtain very accurate positioning solutions out of the GNSS observations. The Integer Least Squares (ILS) principle, a derivation of the least-squares principle applied to a linear system of equations in which some of the unknowns are subject to an integer constraint, was demonstrated to be optimal among the class of admissible integer estimators. In this contribution it is shown how to embed into the functional model a set of nonlinear geometrical constraints, which arise when considering a set of antennae mounted on a rigid platform. A method to solve for the new model is presented and tested: it is shown that the strengthened underlying model leads to an improved capacity of fixing the correct integer ambiguities.

Keywords

Constrained methods GNSS Integer ambiguity resolution 

Notes

Acknowledgements

Professor P.J.G. Teunissen is the recipient of an Australian Research Council Federation Fellowship (project number FF0883188): this support is greatly acknowledged.

The research of S. Verhagen is supported by the Dutch Technology Foundation STW, applied science division of NWO and the Technology Program of the Ministry of Economic Affairs.

References

  1. Battin RH (1987) An introduction to the mathematics and methods of astrodynamics. AIAA Education Series, New YorkGoogle Scholar
  2. Buist PJ (2007) The baseline constrained LAMBDA method for single epoch, single frequency attitude determination applications. In: Proceedings of ION GPS, 2007Google Scholar
  3. Giorgi G, Buist PJ (2008) Single-epoch, single frequency, standalone full attitude determination: experimental results. In: 4th ESA workshop on satellite navigation user equipment technologies, NAVITEC, 2008Google Scholar
  4. Giorgi G, Teunissen PJG, Buist PJ (2008) A search and shrink approach for the baseline constrained LAMBDA: experimental results. In: Proceedings of the international symposium on GPS/GNSS 2008, Tokyo, Japan, 2008Google Scholar
  5. Goldstein H (1980) Classical mechanics. Addison-Wesley Pub. Co., MassachusettsGoogle Scholar
  6. Park C, Teunissen PJG (2003) A new carrier phase ambiguity estimation for GNSS attitude determination systems. In: Proceedings of international GPS/GNSS symposium, Tokyo, 2003Google Scholar
  7. Park C, Teunissen PJG (2008) A baseline constrained LAMBDA method for integer ambiguity resolution of GNSS attitude determination systems. J Contr Robot Syst (in Korean), 14(6):587–594CrossRefGoogle Scholar
  8. Teunissen PJG (1993) Least squares estimation of the integer GPS ambiguities. Invited lecture, Section IV theory and methodology, IAG General Meeting, Beijing. Also in: LGR series No.6, Delft Geodetic Computing Center, Delft University of TechnologyGoogle Scholar
  9. Teunissen PJG (1994) A new method for fast carrier phase ambiguity estimation. In: Proceedings IEEE position location and navigation symposium, PLANS ‘94, pp 562–573Google Scholar
  10. Teunissen PJG (1995) The least-squares ambiguity decorrelation adjustment: a method for fast GPS integer ambiguity estimation. J Geodes 70:65–82CrossRefGoogle Scholar
  11. Teunissen PJG, Kleusberg A (1998) GPS for geodesy. Springer, BerlinCrossRefGoogle Scholar
  12. Teunissen PJG (1999) An optimality property of the integer least-squares estimator. J Geodes 73(11):587–593CrossRefGoogle Scholar
  13. Teunissen PJG (2006) The LAMBDA method for the GNSS compass. Artificial Satellites. J Planet Geodes 41(3):88–103Google Scholar
  14. Teunissen PJG (2007) A general multivariate formulation of the multi-antenna GNSS attitude determination problem. Artificial Satellites, 42(2):97–111CrossRefGoogle Scholar
  15. Teunissen PJG (2008) GNSS ambiguity resolution for attitude determination: theory and method. In: Proceedings of the international symposium on GPS/GNSS 2008, Tokyo, Japan, 11–14 November, 2008Google Scholar
  16. Teunissen PJG (2010) Integer least squares theory for the GNSS compass. J Geodes, 84:433–447CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • G. Giorgi
    • 1
  • P. J. G. Teunissen
    • 1
    • 2
  • S. Verhagen
    • 1
  • P. J. Buist
    • 1
  1. 1.Delft Institute of Earth Observation and Space Systems (DEOS)Delft University of TechnologyDelftThe Netherlands
  2. 2.Department of Spatial SciencesCurtin University of TechnologyPerthAustralia

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