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Uniqueness and Nonuniqueness of the GNSS Carrier-Phase Compass Readings

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VII Hotine-Marussi Symposium on Mathematical Geodesy

Part of the book series: International Association of Geodesy Symposia ((IAG SYMPOSIA,volume 137))

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Abstract

In this contribution we analyse the possible nonuniqueness in the least-squares solution of the GNSS carrier-phase compass model. It is shown that this lack of uniqueness may manifest itself in the fixed baseline estimator and therefore in the GNSS compass readings. We present the conditions under which nonuniqueness occurs and give explicit expressions for these nonunique least-squares solutions.

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References

  • Buist P (2007) The baseline constrained LAMBDA method for single epoch, single frequency attitude determination applications. Proceedings of ION GPS-2007, 2007

    Google Scholar 

  • Cohen CE (1992) Attitude determination using GPS. PhD Thesis, Stanford University

    Google Scholar 

  • Giorgi G, Teunissen PJG, Buist P (2008) A search and shrink approach for the baseline constrained LAMBDA method: experimental results. Proceedings International GPS/GNSS Symposium, Tokyo, Japan, Nov. 11–14, 2008

    Google Scholar 

  • Hide C, Pinchin DJ (2007) Development of a low cost multiple GPS antenna attitude system. Proceedings ION GNSS 2007, 88–95, 2007

    Google Scholar 

  • Hofmann-Wellenhoff B, H Lichtenegger (2001): Global positioning system: theory and practice, 5nd edn. Springer, Berlin

    Book  Google Scholar 

  • Kuylen LV, Nemry P, Boon F, Simsky A, Lorga JFM (2006) Comparison of attitude performance for multi-antenna receivers. Eur J Navigation, 4(2)

    Google Scholar 

  • Leick A (2003) GPS satellite surveying, 3rd edn. Wiley, New York

    Google Scholar 

  • Lu G (1995) Development of a GPS multi-antenna system for attitude determination. UCGE Reports 20073, Dept. of Geomatics Eng., University of Calgary, 1995

    Google Scholar 

  • Misra P, Enge P (2001) Global positioning system: signals, measurements, and performance. Ganga-Jamuna Press, Lincoln, MA

    Google Scholar 

  • Montgomery P, IY Bar-Itzhack, J Garrick (1997): Algorithm for attitude determination using GPS. Proceedings of AIAA Guidance, Navigation and Control Conf., New Orleans, LA, USA. Aug. 1997, Paper no. AIAA 97-3616, 1997.

    Google Scholar 

  • Park C, Teunissen PJG (2003) A new carrier phase ambiguity estimation for gnss attitude determination systems. Proceedings of International GPS/GNSS Symposium, Tokyo, 2003.

    Google Scholar 

  • Park C, Teunissen PJG (2007) A baseline constrained lambda method for integer ambiguity resolution of GNSS attitude determination systems. J Control, Robotics Systems 14(6):587–594

    Google Scholar 

  • Simsky A, Vander Kuylen L, Boon F (2005) Single-board attitude determination system based on the PolaRx2@GPS receiver. Proc ENC GNSS 2005, Munich, Germany, 19–22 July, 2005.

    Google Scholar 

  • Strang G, Borre K (1997) Linear algebra, geodesy, and GPS. Wellesley-Cambridge Press, Wellesley, MA

    Google Scholar 

  • Teunissen PJG (1994) A new method for fast carrier phase ambiguity estimation. Proceedings IEEE PLANS’94, Position Location and Navigation Symposium, pp 562–573, 1994

    Google Scholar 

  • Teunissen PJG (1995) The least-squares ambiguity decorrelation adjustment: a method for fast GPS integer ambiguity estimation. J Geodesy 70:65–82

    Article  Google Scholar 

  • Teunissen PJG (2006) The LAMBDA method for the GNSS compass. Artificial Satellites, 41(3):89–103

    Article  Google Scholar 

  • Teunissen PJG, Kleusberg (eds) (1998) GPS for Geodesy, 2nd enlarged (edn) Springer, Berlin

    Google Scholar 

  • Tu CH, KY Wang, WC Melton (1996) GPS compass: a novel navigation equipment. Proceedings of ION National Technical Meeting, Santa Monica, CA, USA, 1996

    Google Scholar 

Download references

Acknowledgements

The research of the author has been supported by an Australian Research Council Federation Fellowship (project number FF0883188). This support is gratefully acknowledged.

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Authors and Affiliations

  1. Delft Institute of Earth Observation and Space Systems, Delft University of Technology, Delft, The Netherlands

    P. J. G. Teunissen

  2. Department of Spatial Sciences, Curtin University of Technology, Perth, Australia

    P. J. G. Teunissen

Authors
  1. P. J. G. Teunissen
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Corresponding author

Correspondence to P. J. G. Teunissen .

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Editors and Affiliations

  1. Institute of Geodesy, Geschwister-Scholl-Str. 24D, Stuttgart, 70174, Germany

    Nico Sneeuw

  2. Research Institute of Geodesy, Ondrejov, 25165, Czech Republic

    Pavel Novák

  3. Università di Roma "La Sapienza", via Eudossiana 18, Rome, 00185, Italy

    Mattia Crespi

  4. Politecnico di Milano, Milan, Italy

    Fernando Sansò

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© 2012 Springer-Verlag Berlin Heidelberg

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Teunissen, P.J.G. (2012). Uniqueness and Nonuniqueness of the GNSS Carrier-Phase Compass Readings. In: Sneeuw, N., Novák, P., Crespi, M., Sansò, F. (eds) VII Hotine-Marussi Symposium on Mathematical Geodesy. International Association of Geodesy Symposia, vol 137. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22078-4_14

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