GNSS Carrier Phase Ambiguity Resolution: Challenges and Open Problems

  • P.J.G Teunissen
  • S Verhagen
Part of the International Association of Geodesy Symposia book series (IAG SYMPOSIA, volume 133)


Integer carrier phase ambiguity resolution is the key to fast and high-precision global navigation satellite system (GNSS) positioning and application. Although considerable progress has been made over the years in developing a proper theory for ambiguity resolution, the necessary theory is far from complete.

In this contribution we address three topics for which further developments are needed. They are: (1) Ambiguity acceptance testing; (2) Ambiguity subset selection; and (3) Integer-based GNSS model validation. We will address the shortcommings of the present theory and practices, and discuss directions for possible solutions


Ambiguity acceptance tests Ambiguity subset selection Integer based GNSS model validation 


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  1. Abidin, H. A. (1993). Computational and geometrical aspects of on-the-fly ambiguity resolution. Ph.D. thesis, Dept. of Surveying Engineering, Techn. Report no. 104, University of New Brunswick, Canada, page 314Google Scholar
  2. Chen, Y. (1997). An approach to validate the resolved ambiguities in GPS rapid positioning. Proc. of the International Symposium on Kinematic Systems in Geodesy, Geomatics and Navigation, Banff, Canada, pages 301–304Google Scholar
  3. Euler, H. J. and Schaffrin, B. (1991). On a measure for the discernibility between different ambiguity solutions in the static-kinematic GPS-mode. IAG Symposia no. 107, Kinematic Systems in Geodesy, Surveying, and Remote Sensing, Springer-Verlag, New York, pages 285–295Google Scholar
  4. Han, S. and Rizos, C. (1996). Validation and rejection criteria for integer least-squares estimation. Survey Review, 33(260):375–382Google Scholar
  5. Hofmann-Wellenhoff, B., Lichtenegger, H., and Collins, J. (2001). Global Positioning System: Theory and Practice. Springer-Verlag, Berlin, 5th editionGoogle Scholar
  6. Ji, S., Chen, W., Zhao, C., Ding, X., and Chen, Y. (2007). Single epoch ambiguity resolution for Galileo with the CAR and LAMBDA methods. GPS Solutions, DOI 10.1007/s10291-007-0057-9 Google Scholar
  7. Joosten, P. and Tiberius, C. C. J. M. (2000). Fixing the ambiguities: are you sure they’re right. GPS World, 11(5):46–51Google Scholar
  8. Koch, K. R. (1999). Parameter Estimation and Hypothesis Testing in Linear Models. Springer Verlag, Berlin, 2nd editionGoogle Scholar
  9. Lee, H. K., Wang, J., and Rizos, C. (2005). An integer ambiguity resolution procedure for GPS/pseudolite/INS integration. Journal of Geodesy, 79(4–5): 242–255CrossRefGoogle Scholar
  10. Leick, A. (2003). GPS Satellite Surveying. John Wiley and Sons, New York, 3rd editionGoogle Scholar
  11. Misra, P. and Enge, P. (2001). Global Positioning System: Signals, Measurements, and Performance. Ganga-Jamuna Press, Lincoln, MAGoogle Scholar
  12. Strang, G. and Borre, K. (1997). Linear Algebra, Geodesy, and GPS. Wellesley-Cambridge Press, Wellesley, MAGoogle Scholar
  13. Teunissen, P.J.G. (1997a). A canonical theory for short GPS baselines. Part IV: Precision versus reliability. Journal of Geodesy, 71:513–525CrossRefGoogle Scholar
  14. Teunissen, P.J.G. (1997b). On the GPS widelane and its decorrelation property. Journal of Geodesy, 71(9):577–587CrossRefGoogle Scholar
  15. Teunissen, P.J.G. (1998a). On the integer normal distribution of the GPS ambiguities. Artificial Satellites, 33(2):49–64Google Scholar
  16. Teunissen, P.J.G. (1998b). Success probability of integer GPS ambiguity rounding and bootstrapping. Journal of Geodesy, 72:606–612CrossRefGoogle Scholar
  17. Teunissen, P.J.G. (1999). An optimality property of the integer least-squares estimator. Journal of Geodesy, 73(11):587–593CrossRefGoogle Scholar
  18. Teunissen, P.J.G. (2001). GNSS ambiguity bootstrapping: Theory and applications. Proc. KIS2001, International Symposium on Kinematic Systems in Geodesy, Geomatics and Navigation, June 5–8, Banff, Canada, pages 246–254Google Scholar
  19. Teunissen, P.J.G. (2003). Integer aperture GNSS ambiguity resolution. Artificial Satellites, 38(3):79–88Google Scholar
  20. Teunissen, P.J.G. (2006). Testing Theory, an Introduction. Delft University Press, Delft, 2nd editionGoogle Scholar
  21. Teunissen, P.J.G. (2007). Least-squares prediction in linear models with integer unknowns. Journal of Geodesy, DOI:10.1007/s00190-007-0138-0 Google Scholar
  22. Teunissen, P.J.G., Joosten, P., and Tiberius, C. C. J. M. (1999). Geometry-free ambiguity success rates in case of partial fixing. Proc. of National Technical Meeting & 19th Biennal Guidance Test Symposium ION 1999, San Diego CA, pages 201–207Google Scholar
  23. Teunissen, P.J.G. and Kleusberg, A. (1998). GPS for Geodesy. Springer, Berlin Heidelberg New York, 2nd editionGoogle Scholar
  24. Teunissen, P.J.G. and Verhagen, S. (2004). On the foundation of the popular ratio test for GNSS ambiguity resolution. Proc. of ION GNSS-2004, Long Beach CA, pages 2529–2540Google Scholar
  25. Teunissen, P.J.G. and Verhagen, S. (2007a). GNSS Phase Ambiguity Validation: A Review. Proc. Space, Aeronautical and Navigational Electronics Symposium SANE2007, The Institute of Electronics, Information and Communication Engineers (IEICE), Japan, 107(2):1–6Google Scholar
  26. Teunissen, P.J.G. and Verhagen, S. (2007b). The GNSS ratio-test revisited. Submitted to Survey Review Google Scholar
  27. Verhagen, S. (2005a). On the reliability of integer ambiguity resolution. Navigation, 52(2):99–110Google Scholar
  28. Verhagen, S. (2005b). The GNSS integer ambiguities: estimation and validation. Ph.D. thesis, Publications on Geodesy, 58, Netherlands Geodetic Commission, DelftGoogle Scholar
  29. Verhagen, S. and Teunissen, P.J.G. (2006). New global navigation satellite system ambiguity resolution method.compared to existing approaches. Journal of Guidance, Control, and Dynamics, 29(4):981–991CrossRefGoogle Scholar
  30. Vollath, U., Sauer, K., Amarillo, F., and Pereira, J. (2003). Three or four carriers – how many are enough? Proc. of ION GNSS-2003, Portland OR, pages 1470–1477Google Scholar
  31. Wei, M. and Schwarz, K. P. (1995). Fast ambiguity resolution using an integer nonlinear programming method. Proc. of ION GPS-1995, Palm Springs CA, pages 1101–1110Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • P.J.G Teunissen
    • 1
  • S Verhagen
    • 1
  1. 1.Delft Institute of Earth Observation and Space systemsDelft University of TechnologyThe Netherlands

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