Advertisement

GPS Solutions

, Volume 17, Issue 4, pp 535–548 | Cite as

The ratio test for future GNSS ambiguity resolution

  • Sandra Verhagen
  • Peter J. G. Teunissen
Original Article

Abstract

The performance of the popular ambiguity ratio test is analyzed. Based on experimental and simulated data, it is demonstrated that the current usage of the ratio test with fixed critical value is not sustainable in light of the enhanced variability that future global navigation satellite system (GNSS) ambiguity resolution will bring. As its replacement, the model-driven ratio test with fixed failure rate is proposed. The characteristics of this fixed-failure rate ratio test are described, and a performance analysis is given. The relation between its critical value and various GNSS model parameters is also studied. Finally, a procedure is presented for the creation of fixed failure rate look-up tables for the critical values of the ratio test.

Keywords

Integer ambiguity resolution Ratio test Fixed failure rate Integer aperture estimation GNSS 

Notes

Acknowledgments

Peter Teunissen is Federation Fellow of the Australian Research Council (project FF0883188). The research of Sandra Verhagen is supported by the Dutch Technology Foundation STW, applied science division of NWO and the Technology Program of the Ministry of Economic Affairs. Part of this work was done in the framework of the project ‘New Carrier Phase Processing Strategies for Next Generation GNSS Positioning’ of the Cooperative Research Centre for Spatial Information (CRC-SI2). All this support is gratefully acknowledged.

References

  1. Abidin HA (1993) Computational and geometrical aspects of on-the-fly ambiguity resolution. Dissertation, Department of Surveying Engineering, Technical Report No 104, University of New Brunswick, CanadaGoogle Scholar
  2. Chen Y (1997) An approach to validate the resolved ambiguities in GPS rapid positioning. In: Proceedings of the International symposium on kinematic systems in geodesy, geomatics and navigation, Banff, Canada, pp 301–304Google Scholar
  3. Euler HJ, Schaffrin B (1990) On a measure for the discernibility between different ambiguity solutions in the static-kinematic GPS-mode. In: IAG Symposia no.107, kinematic systems in geodesy, surveying, and remote sensing, Springer-Verlag, New York, pp 285–295Google Scholar
  4. Frei E, Beutler G (1990) Rapid static positioning based on the fast ambiguity resolution approach FARA: theory and first results. Manuscripta Geodaetica 15(6):325–356Google Scholar
  5. Ha S (1997) Quality control issues relating to instantaneous ambiguity resolution for real-time GPS kinematic positioning. J Geodesy 71(6):351–361CrossRefGoogle Scholar
  6. Han S, Rizos C (1996a) Validation and rejection criteria for integer least-squares estimation. Survey Review 33(260):375–382CrossRefGoogle Scholar
  7. Han S, Rizos C (1996b) Integrated methods for instantaneous ambiguity resolution using new-generation GPS receivers. In: Proceedings of the IEEE PLANS’96, Atlanta GA, pp 245–261Google Scholar
  8. Landau H, Euler HJ (1992) On-the-fly ambiguity resolution for precise differential positioning. In: Proceedings of the ION GPS-1992, Albuquerque NM, pp 607–613Google Scholar
  9. Odijk D (2000) Weighting ionospheric corrections to improve fast GPS positioning over medium distances. In: Proceedings of the ION GPS-2000, Salt Lake City UT, pp 1113–1123Google Scholar
  10. Odijk D, Teunissen PJG, Huisman L (2012) First results of mixed GPS + GIOVE single-frequency RTK in Australia. J Sp Sci 57:3–18CrossRefGoogle Scholar
  11. Parkins A (2011) Increasing GNSS RTK availability with a new single-epoch batch partial ambiguity resolution algorithm. GPS Solut 15:391–402CrossRefGoogle Scholar
  12. Tandy M, Young KW (2012) Variable duration fixed failure rate ambiguity resolution. GPS Solut. doi: 10.1007/s10291-012-0265-9 Google Scholar
  13. Teunissen PJG (1995) The least-squares ambiguity decorrelation adjustment: a method for fast GPS ambiguity resolution. J Geodesy 70(1–2):65–82CrossRefGoogle Scholar
  14. Teunissen PJG (1999) An optimality property of the integer least-squares estimator. J Geodesy 73(11):587–593CrossRefGoogle Scholar
  15. Teunissen PJG (2003) Integer aperture GNSS ambiguity resolution. Artif Satell 38(3):79–88Google Scholar
  16. Teunissen PJG (2004) GNSS ambiguity resolution. J Geodesy 78:235–244CrossRefGoogle Scholar
  17. Teunissen PJG (2005) Penalized GNSS ambiguity resolution with optimally controlled failure-rate. Artif Satell 40(4):219–227Google Scholar
  18. Teunissen PJG, Verhagen S (2009) The GNSS ambiguity ratio-test revisited: a better way of using it. Survey Rev 41(312):138–151CrossRefGoogle Scholar
  19. Tiberius CCJM, De Jonge PJ (1995) Fast positioning using the LAMBDA method. In: Proceedings of the DSNS’95, Bergen, NorwayGoogle Scholar
  20. Verhagen S (2002) Studying the performance of global navigation satellite systems: a new software tool. GPS World 13(6):60–65Google Scholar
  21. Verhagen S (2004) Integer ambiguity validation: an open problem? GPS Solut 8(1):36–43CrossRefGoogle Scholar
  22. Verhagen S (2005a) The GNSS integer ambiguities: estimation and validation. Dissertation, Publications on Geodesy, 58, Netherlands Geodetic Commission, DelftGoogle Scholar
  23. Verhagen S (2005b) On the reliability of integer ambiguity resolution. Navigation 52(2):99–110Google Scholar
  24. Verhagen S, Teunissen PJG (2006) New global navigation satellite system ambiguity resolution method compared to existing approaches. J Guid Cont Dyn 29(4):981–991CrossRefGoogle Scholar
  25. Wang J, Stewart MP, Tsakiri M (1998) A discrimination test procedure for ambiguity resolution on-the-fly. J Geodesy 72(11):644–653CrossRefGoogle Scholar
  26. Wei M, Schwarz KP (1995) Fast ambiguity resolution using an integer nonlinear programming method. In: Proceedings of the ION GPS-1995, Palm Springs CA, pp 1101–1110Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Delft University of TechnologyDelftThe Netherlands
  2. 2.Curtin UniversityPerthAustralia

Personalised recommendations