On the precision and reliability of near real-time GPS phase observation ambiguities

  • H. Kutterer
Conference paper
Part of the International Association of Geodesy Symposia book series (IAG SYMPOSIA, volume 121)


During the past decade the integer fixing of the GPS (Global Positioning System) carrier phase ambiguities has been studied in many papers. The available techniques are rather sophisticated regarding the set-up and analysis of the ambiguity search space. Consistently, the number of observation epochs necessary for the unique solution is strongly reduced. As incorrect solutions may occur, it is essential to study their impact on the coordinate estimates and their precision. Thus quality issues concerning the ambiguity resolution techniques are both of practical and theoretical interest

The paper focuses on the theoretical aspects of the near real-time case with short baseline lengths. Measures of a degree of confidence are introduced for the selection of the ambiguity parameters. An approach is sketched for describing the precision of the ambiguities regarding their integer nature. Reliability aspects are considered taking possibly incorrect ambiguity solutions into account. A proposal concerning the interpretation of the results for practical use concludes the study


Global Positioning System carrier phase ambiguity 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Abidin H.Z. (1993): On-the-fly ambiguity resolution: formulation and resultsmanuscripta geodaetica(1993): 18: 380–405Google Scholar
  2. Betti B., M. Crespi, and F. Sansò 1993: A geometric illustration of ambiguity resolution in GPS theory and a Bayesian approach manuscripta geodaetica(1993)18:317–330Google Scholar
  3. Counselman C.C., and Gourevitch S.A. (1981): Miniature interferometer terminals for earth surveying: ambiguity and multipath with the Global Positioning System IEEE Transactions on Geoscience and Remote Sensing. GE-19(4): 244–252CrossRefGoogle Scholar
  4. Frei E. and G. Beutler (1991):Raid static positioning based on the fast ambiguity resolution approach “FARX”: theory and first results . manuscripta geodaetica(1990) 15:325–356Google Scholar
  5. Hofmann-Wellenhof B. H. Lichteneger and J. Collins (1997) GPS — Theory and-Practice (4th edition). Sringer Wien/New YorkGoogle Scholar
  6. Parkinson B.W. and J.J. Spilker (1996): Global Positioning System: Theory and Applications Vol. l. Progress in Astronautics and Aeronautics (Vol. 163) American Institute of Aeronautics and Astronautics Washington DC U.S.AGoogle Scholar
  7. Rao C.R. and S.K. Mitra 1971: Generalized Inverse of Matrices and its Applications. Wiley, New YorkGoogle Scholar
  8. Teunissen P.J.G . (1996): GPS carrier phase ambiguity fixing concepts. In: Kleusberg, A. and Teunissen PJG.:GPS or GeodesySpringer Berlin/HeidelberGoogle Scholar
  9. Teunisse P.J.G. (1997): A canonical theory for short GPS baselines I-1VJournal of Geodesy(1997)71: 320–336 389–401, 486–501 513–525Google Scholar
  10. Teunissen P.J.G. (1998): Success probability of integer GPS ambiguity rounding and bootstrapping Journal of Geodesy(1998) 72:606–612CrossRefGoogle Scholar
  11. Teunissen P.J.G. (1999): The probability distribution of the GPS baseline for a class of integer ambiguity estimators Journal o Geodesy1999 73: 275–284CrossRefGoogle Scholar
  12. Viertl R . (1997): Einführung in die Stochastik (2. Aufl.). Springer, Wien/New YorkGoogle Scholar
  13. Walley, P . 1991: Statistical Reasoning with Imprecise Probabilities. Chapman and Hall London/New YorkGoogle Scholar
  14. Xu P.E. Cannon and G. Lachapelle 1995: Mixed integer pro-gramming for the resolution of GPS carrier phase ambiguities. Paper resented at the IUGG95 assembly, July 2–14 1995, Boulder Colorado U.S.AGoogle Scholar

Copyright information

© SPringer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • H. Kutterer
    • 1
  1. 1.Geodätisches InstitutUniversität KarlsrueKarlsruheGermany

Personalised recommendations