Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Artificial Satellites

The Journal of Space Research Centre of Polish Academy of Sciences

4 Issues per year

CiteScore 2016: 0.33

SCImago Journal Rank (SJR) 2016: 0.179
Source Normalized Impact per Paper (SNIP) 2016: 0.560

Open Access
See all formats and pricing
More options …
Volume 47, Issue 3


On-the-fly Ambiguity Resolution Using an Estimator of the Modified Ambiguity Covariance Matrix for the GNSS Positioning Model Based on Phase Data

S. Cellmer
Published Online: 2012-08-09 | DOI: https://doi.org/10.2478/v10018-012-0015-9

On-the-fly Ambiguity Resolution Using an Estimator of the Modified Ambiguity Covariance Matrix for the GNSS Positioning Model Based on Phase Data

On-the-fly ambiguity resolution (OTF AR) is based on a small data set, obtained from a very short observation session or even from a single epoch observation. In these cases, a classical approach to ambiguity resolution (e.g. the Lambda method) can meet some numerical problems. The basis of the Lambda method is an integer decorrelation of the positive definite ambiguity covariance matrix (ACM). The necessary condition for the proper performing of this procedure is a positive definiteness of ACM. However, this condition is not satisfied in cases of very short observation sessions or single epoch positioning if phase-only observations are used. The subject of this contribution is such a case where phase-only observations are used in the final part of the computational process. The modification of ACM is proposed in order to ensure its positive definiteness. An estimator of modified ACM is a good ACM approximation for the purpose of performing the LAMBDA method. Another problem of short sessions (or a single epoch) positioning is the poor quality of the float solution. In this paper, a cascade adjustment with wide-lane combinations of signals L1 and L2 as a method of solving this problem is presented.

Keywords: GNSS data processing; ambiguity resolution; Lambda method

  • Bakula M. (2010) Network Code DGPS Positioning and Reliable Estimation of Position Accuracy, Survey Review, 42, 315, 82-91.Google Scholar

  • Cellmer S, Wielgosz P, Rzepecka Z (2009) GNSS Carrier Phase Processing Using Modified Ambiguity Function Approach, Florence, Italy, May 27-30 2009, EUREF Publication, Mitteilungen des Bundesamtes für Kartographie und Geodäsie (in print).Google Scholar

  • Cellmer S, Wielgosz P, Rzepecka Z (2010) Modified ambiguity function approach for GPS carrier phase positioning, J Geod, Vol. 84, 264-275.Google Scholar

  • Cellmer S., (2011a): The real time precise positioning using MAFA method, The 8th International Conference ENVIRONMENTAL ENGINEERING, selected papers, Vol. III, Vilnius, 1310-1314.Google Scholar

  • Cellmer S. (2011b), Using the Integer Decorrelation Procedure to increase of the efficiency of the MAFA Method, Artificial Satellites, Vol. 46, No. 3, 103-110.Google Scholar

  • Cocard M and Geiger A (1992) Systematic Search for all Possible Widelanes. Proc. The Sixth International Geodetic Symposium on Satellite Positioning, Columbus Ohio March 1992, Vol. 17-20, 312-318.Google Scholar

  • Cocard M, Bourgon S Kamali O, Collins P (2008) A systematic investigation of optimal carrier-phase combinations for modernized triple-frequency GPS, J Geod, Vol. 82, 555-564.Google Scholar

  • Dach R, Hugentobler U, Fridez P, Meindl M (2007) BERNESE GPS Software Version 5.0., Astronomical Institute, University of BerneGoogle Scholar

  • Gui Q, Han S (2007) New algorithm of GPS rapid positioning based on double k-type ridge estimation. J Surv Eng 133(4):173-178Google Scholar

  • Han S and Rizos C (1996) Improving the computational efficiency of the ambiguity function algorithm. J Geod 1996, Vol. 70, No. 6, 330-341.Google Scholar

  • Henkel and Gunter (2007) Integrity Analysis of Cascaded Integer Resolution with Decorrelation Transformations. Proc. The 2007 National Technical Meeting of The Institute of Navigation January 22 - 24, 2007, 903-910Google Scholar

  • Hofmann-Wellenhof B, Lichtenegger H, Wasle E. (2008) GNSS-Global Navigation Satellite Systems - GPS, GLONASS, Galileo & more, Springer-Verlag WienGoogle Scholar

  • Joosten P (2001) The LAMBDA-Method: MatlabTM Implementation, Version 2.1 Mathematical Geodesy and Positioning, Civil Engineering and Geosciences, Delft University of Technology, The NetherlandsGoogle Scholar

  • Joosten P and Tiberius CCJM (2002) LAMBDA: FAQs. GPS Solutions, 6 (1-2), 109-114Google Scholar

  • Jung J and Enge P (2000) Optimization of Cascade Integer Resolution with Three Civil GPS Frequencies Proc. ION GPS'2000, Salt Lake City, September 2000Google Scholar

  • Kashani, I., Grejner-Brzezinska, D. A., and Wielgosz, P., (2005), Towards Instantaneous Network-Based RTK GPS Over 100 km Distance, Navigation, Vol. 52, No. 4, 239-245Google Scholar

  • Leick A (2004) GPS Satellite Surveying. 3rd edition, John Wiley and Sons, Inc. 2004Google Scholar

  • Li B, Shen Y and Feng Y (2010) Fast GNSS ambiguity resolution as an ill-posed problem J Geod, Vol. 84, No. 11, 683-698Google Scholar

  • Ou J, Wang Z (2004) An improved regularization method to resolve integer ambiguity in rapid positioning using single frequency GPS receivers. Chin Sci Bull 49(2):196-200Google Scholar

  • Shagimuratov, I. I., Baran, L. W., Wielgosz, P., and Yakimova, G. A., (2002), The structure of mid- and high-latitude ionosphere during September 1999 storm event obtained from GPS observations, Annales Geophysicae, Vol. 20, No 6, 665-671Google Scholar

  • Shen Y, Li B (2007) Regularized solution to fast GPS ambiguity resolution. J Surv Eng 133(4):168-172Web of ScienceGoogle Scholar

  • Teunissen PJG (1993) Least squares estimation of the integer GPS ambiguities. Invited lecture, Section IV: theory and methodology. IAG General Meeting, BeijingGoogle Scholar

  • Teunissen P JG (1995) The least-squares ambiguity decorrelation adjustment: a method for fast GPS integer ambiguity estimation, J Geod, 1995, Vol. 70, 65-82.Google Scholar

  • Teunissen PJG, de Jonge PJ and Tiberius CCJM (1996) The volume of the GPS ambiguity search space and its relevance for integer ambiguity resolution, Proc. ION GPS '96 889-898, Kansas City USA, 17-20 September 1996.Google Scholar

  • Teunissen PJG and Kleusberg A (1998) GPS for Geodesy, Springer — Verlag, Berlin Heidelberg New York, 1998Google Scholar

  • Teunissen PJG (1999) An optimality property of the integer least squares estimator, J Geod 73:587-593Web of ScienceGoogle Scholar

  • Urquhart L (2009) An Analysis of Multi-Frequency Carrier Phase Linear Combinations for GNSS, Senior technical report, Department of Geodesy and Geomatics Engineering Technical Report No. 263, University of New Brunswick, Fredericton, Canada, 71Google Scholar

  • Verhagen, S. (2005) "On the Reliability of Integer Ambiguity Resolution," Navigation, Vol. 52, No. 2, pp. 99-110.Google Scholar

  • Verhagen S. and Teunissen PJG (2006) New Global Navigation Satellite System Ambiguity Resolution Method Compared to Existing Approaches JOURNAL OF GUIDANCE, CONTROL, AND DYNAMICS Vol. 29, No. 4, July-August 2006 Delft University of Technology, 2629 HS Delft, The NetherlandsGoogle Scholar

  • Wielgosz P (2011) Quality assessment of GPS rapid static positioning with weighted ionospheric parameters in generalized least squares, GPS Solutions Vol. 15, Issue 2, April 2011, 89-99Google Scholar

  • Xu P (2006) Voronoi Cells, Probabilistic Bounds, and Hypothesis Testing in Mixed Integer Linear Models, IEEE Transactions on Information Theory, 2006, Vol. 52, No. 7, 3122-3138.Google Scholar

About the article

Published Online: 2012-08-09

Published in Print: 2012-01-01

Citation Information: Artificial Satellites, Volume 47, Issue 3, Pages 81–90, ISSN (Online) 2083-6104, ISSN (Print) 0208-841X, DOI: https://doi.org/10.2478/v10018-012-0015-9.

Export Citation

This content is open access.

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

S Cellmer
Survey Review, 2013, Volume 45, Number 332, Page 380
Slawomir Cellmer
Acta Geodynamica et Geomaterialia, 2015, Page 1
Slawomir Cellmer
Acta Geodynamica et Geomaterialia, 2013, Page 393

Comments (0)

Please log in or register to comment.
Log in