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.
Bakula M. (2010) Network Code DGPS Positioning and Reliable Estimation of Position Accuracy, Survey Review, 42, 315, 82-91.
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).
Cellmer S, Wielgosz P, Rzepecka Z (2010) Modified ambiguity function approach for GPS carrier phase positioning, J Geod, Vol. 84, 264-275.
Cellmer S., (2011a): The real time precise positioning using MAFA method, The 8th International Conference ENVIRONMENTAL ENGINEERING, selected papers, Vol. III, Vilnius, 1310-1314.
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.
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.
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.
Dach R, Hugentobler U, Fridez P, Meindl M (2007) BERNESE GPS Software Version 5.0., Astronomical Institute, University of Berne
Gui Q, Han S (2007) New algorithm of GPS rapid positioning based on double k-type ridge estimation. J Surv Eng 133(4):173-178
Han S and Rizos C (1996) Improving the computational efficiency of the ambiguity function algorithm. J Geod 1996, Vol. 70, No. 6, 330-341.
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, 903-910
Hofmann-Wellenhof B, Lichtenegger H, Wasle E. (2008) GNSS-Global Navigation Satellite Systems - GPS, GLONASS, Galileo & more, Springer-Verlag Wien
Joosten P (2001) The LAMBDA-Method: MatlabTM Implementation, Version 2.1 Mathematical Geodesy and Positioning, Civil Engineering and Geosciences, Delft University of Technology, The Netherlands
Joosten P and Tiberius CCJM (2002) LAMBDA: FAQs. GPS Solutions, 6 (1-2), 109-114
Jung J and Enge P (2000) Optimization of Cascade Integer Resolution with Three Civil GPS Frequencies Proc. ION GPS'2000, Salt Lake City, September 2000
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, 239-245
Leick A (2004) GPS Satellite Surveying. 3rd edition, John Wiley and Sons, Inc. 2004
Li B, Shen Y and Feng Y (2010) Fast GNSS ambiguity resolution as an ill-posed problem J Geod, Vol. 84, No. 11, 683-698
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):196-200
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, 665-671
Shen Y, Li B (2007) Regularized solution to fast GPS ambiguity resolution. J Surv Eng 133(4):168-172
Teunissen PJG (1993) Least squares estimation of the integer GPS ambiguities. Invited lecture, Section IV: theory and methodology. IAG General Meeting, Beijing
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.
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.
Teunissen PJG and Kleusberg A (1998) GPS for Geodesy, Springer — Verlag, Berlin Heidelberg New York, 1998
Teunissen PJG (1999) An optimality property of the integer least squares estimator, J Geod 73:587-593
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, 71
Verhagen, S. (2005) "On the Reliability of Integer Ambiguity Resolution," Navigation, Vol. 52, No. 2, pp. 99-110.
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 Netherlands
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, 89-99
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.