Mathematical Models for Combined GPS and GLONASS Positioning

Jinling Wang

Abstract:	In combined GPS and GLONASS positioning, a number of options exist to construct the mathematical models. For example, GPS and GLONASS carrier phases can be modelled using GPS-GPS and GLONASS-GLONASS double-differencing (DD) formulation (the separated formulation), or GPS-GLONASS DD formulation (the mixed formulation). Although all the mathematical models are valid for use in data processing, their performance in ambiguity resolution, may be different due to the differences between the GPS and GLONASS frequencies and error sources. Therefore, comparing the reliability of all the mathematical models and identifying the optimal model are of great importance. In this paper, the single-differencing (SD) and double-differencing (DD) procedures are theoretically analysed in the case of combined GPS and GLONASS positioning. The mathematical models and their relative redundancy in combining GPS and GLONASS observations are presented. Based on the test data sets collected by the author, the correct ambiguity rates of the different models are compared, in which the rates range from 78.9% to 97.5%. In order to geometrically evaluate the mathematical models, the concept of model sensitivity to the receiver clock parameters has been introduced, which is measured by the (multiple) correlation coefficients. In the case of single-epoch solutions, it has been theoretically proved that the models the mixed DD carrier phase formulation have a higher sensitivity to clock errors than the models using the separated DD carrier phase formulation. For the 5 test data sets, the optimal mathematical model has been identified, which uses the DD GPS and SD GLONASS pseudo-ranges together with the GPS-GPS and GLONASS-GLONASS DD carrier phases.
Published in:	Proceedings of the 11th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 1998) September 15 - 18, 1998 Nashville, TN
Pages:	1333 - 1344
Cite this article:	Wang, Jinling, "Mathematical Models for Combined GPS and GLONASS Positioning," Proceedings of the 11th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 1998), Nashville, TN, September 1998, pp. 1333-1344.
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