Variance Component Estimation to Facilitate GPS Ambiguity Resolution

Joz Wu and Chung-Ming Tsai

Abstract:	For GPS kinematic positioning, the carrier phase ambiguity resolution and the stochastic measurement modeling are two key subjects that deserve research efforts. In resolving dual-frequency whole-cycle ambiguities, a processing algorithm needs to be correct, reliable and fast. In modeling measurement stochastics, the algorithm should be realistic and optimal. This paper introduces the necessary theory, leading to a decorrelating transformation technique. It achieves the objective to fix ambiguities by reducing the number of potentially correct ambiguity parameters. Another technique used for estimating variance components is then introduced to modify the prior measurement covariance matrix. The theoretical formulation is derived from the best invariant quadratic unbiased estimator. By utilizing the integer transformation and the variance estimation algorithms, ManGo software program was made available to study a 7.5 km terrestrial baseline. Although the baseline was statically observed, the processings were conducted in a time-varying mode, so as to obtain both kinematic positioning precision and accuracy. Based on several measuring epochs of GPS L1 and L2 phase data, the diagonalizing transformation of an ambiguity covariance matrix already demarcates a confidence region that encompasses the correct integer-valued ambiguity solution. Moreover, the variance components estimator yields distinct, multiplicative factors, one variance for the measured L1 carrier phases and the other variance for the L2 phases. An adaptation of the prior covariance matrix to real-world phase measurements can, to some extent, benefit accurate kinematic GPS positioning.
Published in:	Proceedings of the 15th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 2002) September 24 - 27, 2002 Oregon Convention Center Portland, OR
Pages:	2809 - 2815
Cite this article:	Wu, Joz, Tsai, Chung-Ming, "Variance Component Estimation to Facilitate GPS Ambiguity Resolution," Proceedings of the 15th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 2002), Portland, OR, September 2002, pp. 2809-2815.
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