Comparison of GPS Solution Distributions with Respect to Different Pseudorange Error Distributions between Linearized Least Squares and Bancroft’s Algorithm

JiHong Zhang

Abstract:	In the past several years, Bancroft’s algorithm has been developed as an effective method to solve the closed-form solution of the GPS pseudorange equations. This paper focuses on the question of the actual distributions of GPS solution with respect to different pseudorange error probability distributions. Based on both Bancroft’s approach and conventional iterative linearized least squares, some simulations are implemented and analyzed using different pseudorange error probability distributions (e.g., uncorrelated additive Gaussian distribution, correlated additive Gaussian distribution, and longer tailed mixture of Gaussian distributions). Also some stochastic performance between Bancroft’s algorithm and iterative least squares are investigated, especially for the case of non-Gaussian error distribution. The different stochastic performance between these two methods is very clearly shown in case of non-Gaussian pseudorange error distribution.
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:	1401 - 1410
Cite this article:	Zhang, JiHong, "Comparison of GPS Solution Distributions with Respect to Different Pseudorange Error Distributions between Linearized Least Squares and Bancroft’s Algorithm," Proceedings of the 11th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 1998), Nashville, TN, September 1998, pp. 1401-1410.
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