Attacking Multipath Problems by Solving Non Linear Integral Equations

Karl Kaindl and Norbert Niklasch

Abstract:	Various publications ([Weill], [Townsend]) discuss the limits for pseudoranging in the presence of multipath effects. It has been shown that in many applications, multipath remains a major source of pseudoranging error. Even by applying elaborated methods ([Weill]), multipath remains a serious problem. This for three reasons: 1. In a real-time environment it is necessary to reduce the computational load drastically. 2. Numerical results of the [Weill] approach can be improved. 3. Hardware based solutions can be implemented purely software based. Even if the performance of a particular algorithm in the presence of multipath were close to the limit, costly attempts to significantly improve the performance could be avoided. [Weill] has shown the ultimate limit for pseudorange accuracy in the 2-path case. In this paper we develop an algorithm using classical estimation theory by solving non linear integral equations. In the case of 2- path that means to solve a non linear equation system for four variables. This can be easily extended to 3- or 4-path case solving non linear equations simultaneously for six or eight variables respectively. The two main problems in this approach lie in finding an appropriate initial point 0 x for the iteration which is near the solution ∗ x and the speed of convergence. We used a combined method which starts with raw initial approximations 0 x . To be certain in which area convergence would take place we scanned [0,1]- interval in the 4-dimensional Euclidian space and investigated each grid point for its limit. There are some very interesting results to report. The speed of convergence is locally quadratic.
Published in:	Proceedings of the 14th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 2001) September 11 - 14, 2001 Salt Palace Convention Center Salt Lake City, UT
Pages:	2153 - 2160
Cite this article:	Kaindl, Karl, Niklasch, Norbert, "Attacking Multipath Problems by Solving Non Linear Integral Equations," Proceedings of the 14th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 2001), Salt Lake City, UT, September 2001, pp. 2153-2160.
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