Going for the Optimum: Penalized Nonlinear Maximum Likelihood Proved to Return Optimized Multipath Signal Decomposition Parameters

K. Kaindl, S. Pilz

Abstract:	Recent research results have shown that problems connected to multipath are ill conditioned problems. Thus, being one of the major error sources (up to 30m) in satellite navigation, multipath mitigation needs a very sensitive treatment. Many publications [1], [3], [4], discuss the limits for pseudoranging in the presence of multipath effects. Although great endeavour has put forward the insight towards the core of the problem, there is still room improving the parameter estimation using biased estimation theory to come to an improved pseudoranging result. Theoretically, multipath errors can be reduced under 1m at best ([1], [2]). From the practical point we think this theoretical benchmark is hardly reachable. Most recently, [5] has shown the benefit using nonlinear estimation theory for solving multipath problems numerically. There it was pointed out how parameters for a single reflected signal (2-path problem) were estimated (amplitude, time delay) to improve DLL path separation characteristics. Further on, depending on the type of multipath problem, this results in path separation errors up to 5m ([6]). It tuned out that the crucial point of that approach was a suboptimal wave decomposition of the direct signal and the incoming multipath signal. Generally said, the multipath signal can be interpreted as a bias from the expectation value. During our studies have seen that the problem is better modelled, if the ill conditioning is described by introducing a bias, i.e. or , for a parameter we want to estimate. In this paper we used parameter estimation theory, optimized for the presence of multipath effects. For the first time, we present methods using non linear parameter estimation theory for the biased case.
Published in:	Proceedings of the 16th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS/GNSS 2003) September 9 - 12, 2003 Oregon Convention Center Portland, OR
Pages:	819 - 828
Cite this article:	Kaindl, K., Pilz, S., "Going for the Optimum: Penalized Nonlinear Maximum Likelihood Proved to Return Optimized Multipath Signal Decomposition Parameters," Proceedings of the 16th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS/GNSS 2003), Portland, OR, September 2003, pp. 819-828.
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