FDM and FEM Filters in Terrain Navigation

Ingemar Nygren and Magnus Jansson

Abstract:	Terrain navigation in nearly flat areas is a difficult task since the probability density function (PDF) of the vehicle position typically is multimodal due to terrain repeatability. Traditional methods as TERCOM, TERPROM or similar methods fail in such situations. Instead, Bayesian methods have proven to be useful. A prerequisite for all terrain navigation methods in nearly flat areas is extremely informative measurements of the terrain topography. In addition, methods for efficiently propagating the multimodal probability density function of the vehicle are needed. This paper describes a Bayesian filtering method based on finite differences or finite elements that can efficiently handle the propagation of multimodal PDFs. The paper also goes briefly into the theory behind the filters starting with a problem formulation by stochastic differential equations. The proposed filtering method has been successfully tested with real measurement data and maps and it is fast enough to allow the filter to be used in real time even for fast vehicles. Besides being optimal, the method is highly robust, conditions for stability are well understood, and error estimates are available. Another advantage of the method is that readily available professional software for solving partial differential equations can be adopted.
Published in:	Proceedings of the 2007 National Technical Meeting of The Institute of Navigation January 22 - 24, 2007 The Catamaran Resort Hotel San Diego, CA
Pages:	1155 - 1166
Cite this article:	Nygren, Ingemar, Jansson, Magnus, "FDM and FEM Filters in Terrain Navigation," Proceedings of the 2007 National Technical Meeting of The Institute of Navigation, San Diego, CA, January 2007, pp. 1155-1166.
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