FDM and FEM Filters in Terrain Navigation

摘要

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. rnA 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. rnThe 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.