Comparison of Gain Function Approximation Methods in the Feedback Particle Filter

This paper is concerned with a study of the different proposed gain-function approximation methods in the feedback particle filter. The feedback particle filter (FPF) has been introduced in a series of papers as a control-oriented, resampling-free, variant of the particle filter. The FPF applies a feedback gain to control each particle, where the gain function is found as a solution to a boundary value problem. approximate solutions are usually necessary, because closed-form expressions can only be computed in certain special cases. By now there exist a number of different methods to approximate the optimal gain function, but it is unclear which method is preferred over another. This paper provides an analysis of some of the recently proposed gain-approximation methods. We discuss computational and algorithmic complexity, and compare performance using well-known benchmark examples.