A comparative study of nonlinear filtering techniques

In a recent work it is shown that importance sampling can be avoided in the particle filter through an innovation structure inspired by traditional nonlinear filtering combined with optimal control formalisms. The resulting algorithm is referred to as feedback particle filter. The purpose of this paper is to provide a comparative study of the feedback particle filter (FPF). Two types of comparisons are discussed: i) with the extended Kalman filter, and ii) with the conventional resampling-based particle filters. The comparison with Kalman filter is used to highlight the feedback structure of the FPF. Also computational cost estimates are discussed, in terms of number of operations relative to EKF. Comparison with the conventional particle filtering approaches is based on a numerical example taken from the survey article on the topic of nonlinear filtering [2]. Comparisons are provided for both computational cost and accuracy. A secondary purpose of this paper is to provide a summary of the FPF algorithm, that can aid practitioners to rapidly implement the algorithm. A detailed algorithm (pseudo-code) is included, and compared against an EKF algorithm. Such comparisons also help highlight the feedback structure of the FPF algorithm.extended Kalman filter,