Adaptive particle filter with fixed empirical density quality

Abstract

Abstract The paper deals with the particle filter in state estimation of a discrete-time nonlinear non-Gaussian system. The goal of the paper is to design a sample size adaptation technique to guarantee the quality of an empirical probability density function (pdf) which approximates a target filtering pdf. The quality is measured by inaccuracy (cross-information) between the empirical pdf and the filtering pdf. It is shown that for increasing sample size the inaccuracy converges to the Shannon differential entropy (SDE) of the filtering pdf. The proposed technique adapts the sample size to keep a difference between the inaccuracy and the SDE within prespecified bounds with a pre-specified probability. The particle filter with the proposed sample size adaptation technique is illustrated in a numerical example.