On the Design of Stochastic Particle Flow Filters

Abstract

There are mainly two types of particle flows in the design of particle flow filters: The deterministic flows and the stochastic flows as diffusion processes. These two types of flows seem to share little commonality. In this paper, we revisit the design of particle flow filters and build a connection between these two types of particle flows: a deterministic flow can be obtained by modifying a stochastic flow, and vice versa. Particle flows are represented by differential equations which are often realized in practice by difference equations through discretization. The accuracy of such numerical approximations is impacted by the transient dynamics of particle flows. We examine the role of the diffusion matrix in changing the transient dynamics of stochastic particle flows. We propose methods for the design of the diffusion matrix to improve the transient dynamics of particle flows from three perspectives: condition number reduction, feedback control, and covariance reduction. Analytical forms of optimal diffusion matrices are obtained for reducing filtering errors. Numerical examples are included to illustrate the results.