On the Role of the Diffusion Matrix in Stiffness Mitigation for Stochastic Particle Flow Filters

Stochastic particle flow filters are driven by diffusion processes. Recently it has been discovered that a stochastic particle flow filter exists for any given diffusion matrix. Therefore, the diffusion matrix effectively acts as a design parameter. A variety of diffusion matrices have been proposed in the literature. One natural question is: How to select the diffusion matrix to improve filtering performance? Particle flow filters are described by stochastic differential equations and realized through numerical discretization whose accuracy is affected by both the stiffness of the differential equations and the value of the diffusion matrix. In this paper, we examine the role of the diffusion matrix in stiffness mitigation of stochastic particle flows and its trade-off with numerical accuracy. Objective functions are proposed to balance several conflicting factors of stiffness mitigation and numerical accuracy. Analytic solutions of optimal diffusion matrices are derived for stiffness mitigation of stochastic particle flows. Results are illustrated using numerical examples.