Stability and Convergence of Stochastic Particle Flow Filters

TL;DR

This paper analyzes the stability and convergence properties of a family of stochastic particle flow filters used in nonlinear filtering and Bayesian inference, demonstrating their stability without Gaussian assumptions.

Contribution

It establishes the stability of stochastic particle flow filters using Lyapunov stability, without relying on Gaussian measurement likelihoods.

Findings

Particles maintain the desired posterior distribution.

Particles stay close but do not converge to the maximum likelihood estimate.

Stability is maintained for the entire family of filters.

Abstract

In this paper, we examine dynamic properties of particle flows for a recently derived parameterized family of stochastic particle flow filters for nonlinear filtering and Bayesian inference. In particular, we establish that particles maintain desired posterior distribution without the Gaussian assumption on measurement likelihood. Adopting the concept of Lyapunov stability, we further show that particles stay close but do not converge to the maximum likelihood estimate of the posterior distribution. The results demonstrate that stability of particle flows is maintained for this family of stochastic particle flow filters.