Variance reduction for particle filters of systems with time-scale separation

TL;DR

This paper introduces a particle filter method tailored for systems with time-scale separation, leveraging averaging and Rao-Blackwellization to reduce variance and computational cost, demonstrated on multiscale stochastic models.

Contribution

The paper develops a novel particle filter that exploits time-scale separation for variance reduction and efficiency improvements using averaging and Rao-Blackwellization techniques.

Findings

Faster particle filter with lower variance compared to traditional methods.

Effective on multiscale stochastic differential equations.

Validated on chemical reaction-inspired jump diffusion models.

Abstract

We present a particle filter construction for a system that exhibits time-scale separation. The separation of time-scales allows two simplifications that we exploit: i) The use of the averaging principle for the dimensional reduction of the system needed to solve for each particle and ii) the factorization of the transition probability which allows the Rao-Blackwellization of the filtering step. Both simplifications can be implemented using the coarse projective integration framework. The resulting particle filter is faster and has smaller variance than the particle filter based on the original system. The method is tested on a multiscale stochastic differential equation and on a multiscale pure jump diffusion motivated by chemical reactions.