Efficient particle filtering through residual nudging

TL;DR

This paper proposes residual nudging, a technique to improve particle filter accuracy and stability by controlling the residual norm of state estimates, especially effective with fewer particles.

Contribution

The paper introduces residual nudging, a novel method to enhance particle filter performance by adjusting residuals in the observation space.

Findings

Residual nudging improves filter accuracy.

Residual nudging enhances stability against divergence.

Effective with a small number of particles.

Abstract

We introduce an auxiliary technique, called residual nudging, to the particle filter to enhance its performance in cases that it performs poorly. The main idea of residual nudging is to monitor, and if necessary, adjust the residual norm of a state estimate in the observation space so that it does not exceed a pre-specified threshold. We suggest a rule to choose the pre-specified threshold, and construct a state estimate accordingly to achieve this objective. Numerical experiments suggest that introducing residual nudging to a particle filter may (substantially) improve its performance, in terms of filter accuracy and/or stability against divergence, especially when the particle filter is implemented with a relatively small number of particles.