A modified particle filter that reduces weight collapse

TL;DR

This paper introduces a simple modification to particle filters that reduces weight collapse by balancing particle weights through an energy-based approach, leading to improved state estimation in various models.

Contribution

A novel, easy-to-implement modification to particle filters that mitigates weight degeneracy using energy-based weight adjustments.

Findings

Improved weight distribution over classical particle filters.

Enhanced state estimation accuracy in linear and nonlinear models.

Outperforms classical particle filters and ensemble Kalman filters in experiments.

Abstract

Particle filters are a widely used Monte Carlo based data assimilation technique that estimates the probability distribution of a system's state conditioned on observations through a collection of weights and particles. A known problem for particle filters is weight collapse, or degeneracy, where a single weight attains a value of one while all others are close to zero, thereby collapsing the estimated distribution. We address this issue by introducing a novel modification to the particle filter that is simple to implement and inspired by energy-based diversity measures. Our approach adjusts particle weights to minimize a two-body energy potential, promoting balanced weight distributions and mitigating collapse. We demonstrate the performance of this modified particle filter in a series of numerical experiments with linear and nonlinear dynamical models, where we compare with the classical particle filter and ensemble Kalman filters in the nonlinear case. We find that our new approach improves weight distributions compared to the classical particle filter and thereby improve state estimates.