Improving the particle filter in high dimensions using conjugate artificial process noise

TL;DR

This paper introduces a modified particle filter that adds artificial process noise and combines proposals to improve high-dimensional state inference, reducing degeneracy and enhancing performance in complex models.

Contribution

The authors propose a novel particle filtering method that incorporates artificial process noise and a hybrid proposal, addressing high-dimensional challenges and outperforming standard filters.

Findings

Significant performance improvement over standard particle filters.

Effective in both linear-Gaussian and non-linear models.

Reduces particle degeneracy in high-dimensional settings.

Abstract

The particle filter is one of the most successful methods for state inference and identification of general non-linear and non-Gaussian models. However, standard particle filters suffer from degeneracy of the particle weights, in particular for high-dimensional problems. We propose a method for improving the performance of the particle filter for certain challenging state space models, with implications for high-dimensional inference. First we approximate the model by adding artificial process noise in an additional state update, then we design a proposal that combines the standard and the locally optimal proposal. This results in a bias-variance trade-off, where adding more noise reduces the variance of the estimate but increases the model bias. The performance of the proposed method is empirically evaluated on a linear-Gaussian state space model and on the non-linear Lorenz'96 model. For both models we observe a significant improvement in performance over the standard particle filter.