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

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.