Bridging the ensemble Kalman and particle filter

TL;DR

This paper introduces a novel method that smoothly transitions between ensemble Kalman and particle filters, improving handling of non-Gaussian features in high-dimensional filtering with limited samples.

Contribution

It proposes a continuous transition procedure with automatic parameter selection to combine the strengths of ensemble Kalman and particle filters.

Findings

Effective handling of non-Gaussian features in high-dimensional settings.

Automatic parameter choice improves filter performance.

Reduces sample degeneracy while capturing complex distribution features.

Abstract

In many applications of Monte Carlo nonlinear filtering, the propagation step is computationally expensive, and hence, the sample size is limited. With small sample sizes, the update step becomes crucial. Particle filtering suffers from the well-known problem of sample degeneracy. Ensemble Kalman filtering avoids this, at the expense of treating non-Gaussian features of the forecast distribution incorrectly. Here we introduce a procedure which makes a continuous transition indexed by gamma in [0,1] between the ensemble and the particle filter update. We propose automatic choices of the parameter gamma such that the update stays as close as possible to the particle filter update subject to avoiding degeneracy. In various examples, we show that this procedure leads to updates which are able to handle non-Gaussian features of the prediction sample even in high-dimensional situations.