A Stochastic Covariance Shrinkage Approach to Particle Rejuvenation in the Ensemble Transform Particle Filter

TL;DR

This paper introduces a novel stochastic covariance shrinkage method for particle rejuvenation in ensemble transform particle filters, enhancing performance with fewer particles by incorporating climatological prior information.

Contribution

It proposes a new rejuvenation technique using stochastic covariance shrinkage and climatological samples, improving filter robustness with small ensemble sizes.

Findings

Significant improvement in analysis accuracy for low ensemble sizes.

Enhanced particle filter performance with the proposed rejuvenation method.

Applicable to ensemble transport particle filters and their second order variants.

Abstract

Rejuvenation in particle filters is necessary to prevent the collapse of the weights when the number of particles is insufficient to sample the high probability regions of the state space. Rejuvenation is often implemented in a heuristic manner by the addition of stochastic samples that widen the support of the ensemble. This work aims at improving canonical rejuvenation methodology by the introduction of additional prior information obtained from climatological samples; the dynamical particles used for importance sampling are augmented with samples obtained from stochastic covariance shrinkage. The ensemble transport particle filter, and its second order variant, are extended with the proposed rejuvenation approach. Numerical experiments show that modified filters significantly improve the analyses for low dynamical ensemble sizes.