A Gaussian mixture ensemble transform filter

TL;DR

The paper introduces the ensemble Gaussian mixture filter (EGMF), a generalization of the ensemble Kalman filter that can handle non-Gaussian distributions, demonstrated on simple dynamical systems.

Contribution

It presents a new ensemble filter algorithm capable of tracking non-Gaussian distributions, extending the ensemble Kalman filter framework.

Findings

EGMF successfully tracks non-Gaussian, multimodal distributions.

Demonstrated on Brownian, Langevin, and Lorenz-63 models.

Capable of handling complex dynamical systems with non-Gaussian features.

Abstract

We generalize the popular ensemble Kalman filter to an ensemble transform filter where the prior distribution can take the form of a Gaussian mixture or a Gaussian kernel density estimator. The design of the filter is based on a continuous formulation of the Bayesian filter analysis step. We call the new filter algorithm the ensemble Gaussian mixture filter (EGMF). The EGMF is implemented for three simple test problems (Brownian dynamics in one dimension, Langevin dynamics in two dimensions, and the three dimensional Lorenz-63 model). It is demonstrated that the EGMF is capable to track systems with non-Gaussian uni- and multimodal ensemble distributions.