The Ensemble Epanechnikov Mixture Filter

TL;DR

This paper introduces the ensemble Epanechnikov mixture filter (EnEMF), a cost-efficient sequential filtering method using the optimal Epanechnikov kernel, demonstrating robustness and improved accuracy in high-dimensional systems.

Contribution

It presents the practical implementation of EnEMF, showing its advantages over Gaussian mixture filters in high-dimensional and dynamic scenarios.

Findings

EnEMF is robust to increasing dimensions.

EnEMF reduces error per particle in Lorenz '96 system.

EnEMF is as cost-efficient as Gaussian mixture filters.

Abstract

In the high-dimensional setting, Gaussian mixture kernel density estimates become increasingly suboptimal. In this work we aim to show that it is practical to instead use the optimal multivariate Epanechnikov kernel. We make use of this optimal Epanechnikov mixture kernel density estimate for the sequential filtering scenario through what we term the ensemble Epanechnikov mixture filter (EnEMF). We provide a practical implementation of the EnEMF that is as cost efficient as the comparable ensemble Gaussian mixture filter. We show on a static example that the EnEMF is robust to growth in dimension, and also that the EnEMF has a significant reduction in error per particle on the 40-variable Lorenz '96 system.