# The Ensemble Epanechnikov Mixture Filter

arXiv: https://arxiv.org/abs/2408.11164 · HTML: https://mlsanity.com/paper/2408.11164/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 27 references that are in the map.
- First posted on arXiv 20 Aug 2024.

## Builds on (most cited first, 4 of 4)

- [A Bayesian Approach to Multivariate Adaptive Localization in Ensemble-Based Data Assimilation with Time-Dependent Extensions](https://mlsanity.com/paper/1809.08984/) (2018)
- [An Adaptive Covariance Parameterization Technique for the Ensemble Gaussian Mixture Filter](https://mlsanity.com/paper/2212.10323/) (2022)
- [Ensemble-localized Kernel Density Estimation with Applications to the Ensemble Gaussian Mixture Filter](https://mlsanity.com/paper/2308.14143/) (2023)
- [What are You Weighting For? Improved Weights for Gaussian Mixture Filtering With Application to Cislunar Orbit Determination](https://mlsanity.com/paper/2405.11081/) (2024)

## Abstract (arXiv)

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.