The Ensemble Epanechnikov Mixture Filter

• URL: http://arxiv.org/abs/2408.11164v1
• Date: Tue, 20 Aug 2024 19:50:59 GMT
• Title: The Ensemble Epanechnikov Mixture Filter
• Authors: Andrey A. Popov, Renato Zanetti,
• Abstract summary: We make use of the optimal Epanechnikov mixture kernel density estimate for the sequential filtering scenario through what we term the ensemble Epanechnikov mixture filter (EnEMF) 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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