Affine-Mapping based Variational Ensemble Kalman Filter

TL;DR

This paper introduces an affine-mapping variational Ensemble Kalman filter that constructs an affine transformation from prior to posterior ensembles using a variational approach, improving Bayesian filtering.

Contribution

It presents a novel affine-mapping based variational framework for Ensemble Kalman filtering, with theoretical analysis and a gradient descent solution.

Findings

Demonstrates competitive performance against existing methods

Provides theoretical properties of the optimization problem

Uses a gradient descent scheme for computation

Abstract

We propose an affine-mapping based variational Ensemble Kalman filter for sequential Bayesian filtering problems with generic observation models. Specifically, the proposed method is formulated as to construct an affine mapping from the prior ensemble to the posterior one, and the affine mapping is computed via a variational Bayesian formulation, i.e., by minimizing the Kullback-Leibler divergence between the transformed distribution through the affine mapping and the actual posterior. Some theoretical properties of resulting optimization problem are studied and a gradient descent scheme is proposed to solve the resulting optimization problem. With numerical examples we demonstrate that the method has competitive performance against existing methods.