Linear-Mapping based Variational Ensemble Kalman Filter

We propose a linear-mapping based variational Ensemble Kalman filter for sequential Bayesian filtering problems with generic observation models. Specifically, the proposed method is formulated as to construct a linear mapping from the prior ensemble to the posterior one, and the linear mapping is computed via a variational Bayesian formulation, i.e., by minimizing the Kullback-Leibler divergence between the transformed distribution by the linear mapping and the actual posterior. 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.