  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.
