Affine-Mapping based Variational Ensemble Kalman Filter
This work addresses filtering problems in domains like data assimilation or state estimation, but it appears incremental as it builds on existing Ensemble Kalman filter methods with a variational twist.
The authors tackled sequential Bayesian filtering with generic observation models by proposing an affine-mapping based variational Ensemble Kalman filter, which constructs an affine mapping from prior to posterior ensembles via variational Bayesian minimization of Kullback-Leibler divergence, and demonstrated competitive performance against existing methods in numerical examples.
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.