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.
翻译:我们建议为波亚州相继过滤的通用观测模型问题建立一个基于折叠图的基于变式图谱的Kalman过滤器,具体地说,拟议方法旨在构建从先前的组合图到后继模型的折叠图,通过一种变式贝亚斯式的配方,即通过尽可能缩小通过松动图和实际的后继图和后继器的变形分布之间的Kullback-Leibel差异,来计算折叠图。正在研究由此产生的优化问题的一些理论属性,并提议了一个梯度下降计划来解决由此产生的优化问题。我们用数字实例证明,该方法与现有方法相比具有竞争性性能。