An Iterative Nonlinear Filter Based on Posterior Distribution Approximation via Penalized Kullback–Leibler Divergence Minimization
Sanfeng Hu, Liping Guo, Jie Zhou · IEEE Signal Processing Letters · 2022
This letter deals with Gaussian approximation of complicated posterior distribution involved in the Bayesian paradigm for nonlinear dynamic systems. A general formulation for Gaussian approximation is first provided by equivalently representing posterior distribution as a Gaussian one with some constraint via embedding technique. In this work, it is specified as a penalized Kullback–Leibler divergence minimization problem. This minimization is solved for the expected Gaussian approximation by utilizing a pre-selected cubature rule and the conditional gradient method. Then, a novel iterative filter is developed for nonlinear dynamic systems. In addition, it is also proved to be optimal in linear cases and demonstrated to be effective through simulations.