Iterative Nonlinear Kalman Filtering via Variational Evidence Lower Bound Maximization

Abstract

In this paper, the problem of nonlinear Kalman filtering is considered from the viewpoint of variational evidence lower bound maximization, where the posterior distribution is approximated iteratively by a solvable variational distribution. In this way, the hardly intractable integration of the nonlinear posterior probability density function can be converted to the optimization of evidence lower bound. Based on linearization, an iterative nonlinear filter is derived in a closed form. Examples of tracking a moving target by three range-only sensors and univariate nonstationary growth model are presented to demonstrate the efficiency of proposed method compared with several nonlinear filters, as well as the interpretation of ELBO with different iterations and Kullback-Leibler divergence between estimated posterior distribution and true probability density.