Bayesian Nonlinear Filtering via Information Geometric Optimization

Abstract

In this paper, Bayesian nonlinear filtering is considered from the viewpoint of information geometry and a novel filtering method is proposed based on information geometric optimization. Under the Bayesian filtering framework, we derive a relationship between the nonlinear characteristics of filtering and the metric tensor of the corresponding statistical manifold. Bayesian joint distributions are used to construct the statistical manifold. In this case, nonlinear filtering can be converted to an optimization problem on the statistical manifold and the adaptive natural gradient descent method is used to seek the optimal estimate. The proposed method provides a general filtering formulation and the Kalman filter, the Extended Kalman filter (EKF) and the Iterated Extended Kalman filter (IEKF) can be seen as special cases of this formulation. The performance of the proposed method is evaluated on a passive target tracking problem and the results demonstrate the superiority of the proposed method compared to various Kalman filter methods.