Gaussian Approximation Filter Based on Divergence Minimization for Nonlinear Dynamic Systems

In the Bayesian filtering paradigm, approximation of posterior distribution is an important research topic for nonlinear dynamic systems. In this paper, we aim at obtaining its Gaussian approximation via KL divergence minimization. We formulate the problem as a nonlinear programming problem with linear constraints and resort to the feasible direction method for the solution. Since the gradient of the objective function involves intractable integrals, we adopt a cubature rule to calculate the gradient, which is suitable for real-time filtering for its simplicity, efficiency, and accuracy. Based on the Gaussian approximation, a nonlinear filter is derived, and it is demonstrated to be effective by simulations.