Nonlinear Gaussian filtering via radial basis function approximation

This paper presents a novel type of Gaussian filter - the radial basis Gaussian filter (RB-GF) - for nonlinear state estimation. In the RB-GF, we propose to use radial basis functions (RBFs) to approximate the nonlinear process and measurement functions of a system, considering the superior approximation performance of RBFs. Optimal determination of the approximators is achieved by RBF neural network (RBFNN) learning. Using the RBF based function approximation, the challenging problem of integral evaluation in Gaussian filtering can be well solved, guaranteeing the filtering performance of the RB-GF. The proposed filter is studied through numerical simulation, in which a comparison with other existing methods validates its effectiveness.