Maximum Correntropy Derivative-Free Robust Kalman Filter and Smoother

Abstract

We consider the problem of robust estimation involving filtering and\nsmoothing for nonlinear state space models which are disturbed by heavy-tailed\nimpulsive noises. To deal with heavy-tailed noises and improve the robustness\nof the traditional nonlinear Gaussian Kalman filter and smoother, we propose in\nthis work a general framework of robust filtering and smoothing, which adopts a\nnew maximum correntropy criterion to replace the minimum mean square error for\nstate estimation. To facilitate understanding, we present our robust framework\nin conjunction with the cubature Kalman filter and smoother. A half-quadratic\noptimization method is utilized to solve the formulated robust estimation\nproblems, which leads to a new maximum correntropy derivative-free robust\nKalman filter and smoother. Simulation results show that the proposed methods\nachieve a substantial performance improvement over the conventional and\nexisting robust ones with slight computational time increase.\n