Maximum Correntropy Derivative-Free Robust Kalman Filter and Smoother

TL;DR

This paper introduces a new robust filtering and smoothing framework using maximum correntropy to handle heavy-tailed impulsive noises in nonlinear state space models, enhancing robustness over traditional methods.

Contribution

It proposes a maximum correntropy-based robust Kalman filter and smoother with a derivative-free approach, improving robustness against impulsive noises in nonlinear models.

Findings

Significant performance improvement over traditional filters.

Effective handling of heavy-tailed impulsive noises.

Slight increase in computational time.

Abstract

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