Maximum Correntropy Unscented Filter

TL;DR

This paper introduces the maximum correntropy unscented filter (MCUF), a robust nonlinear state estimation method that enhances the UKF's performance under non-Gaussian, impulsive noise conditions using the maximum correntropy criterion.

Contribution

The paper proposes a novel filter combining the unscented transformation with maximum correntropy for improved robustness against impulsive noises in nonlinear systems.

Findings

MCUF outperforms UKF in heavy-tailed noise environments.

The method demonstrates strong robustness in illustrative examples.

Enhanced accuracy in nonlinear state estimation under non-Gaussian noise.

Abstract

The unscented transformation (UT) is an efficient method to solve the state estimation problem for a non-linear dynamic system, utilizing a derivative-free higher-order approximation by approximating a Gaussian distribution rather than approximating a non-linear function. Applying the UT to a Kalman filter type estimator leads to the well-known unscented Kalman filter (UKF). Although the UKF works very well in Gaussian noises, its performance may deteriorate significantly when the noises are non-Gaussian, especially when the system is disturbed by some heavy-tailed impulsive noises. To improve the robustness of the UKF against impulsive noises, a new filter for nonlinear systems is proposed in this work, namely the maximum correntropy unscented filter (MCUF). In MCUF, the UT is applied to obtain the prior estimates of the state and covariance matrix, and a robust statistical linearization regression based on the maximum correntropy criterion (MCC) is then used to obtain the posterior estimates of the state and covariance. The satisfying performance of the new algorithm is confirmed by two illustrative examples.