Maximum Correntropy Unscented Filter
This work addresses robustness in state estimation for nonlinear systems under impulsive noise, an incremental improvement over the UKF for specific noise conditions.
The authors tackled the problem of state estimation in nonlinear systems with non-Gaussian, heavy-tailed impulsive noises, which degrade the performance of the unscented Kalman filter (UKF). They proposed the maximum correntropy unscented filter (MCUF), achieving improved robustness as confirmed by two illustrative examples.
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.