  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.
