  Recent developments in the realm of state estimation of stochastic dynamic
systems in the presence of non-Gaussian noise have induced a new methodology
called the maximum correntropy filtering. The filters designed under the
maximum correntropy criterion (MCC) utilize a similarity measure (or
correntropy) between two random variables as a cost function. They are shown to
improve the estimators' robustness against outliers or impulsive noises. In
this paper we explore the numerical stability of linear filtering technique
proposed recently under the MCC approach. The resulted estimator is called the
maximum correntropy criterion Kalman filter (MCC-KF). The purpose of this study
is two-fold. First, the previously derived MCC-KF equations are revise and the
related Kalman-like equality conditions are proved. Based on this theoretical
finding, we improve the MCC-KF technique in the sense that the new method
possesses a better estimation quality with the reduced computational cost
compared with the previously proposed MCC-KF variant. Second, we devise some
square-root implementations for the newly-designed improved estimator. The
square-root algorithms are well known to be inherently more stable than the
conventional Kalman-like implementations, which process the full error
covariance matrix in each iteration step of the filter. Additionally, following
the latest achievements in the KF community, all square-root algorithms are
formulated here in the so-called array form. All the MCC-KF variants developed
in this paper are demonstrated to outperform the previously proposed MCC-KF
version in two numerical examples.
