  Traditional Kalman filter (KF) is derived under the well-known minimum mean
square error (MMSE) criterion, which is optimal under Gaussian assumption.
However, when the signals are non-Gaussian, especially when the system is
disturbed by some heavy-tailed impulsive noises, the performance of KF will
deteriorate seriously. To improve the robustness of KF against impulsive
noises, we propose in this work a new Kalman filter, called the maximum
correntropy Kalman filter (MCKF), which adopts the robust maximum correntropy
criterion (MCC) as the optimality criterion, instead of using the MMSE. Similar
to the traditional KF, the state mean and covariance matrix propagation
equations are used to give prior estimations of the state and covariance matrix
in MCKF. A novel fixed-point algorithm is then used to update the posterior
estimations. A sufficient condition that guarantees the convergence of the
fixed-point algorithm is given. Illustration examples are presented to
demonstrate the effectiveness and robustness of the new algorithm.
