Maximum Correntropy Kalman Filter
This work addresses robustness issues in Kalman filters for signal processing applications, particularly in noisy environments, but is incremental as it modifies an existing method.
The authors tackled the problem of Kalman filter performance degradation under non-Gaussian, heavy-tailed impulsive noises by proposing the maximum correntropy Kalman filter (MCKF), which uses a robust criterion and a fixed-point algorithm, demonstrating effectiveness and robustness in examples.
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.