Kalman Filtering Under Information Theoretic Criteria

Generally, the traditional Kalman filter (KF) is derived under the well-known minimum mean square error (MMSE) criterion, which is optimal under the 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 to non-Gaussian noises, several robust Kalman filters are derived in this chapter based on a batch-regression model presented in Chap. 2 and information theoretic criteria in Chap. 3. The first is the maximum correntropy Kalman filter (MCKF), which is developed based on the maximum correntropy criterion (MCC) and a fixed-point iterative algorithm. Some other approaches for MCC-based Kalman filtering are also briefly presented. To further improve the performance of MCKF, a Kalman filter algorithm based on the generalized maximum correntropy criterion (GMCKF) is also derived. The GMCKF is more general and flexible, which includes the MCKF with Gaussian kernel as a special case. In addition, to better deal with more complicated non-Gaussian noises such as noises from multimodal distributions, the minimum error entropy Kalman filter (MEE-KF) is also developed in this chapter, by using MEE criterion.