Maximum correntropy smoothers based on information theoretic learning in non-Gaussian environments

Non-Gaussian noise processing is difficult in dynamics systems, and smoothing plays an important role for state estimation. As an optimization criterion in information theoretic learning, the maximum correntropy has been recently applied to filtering tasks and achieves decent performance in various non-Gaussian scenarios. In this paper, by using maximum correntropy criterion instead of minimum mean square error criterion, two new smoothers called a fixed-point maximum correntropy smoother and a fixed-lag maximum correntropy smoother are proposed to improve smoothing performance in linear dynamics systems with complex non-Gaussian noise. Similar to the traditional Kalman smoother, the proposed smoothers are also online recursive algorithms, which use propagation equations to update the state estimates and the corresponding covariance matrices. In addition, the computational complexities of the proposed smoothers are analyzed, and their performance is further discussed mathematically using estimate covariance. The simulation results demonstrate that the two proposed maximum correntropy smoothers exhibit superior smoothing performance compared to conventional Kalman smoothers when the underlying system is subjected to non-Gaussian noise, and the best observed improvement in performance is approximately 50% and 80%, respectively.