Maximum Correntropy Two-Filter Smoothing

This paper presents recursive two-filter smoothing (TFS) in the criterion of maximizing the correntropy (MC) instead of minimizing the mean square error, to pursue robustness for outlier rejections caused by non-Gaussian noises and obtain high-precision state estimate, which is motivated by non-cooperative target backtracking. Here, non-cooperative target tracking often needs to consider non-Gaussian noises. The MC-based recursive TFS (abbreviated as MRTFS) is put forward, where both the forward and backward filters are performed independently and recursively in the criterion of MC. Meanwhile, an MC-based fusion rule is further designed to obtain the final smoothed estimate by fusing the forward filtered estimate and backward predicted estimate step by step, in order to improve estimation accuracy. A target backtracking example with non-Gaussian noises is simulated to show the advantage of estimation accuracy of the proposed MRTFS over Kalman filter/smoothers, MC-based Kalman filter/Rauch-Tung-Striebel smoother, in terms of different kernel bandwidths and levels of process noises.