Maximum Correntropy Two-Filter Smoothing for Nonlinear Systems With Non-Gaussian Noises
针对非高斯噪声（如重尾分布或异常值）下的非线性系统，提出基于最大相关熵的双滤波器平滑方法，通过融合前向和后向滤波结果提高估计精度，实验表明其优于扩展卡尔曼滤波等传统方法。
This article presents two-filter smoothing (TFS) by maximizing the correntropy rather than minimizing the mean square error, for nonlinear systems with non-Gaussian noises, such as heavy-tailed distributed noises or outliers, motivated by high-precision noncooperative target backtracking. The maximum correntropy (MC) recursive TFS, abbreviated as MRTFS, is first derived, where the smoothed estimate is obtained by fusing forward and backward filtering results step by step through maximizing the correntropy. Then, the information filtering form of the above MRTFS is proposed in order to loose the initial conditions of forward and backward filtering and enhance the structural conciseness of MRTFS. Considering that the fixed-point iteration is adopted to realize MC-based forward-time filtering, backward-time filtering, and two-filter fusion, its convergence is shown in the premise that the interested state vector is bounded and the kernel bandwidth of the correntropy is larger than a special threshold. Meanwhile, the computational complexity of MRTFS is analyzed, which is similar to that of extended Kalman-like TFS. An experiment of noncooperative target backtracking shows that estimation accuracy of the proposed method is superior to that of extended Kalman filter (EKF), TFS, Rauch–Tung–Striebel smoother (RTS) and MC-based EKF/RTS, in terms of estimation confidence ellipses, different levels of kernel bandwidths and iterations.