The Kernel Recursive Maximum Total Correntropy Algorithm

Focusing on the performance deterioration of nonlinear filtering algorithms in the error-in-variable (EIV) model, a nonlinear version of maximum total correntropy (MTC) algorithm called kernel recursive maximum total correntropy (KRMTC) is proposed in this brief, which constructs a nonlinear relationship based on MTC criterion between inputs and outputs in high-dimensional feature space. Compared with existing kernel adaptive filtering (KAF) algorithms based on traditional mean square error (MSE) and maximum correntropy criteria (MCC), the proposed algorithm can handle nonlinear modeling problems in the EIV model well. In addition, an approximate linear dependency (ALD) criterion is applied to reduce the computational complexity of KRMTC. To verify the feasibility of the proposed algorithm, firstly, the convergence of the KRMTC algorithm under some assumptions is discussed and its local convergence condition is given. Secondly, the proposed algorithm is applied to the Lorenz time-series prediction and wind prediction simulations. Simulation results display that the KRMTC algorithm has better performance than kernel recursive least squares (KRLS) and kernel recursive maximum correntropy (KRMC) algorithms in EIV case.