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This paper presents novel kernel adaptive filters with feedback, namely, kernel recursive maximum correntropy with multiple feedback (KRMC-MF) and its simplified version, a linear recurrent kernel online learning algorithm based on maximum correntropy criterion (LRKOL-MCC). In LRKOL-MCC and KRMC-MF, single output and multiple outputs based on single delay are utilized to construct their feedback structure, respectively. Compared with the minimum mean square error criterion, the maximum correntropy criterion (MCC) adopted by LRKOL-MCC and KRMC-MF captures higher order statistics of errors. The proposed filters are, therefore, robust against outliers. Therefore, the past information can be reused to improve filtering performance in terms of the steady-state mean square error. The convergence characteristics of the filter parameters in LRKOL-MCC and KRMC-MF are also derived. Simulations on chaotic time-series prediction and nonlinear regression illustrate the desirable accuracy and robustness of the proposed filters.

Kernel Adaptive Filters With Feedback Based on Maximum Correntropy