Nonlinear Spline Adaptive Filtering under Maximum Correntropy Criterion

The nonlinear spline adaptive filtering under least mean square (SAF-LMS) uses the mean square error (MSE) based cost function to identify the Wiener-type nonlinear systems, which is rational under the assumption of Gaussian distributions. However, the mere second-order statistics are often not suitable for nonlinear and/or non-Gaussian systems. To address this issue, a new nonlinear adaptive filter, called nonlinear spline adaptive filtering under maximum correntropy criterion (SAF-MCC), is proposed in this work. Compared with the SAF-LMS, the SAF-MCC uses the maximum correntropy criterion (MCC) to replace the MSE criterion to improve the convergence performance especially in heavy-tailed non Gaussian environments. Simulation results confirm the superior performance of the new algorithm.