Generalized kernel maximum correntropy criterion with variable center: Formulation and performance analysis

Abstract

Recently, the kernel adaptive filtering algorithm with the generalized maximum correntropy criterion (GMCC) has gained attention due to its excellent nonlinear system modeling ability and robustness to non-Gaussian noise. However, since the default center of the GMCC is located at zero, it hampers its performance in the non-zero mean noise environment. To overcome the problem, this paper proposes a kernel adaptive filtering algorithm based on the GMCC with variable center (GMCC-VC) called generalized kernel maximum correntropy criterion with variable center (GKMCC-VC). In addition, the online vector quantization (VQ) method is introduced to the GKMCC-VC algorithm for suppressing the increasing network size. The probability of divergence, the mean-square steady-state behavior, and the convergence condition of the GKMCC-VC algorithm are also obtained under some assumptions. The potential relationship between the GMCC-VC and the generalized minimum error entropy (GMEE) criteria is discussed in the paper. Finally, the simulation results verify the superiority of the proposed algorithm in modeling nonlinear systems and the correctness of the theoretical model.