Robust variable kernel width for maximum correntropy criterion algorithm

Abstract

Maximum correntropy criterion (MCC) has been widely adopted for parameter estimation in the environment of non-Gaussian noise due to its robust characteristics to non-Gaussian noises. However, choosing a proper fixed value of kernel width in MCC algorithm is not an easy task. An improper fixed value of kernel width would degrade the performance of MCC algorithm. Therefore, in this paper, we propose a robust MCC algorithm with variable kernel width (RVKW-MCC) for adaptive filtering under non-Gaussian noises. The optimal value of kernel width at each time iteration is derived by minimizing the cost function with a Tikhonov regularization term imposed to the mean square deviation (MSD) term. We also employ a novel method of function approximation to calculate the optimal kernel width. Theoretical analysis for mean stability condition and steady-state excess mean-square-error (EMSE) are then provided. Finally, by comparing the proposed RVKW-MCC algorithm with several other existing algorithms in numerical simulations, we find that the RVKW-MCC algorithm is more robust under different settings of impulsive noise. Our algorithm shows higher convergence rate and relatively low steady-state values of EMSE than the MCC algorithm with fixed kernel width and several existing MCC algorithms with variable kernel width under non-Gaussian noises.