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.

在非高斯噪声环境中，由于最大熵准则（MCC）对非高斯噪声的鲁棒性，已被广泛用于参数估计。但是，在MCC算法中选择适当的内核宽度固定值并非易事。内核宽度的固定值不合适会降低MCC算法的性能。因此，在本文中，我们提出了一种具有可变内核宽度（RVKW-MCC）的鲁棒MCC算法，用于非高斯噪声下的自适应滤波。每次迭代时内核宽度的最佳值是通过使用均方差（MSD）项的Tikhonov正则化项最小化成本函数得出的。我们还采用一种新颖的函数逼近方法来计算最佳内核宽度。然后提供了对平均稳定条件和稳态超额均方误差（EMSE）的理论分析。最后，通过在数值模拟中将提出的RVKW-MCC算法与其他几种现有算法进行比较，我们发现RVKW-MCC算法在脉冲噪声的不同设置下更鲁棒。与具有固定核宽度的MCC算法和在非高斯噪声下具有可变核宽度的几种现有MCC算法相比，我们的算法显示出更高的收敛速度和相对较低的EMSE稳态值。