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As a robust adaptation criterion, the maximum correntropy criterion (MCC) has gained increased attention due to its successful application in the adaptation, especially in nonlinear and non-Gaussian situations. In this paper, the second-order Volterra (SOV) filter based on MCC is derived, which is called MCC-SOV. It combines the advantages of the SOV filter and MCC. However, similar to the conventional adaptive algorithm, the proposed MCC-SOV filter has a tradeoff between convergence rate and steady-state error. In order to solve this problem, we present a combination of the MCC-SOV filter by combining Volterra kernels, which is called CK-MCC-SOV. In addition, a weight transfer method is applied to improve the performance of the proposed filter in terms of the convergence rate and the steady-state error. Finally, simulations are carried out to demonstrate the advantages of the proposed filters. [ABSTRACT FROM AUTHOR]

To overcome the performance degradation of adaptive filtering algorithms in the presence of impulsive noise, a novel normalized sign algorithm (NSA) based on a convex combination strategy, called NSA-NSA, is proposed in this paper. The proposed algorithm is capable of solving the conflicting requirement of fast convergence rate and low steady-state error for an individual NSA filter. To further improve the robustness to impulsive noises, a mixing parameter updating formula based on a sign cost function is derived. Moreover, a tracking weight transfer scheme of coefficients from a fast NSA filter to a slow NSA filter is proposed to speed up the convergence rate. The convergence behavior and performance of the new algorithm are verified by theoretical analysis and simulation studies. [ABSTRACT FROM AUTHOR]

Traditional filtering theory is always based on optimization of the expected value of a suitably chosen function of error, such as the minimum mean-square error (MMSE) criterion, the minimum error entropy (MEE) criterion, and so on. None of those criteria could capture all the probabilistic information about the error distribution. In this work, we propose a novel approach to shape the probability density function (PDF) of the errors in adaptive filtering. As the PDF contains all the probabilistic information, the proposed approach can be used to obtain the desired variance or entropy, and is expected to be useful in the complex signal processing and learning systems. In our method, the information divergence between the actual errors and the desired errors is chosen as the cost function, which is estimated by kernel approach. Some important properties of the estimated divergence are presented. Also, for the finite impulse response (FIR) filter, a stochastic gradient algorithm is derived. Finally, simulation examples illustrate the effectiveness of this algorithm in adaptive system training. [ABSTRACT FROM AUTHOR]