基于广义最大Versoria准则的稀疏自适应滤波算法

针对脉冲噪声干扰环境下传统稀疏自适应滤波稳态性能差，甚至无法收敛等问题，同时为提高稀疏参数辨识的精度的同时不增加过多计算代价，提出了一种基于广义最大Versoria准则（GMVC）的稀疏自适应滤波算法——带有CIM约束的GMVC（CIMGMVC）。首先，利用广义Versoria函数作为学习准则，其包含误差p阶矩的倒数形式，当脉冲干扰出现导致误差非常大时，GMVC将趋近于0，从而达到抑制脉冲噪声的目的。其次，将互相关熵诱导维度（CIM）作为稀疏惩罚约束和GMVC相结合来构建新代价函数，其中的CIM以高斯概率密度函数为基础，当选择合适核宽度时，可无限逼近于l_{\mathrm{0}}-范数。最后，应用梯度法推导出CIMGMVC算法，并分析了所提算法的均方收敛性。在Matlab平台上采用\alpha-stable分布模型产生脉冲噪声进行仿真，实验结果表明所提出的CIMGMVC算法能有效地抑制非高斯脉冲噪声的干扰，在稳健性方面优于传统稀疏自适应滤波，且稳态误差低于GMVC算法。

Sparse adaptive filtering algorithm based on generalized maximum Versoria criterion

The traditional sparse adaptive filtering has the problems of poor steady-state performance and even unable to converge in impulse noise interface environment. In order to solve the problems and improve the accuracy of sparse parameter identification without increasing too much computational cost， a sparse adaptive filtering algorithm based on Generalized Maximum Versoria Criterion （GMVC） was proposed， namely the GMVC with CIM constraints （CIMGMVC）. Firstly， the generalized Versoria function was employed as the learning criterion， which contained the reciprocal form of the error p-order moment. And thus the purpose of suppressing impulse noise was able to be achieved because the GMVC would approach to 0 when the error caused by the impulse interference was very large. Then， a novel cost function was constructed by combining the Correntropy Induced Metric （CIM） used as the sparse penalty constraint and the GMVC， where the CIM was based on the Gaussian probability density function， and it was able to be infinitely close to l_{\mathrm{0}}-norm when the appropriate kernel width was selected. Finally， the CIMGMVC algorithm was derived by using the gradient method， and the mean square convergence of the proposed algorithm was analyzed. The simulation was performed on Matlab platform， and the \alpha-stable distribution model was used to generate impulse noise. Experimental results show that， the proposed CIMGMVC algorithm can effectively suppress the interference of non-Gaussian impulse noise， it has the better robustness than the traditional sparse adaptive filtering， and has the steady-state error lower than the GMVC algorithm.