α稳定分布噪声下基于梯度范数的VSS-NLMP算法

针对α稳定分布噪声环境下的自适应滤波问题，提出一种新的基于梯度范数的变步长归一化最小平均p范数(variable step size normalized least mean p norm, VSS-NLMP)算法。该算法首先对梯度矢量进行加权平滑，以减小梯度噪声的影响，然后利用梯度矢量能够跟踪自适应过程的均方偏差这一特点，利用梯度矢量的欧氏范数控制步长的变化。给出了新算法的迭代过程，然后对其收敛性进行分析，仿真结果表明本算法较现有变步长NLMP算法有更好的性能。

Gradient-norm based VSS-NLMP algorithm in α-stable environments

According to the problem of adaptive filtering in α stable environments,a gradient-norm based variable step-size normalized least mean p-norm(VSS-NLMP) algorithm is proposed.The squared norm of the smoothed gradient vector,which can track the variation of the mean square deviation at iteration,is used to update the step-size parameter in the algorithm.The weighted average of the gradient vector reduces the noise effectively and results in a more stable and less noisy adaptation of the step-size parameter.The update and convergence of the proposed algorithm are formulated.The simulation results indicate that the proposed algorithm has a better performance compared with the existing VSS-NLMP algorithms.