Abstract: The estimate error is effectively reduced by smoothing gradient vector. The step factor is also updated by the Euclidean norm of the smoothed gradient vector and the fractional lower order moment of the error signal. The first-order and second-order weight coefficients are iteratively updated respectively. So a variable step-size adaptive algorithm for Volterra filter with the background of [α]-stable distribution noise is presented. The convergence performance of this algorithm is also analyzed and proved. Simulations results of a nonlinear system identification showed that the presented algorithm has faster convergence speed and smaller steady-state mis-adjustment than DOVLMP algorithm.

Key words: α-stable distribution noise, Volterra filter, Variable Step-size Normalized Least Mean P norm algorithm（VS-NLMP）, nonlinear system identification

摘要： 通过平滑梯度矢量减小梯度估计误差，采用平滑梯度矢量的欧氏范数和误差信号的分数低阶矩更新步长因子，对一阶和二阶权系数采取分阶迭代更新，得到一种在[α]稳定分布噪声背景下变步长Volterra自适应滤波算法，分析证明了该算法的收敛性能。非线性系统辨识的仿真结果表明，算法较DOVLMP算法具有更快的收敛速度和更小的稳态失调。

关键词: &alpha, 稳定分布噪声, Volterra滤波器, VS-NLMP算法, 非线性系统辨识