Abstract: Because the memory length of nonlinear system is unknown in practical applications, the performance of Volterra adaptive filter with a non-suitable memory length will not be optimal. Faced with this problem, a variable memory length LMP algorithm of second-order Volterra filter is proposed. The second-order weighting coefficients matrix is symmetrical and a symmetric matrix can be decomposed into a diagonal one. So, the output signal expression of each order of Volterra filter is deduced as the inner product of a signal vector and a weighting coefficients vector. And each order of Volterra filter has the same number of weighting coefficients. A second-order Volterra adaptive filter based on DCT （CSVF） and its LMP algorithm （CSVLMP） are proposed. The idea of the variable tap length FIR filtering algorithm is employed. And a second-order Volterra variable memory length LMP algorithm based on DCT （CSVMLMP） is proposed. Simulation results of unknown memory length nonlinear system identification show that, under the background of [α]-stable distribution noise, the proposed algorithm achieves a better compromise among convergence rate, steady-state performance and computation complexity.

Key words: second-order Volterra filter, variable memory length, [α]-stable distribution noise, nonlinear system identification

摘要： 针对实际应用中非线性系统记忆长度未知致使Volterra自适应滤波器可能无法达到最优性能的问题，提出一种二阶Volterra变记忆长度LMP算法。利用Volterra滤波器二阶权系数矩阵的对称性和对称矩阵可对角化分解性质，推导得到了一阶权系数与二阶权系数个数相同的信号矢量与权系数矢量内积的二阶Volterra滤波器输出信号表达式；提出了基于DCT的二阶Volterra自适应滤波器（CSVF）及其LMP算法（CSVLMP）；采用FIR抽头长度的自适应调整思想，提出了基于DCT的二阶Volterra变记忆长度LMP算法（CSVMLMP）。记忆长度未知的非线性系统辨识的仿真结果表明，在[α]稳定分布噪声背景下，该算法在收敛速度、稳态性能和计算复杂度之间达到了较好的折中。

关键词: 二阶Volterra滤波器, 变记忆长度, [&alpha, ]稳定分布噪声, 非线性系统辨识