用于稀疏系统辨识的变步长加权零吸引最小平均p范数算法

在α稳定分布噪声背景下,为了提高稀疏系统自适应辨识算法的稳态性能,提出了基于无噪先验误差功率函数的变步长加权零吸引最小平均p范数基本算法(BVSS-RZA-LMP)和变步长加权零吸引最小平均p范数改进算法(IVSS-RZA-LMP).两种算法分别根据无噪先验误差功率和加权的无噪先验误差功率计算新的步长;步长随无噪先验误差功率的减小而逐渐减小.当算法达到稳态时, IVSS-RZA-LMP算法不再调整权矢量,改进了BVSSRZA-LMP算法稳态性能.α稳定分布噪声背景下的系统辨识仿真结果表明,当系统较稀疏时, IVSS-RZA-LMP算法能够在较快收敛的情况下获得非常小的稳态误差.

Variable step-size reweighted zero attracting least mean p-norm algorithm for sparse system identification

Under α-stable distribution noise environment, the basic variable step-size reweighted zero-attracting least mean p-norm algorithm(BVSS-RZA-LMP) and the improved variable step-size reweighted zero-attracting least mean p-norm algorithm(IVSS-RZA-LMP) algorithm are proposed to improve the steady state performance of adaptive identification algorithm for a sparse system. The step size in the algorithms are calculated according to noise-free prior error power and weighted noise-free prior error power respectively. And it decreases with the reduction of the noise-free prior error power. When the IVSS-RZA-LMP algorithm reaches steady state, its weight vector is no longer adjusted to improved steady-state performance of the BVSS-RZA-LMP algorithm. The simulation results of system identification under α-stable distribution noise show that when the system is sparse, the IVSS-RZA-LMP algorithm can obtain very small steady-state error at a fast convergence rate.