一种α稳定分布下的变步长最小ρ-范数算法

A Variable Step-Size Least ρ-Norm Algorithm under Alpha Stable Noise

本文提出一种新的基于α稳定分布噪声环境下的自适应滤波算法,这种算法针对变步长自适应滤波算法收敛速度和稳态误差相矛盾的不足,建立了步长μ(n)与误差信号e(n)之间的新的非线性函数关系。该函数能够削弱输入端不相关α稳定分布噪声对步长调整的影响,更好地解决稳态误差与收敛时间之间的矛盾。通过系统辨识仿真结果表明,新的算法α对稳定分布下的尖峰脉冲噪声有较强的韧性,比传统的NLMP算法有更快的参数辨识速度和更小的稳态误差,同时还具有很好地跟踪多时变系统的能力。

A novel adaptive filtering algorithm under the α-stable noise conditions is presented in this paper, aiming at the disadvantage of the convergence speed contradicting its steady-state error of variable step-size adaptive filtering algorithms, a novel non-liner functional relationship between μ（n）and error signal e（n）is established. This function relationship can weaken the interference of input uncorrelated alpha stable noise to step-size, meanwhile the algorithm efficiently overcome the discrepancy between the convergence rate and the steady error. When this algorithm is applied to system identification, a significant improvement can be achieved in robustness, identifying speed, smaller steady error and better tracking capability, as compared with the traditional NLMP algorithm under alpha stable noise conditions.