一种变步长凸组合LMS自适应滤波算法改进及分析

摘要

In order to avoid the conflict between the convergence speed and stable state error for a single LMS filter ,and de-grade the performance of the recognition system ,we used combined least mean square (CLMS ) algorithm which is the parallel of fast LMS filter and slow LMS filter .Meanwhile ,to further improve the performance of the CLMS algorithm ,a new variable step-size convex combination of LMS (VSCLMS) algorithm was proposed by improving original VSCLMS .In the proposed algorithm , we considered the variable step-size filter on the basis of minimum mean square weight error (MMSWE) as the fast LMS filter ,and a new constant step-size filter based on steady-state LMS is used as the slow filter .By analyzing theory and experimental results ,the proposed algorithm ,which compared with the original VSCLMS algorithm and CLMS algorithm ,not only has a superior capability of tracking under the environment of noise ,time-varying and unstable condition ,but also can maintain a better convergence .%为了避免单个滤波器在收敛速度与稳态误差上相互制约，从而导致系统性能降低的问题，本文采用凸组合最小均方算法（Combined Least Mean Square ，CLMS ），将快速滤波器和慢速滤波器并联使用，同时为进一步改善CLMS算法的性能，对已有的变步长凸组合最小均方算法（Variable Step-size Convex Combination of LMS ，VSCLMS ）做出改进，提出了一种新的VSCLMS算法。在该算法中，对快速滤波器选用以最小均方权值偏差（Minimization of Mean Square Weight Error ，MMSWE）为准则的按步分析的变步长滤波器；对慢速滤波器采用以稳态最小均方误差（Least Mean Square ， LMS ）为准则的固定步长滤波器。通过理论分析与仿真实验表明，该算法能够在噪声、时变以及非平稳的环境下保持较好的随动性能，且在各个阶段均保持良好的收敛性，与传统的CLMS、VSCLMS算法相比，不仅具有更快的收敛速度，而且拥有稳定的均方性能和较优的跟踪性能，为自适应滤波算法的研究提供了一条可行途径。