多步梯度下降的变步长NLMS算法  

A Variable Step-size NLMS Algorithm Based on Multi-step Gradient Methods

作　　者：徐新龙[1] 张建秋[1] 

机构地区：[1]复旦大学电子工程系,上海200433

出　　处：《复旦学报（自然科学版）》2014年第3期393-402,共10页Journal of Fudan University：Natural Science

基　　金：国家自然科学基金(61171127);专用集成电路与系统国家重点实验室(11MS006)资助项目

摘　　要：如何选取一个合适而可靠的步长来折中归一化最小均方(Normalized Least Mean Squares,NLMS)自适应算法的收敛速度以及稳态误差,一直是自适应NLMS算法应用中未能很好解决的问题.针对这个问题,本文提出了一种多步梯度下降的变步长NLMS自适应算法.分析表明:该算法在利用固定的小步长参数来保证小的稳态误差的同时,通过调整动量项来加速自适应算法的收敛速度,从而很好地解决了自适应NLMS算法应用中收敛速度和稳态误差的平衡问题.理论分析给出了调节动量项的步长参数和算法收敛性及稳态误差之间的关系.仿真结果证明了上述分析的正确性.It is well understood that the choice of the step-size parameter for normalized least mean squares （NLMS） algorithm, within the stability conditions, reflects a tradeoff between fast convergence and good tracking ability on the one hand and low misadjustment on the other hand. However, a good and reliable solution is not easy to find. In this paper, a new NLMS algorithm based oi1 the multi-step gradient methods is proposed. When a small step-size parameter is given to insure the small misadjustment of filtering, analyses show that we can add a momentum term to speed up the convergence, hence we can solve the compromise between fast convergence and good tracking ability. The theoretical analyses give the relationship between the step-size which controls the momentum term and convergence and misadjustment. By such a relationship, a novel variable step-size method for the NLMS algorithm is proposed. Simulation results show the correctness of the analyses.

关 键 词：自适应滤波 归一化最小均方 多步梯度 变步长 

分 类 号：TN911.72[电子电信—通信与信息系统]