一种基于均方偏差分析的通用最小均方算法

A General Least Mean Square Algorithm Based on Mean Square Deviation Analysis

无论是传统的定步长还是最近新提出的变步长最小均方(LMS)算法,在处理特定数学特征的信号时需要对算法参数进行先验的估计才能达到较好的效果。但在实际信号处理过程中,算法参数的估计本就是一个很困难的过程。该文分析了LMS算法的均方偏差及收敛特性,并提出一种以相对误差为变量的变步长LMS算法,能够实现步长控制参数的自估计;可以自适应不同数学特征的信号,具体算例表明新算法有更快的收敛速度和较小的均方误差。

Whether it is the traditional fixed step size or the newly proposed Least Mean Square(LMS)algorithm,a priori estimation of the algorithm parameters is required to achieve better results when processing signals of specific mathematical features.However,in the actual signal processing process,the estimation of the algorithm parameters is a very difficult process.In this paper,the mean square deviation and convergence characteristics of LMS algorithm are analyzed,and a variable step size LMS algorithm with relative error as variable is proposed,which can realize self-estimation of step control parameters.It can adapt signals of different mathematical features.The example shows that the new algorithm has faster convergence speed and smaller mean square error.