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为了解决Widrow-Hoff最小均方(LMS)算法的稳定性问题,文献提出了一种修正LMS算法(简称MLMS算法),它的权系数的调整取决于误差面在新权值点的梯度。文献[1]的讨论比较简单,且只限于一维的情况。本文导出了一般M维MLMS算法的递推公式,并对这种新算法的合理性从原理上和结构上作了较详细的解释,并且将它推广为两种算法。同时,还对MLMS的主要性能——收敛速度、权噪声和失调、输出均方误差等作了较详细的分析。分析结果表明:当步长μ较大时,MLMS法确比LMS法优越。计算机模拟结果与理论分析基本相符。
In order to solve the stability problem of Widrow-Hoff Least Mean Square (LMS) algorithm, a modified LMS algorithm (MLMS algorithm) is proposed in this paper. Its weight coefficient is adjusted by the gradient of the error surface at the new weight point. The discussion in [1] is relatively simple and limited to one-dimensional situations. In this paper, we derive the recursion formula of general M-dimensional MLMS algorithm, and give a more detailed explanation of the rationality of this new algorithm in principle and structure, and generalize it to two algorithms. At the same time, the main performance of MLMS is also analyzed in detail, such as convergence speed, weight noise and offset, mean square error of output. The analysis results show that MLMS method is superior to LMS method when the step size μ is large. Computer simulation results and theoretical analysis basically match.