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为了解决最小均方(leastmeansquare,LMS)算法中收敛速度和稳态误差之间的矛盾,在独立假设的条件下,从滤波器系数均方误差的角度,提出了最优步长定理,证明了最优步长和均方误差之间存在一一对应的关系。并以此构造了最优变步长LMS(optimalvariablestep-size,OVS-LMS)模型。推出了最优步长的递推式,讨论了最优初始化相对步长的选取方法。综合以上的分析结果,提出了该模型的实现算法。计算机仿真证明了该算法和OVS-LMS模型的学习曲线是非常相近的,因而该算法在独立假设条件下是最优的变步长LMS算法。
In order to solve the contradiction between the convergence rate and the steady-state error in the least-mean square (LMS) algorithm, the optimal step-length theorem is proposed from the mean square error of the filter coefficients under the assumption of independent assumption. There is a one-to-one correspondence between the optimal step size and mean square error. In this way, an optimal variable step size LMS (OVS-LMS) model is constructed. The recursion of the optimal step is introduced, and the selection method of the optimal initializing relative step is discussed. Based on the above analysis results, the algorithm of the model is proposed. Computer simulation proves that the learning curve of this algorithm is very similar to that of the OVS-LMS model. Therefore, this algorithm is the best LMS algorithm with independent assumptions.