基于对称非线性函数的变步长LMS自适应滤波算法  

Variable Step Size LMS Adaptive Filtering Algorithm Based on the Symmetric Nonlinear Function

作　　者：肖玮 刘思蔚 唐宇龙 李明 XIAO Wei;LIU Siwei;TANG Yuong;LI Ming(Army Logistics University of PLA,Chongqing 401311,China;Unit 63798 of PLA,Xichang 615000,China)

机构地区：[1]陆军勤务学院,重庆401311 [2]解放军63798部队,四川西昌615000

出　　处：《火力与指挥控制》2023年第2期66-72,85,共8页Fire Control & Command Control

基　　金：国家重点研发计划基金(2018YFB2003905);国家自然科学基金资助项目(61871402)。

摘　　要：为解决自适应最小均方误差(least mean squares,LMS)滤波算法难以平衡稳态误差和收敛速度的问题,提出了基于对称非线性函数的变步长LMS自适应滤波算法。通过自变量取绝对值、叠加非线性拉伸量改进Sig-moid函数,构造一个对称非线性函数用于刻画步长因子与稳态误差的非线性关系。该对称非线性函数具有能够根据误差动态调整步长、更快达到收敛状态的特点。根据构造的对称非线性函数和输入信号功率生成归一化变步长因子,解决噪声逐级放大的问题,进一步提高算法的滤波效果同时,加速收敛。实验表明:该算法在低信噪比、信噪比变化、信号频率变化、滤波器阶数变化、延迟采样点数变化条件下均具有更好的滤波效果、更优的稳定性和更快的收敛速度。In order to solve the problem that the adaptive Least Mean Square(LMS)filtering algorithm is difficult to balance the steady-state error and convergence speed,a variable step size LMS adaptive filtering algorithm based on symmetric nonlinear function is proposed.Firstly,the Sigmoid function is improved by taking the absolute value of the independent variable and superimposing the nonlinear stretching amount,and a symmetric nonlinear function is constructed to depict the nonlinear relationship between the step factor and the steady-state error.The symmetric nonlinear function can dynamically adjust the step size according to the error and reach the convergence state faster.Then the normalized variable step size factor is generated according to the constructed symmetric nonlinear function and input signal power to solve the problem of noise step-by-step amplification,further to improve the filtering effect of the algorithm and to accelerate its convergence at the same time.The experiments show that compared with several typical LMS algorithms,the proposed algorithm has better filtering effect,better stability and faster convergence speed under the conditions of low signal-to-noise ratio,signal-to-noise ratio change,signal frequency change,filter order change and delayed sampling number change.

关 键 词：对称非线性函数 归一化变步长因子 变步长LMS算法 SIGMOID函数 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构]