一种基于均方偏差分析的通用最小均方算法

谢小平; 史雄坤

doi:10.11999/JEIT200639

一种基于均方偏差分析的通用最小均方算法

doi: 10.11999/JEIT200639

谢小平,
史雄坤^,

湖南大学汽车车身先进设计制造国家重点实验室长沙 410012

详细信息

作者简介:
谢小平：男，1978年生，高级实验师，研究方向为NVH

史雄坤：男，1993年生，硕士生，研究方向为信号处理、主动降噪

通讯作者:
史雄坤　1079017622@qq.com

中图分类号: TN911.7
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- 文章访问数: 1294
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- 被引次数: 0
出版历程
- 收稿日期: 2020-07-30
- 修回日期: 2020-12-07
- 网络出版日期: 2020-12-17
- 刊出日期: 2021-08-10

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

Xiaoping XIE,
Xiongkun SHI^,

State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha 410012, China

摘要

摘要: 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。
- 均方偏差分析 /
- 自适应滤波 /
- 相对误差 /
- 通用性
Abstract: 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.
- Mean square deviation analysis /
- Adaptive filter /
- Relative error /
- Universality

HTML全文

图 1 横向自适应LMS滤波器

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图 2 LMS算法系统结构

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图 3 h与${\rm{MSD}}$变化关系

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图 4 $y$随不同$A$的变化情况

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图 5 $A(n)$随不同${q_{\min }}$的变化情况

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图 6 $\mu (n)$随不同${q_{\min }}$的变化情况

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图 7 系统辨识模型

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图 8 式(47)的验证

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图 9 式(48)的验证

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图 10 仿真实验1的结果

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图 11 仿真实验2的结果

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图 12 一段原始语音信号$x(n)$

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图 13 加性噪声$z(n)$

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图 14 含噪声语音信号$d(n)$

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图 15 LMS算法误差

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图 16 GSVSLMS算法误差

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图 17 RELMS算法误差

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