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
计量
- 文章访问数: 1219
- HTML全文浏览量: 455
- PDF下载量: 88
- 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

下载: 全尺寸图片幻灯片

图 2 LMS算法系统结构

下载: 全尺寸图片幻灯片

图 3 h与${\rm{MSD}}$变化关系

下载: 全尺寸图片幻灯片

图 4 $y$随不同$A$的变化情况

下载: 全尺寸图片幻灯片

图 5 $A(n)$随不同${q_{\min }}$的变化情况

下载: 全尺寸图片幻灯片

图 6 $\mu (n)$随不同${q_{\min }}$的变化情况

下载: 全尺寸图片幻灯片

图 7 系统辨识模型

下载: 全尺寸图片幻灯片

图 8 式(47)的验证

下载: 全尺寸图片幻灯片

图 9 式(48)的验证

下载: 全尺寸图片幻灯片

图 10 仿真实验1的结果

下载: 全尺寸图片幻灯片

图 11 仿真实验2的结果

下载: 全尺寸图片幻灯片

图 12 一段原始语音信号$x(n)$

下载: 全尺寸图片幻灯片

图 13 加性噪声$z(n)$

下载: 全尺寸图片幻灯片

图 14 含噪声语音信号$d(n)$

下载: 全尺寸图片幻灯片

图 15 LMS算法误差

下载: 全尺寸图片幻灯片

图 16 GSVSLMS算法误差

下载: 全尺寸图片幻灯片

图 17 RELMS算法误差

下载: 全尺寸图片幻灯片

参考文献(17)

[1]	谢胜利, 何昭水, 高鹰. 信号处理的自适应理论[M]. 北京: 科学出版社, 2006: 2–7.
[2]	HUANG Fuyi, ZHANG Jiashu, and ZHANG Sheng. A family of robust adaptive filtering algorithms based on sigmoid cost[J]. Signal Processing, 2018, 149: 179–192. doi: 10.1016/j.sigpro.2018.03.013
[3]	高鹰, 谢胜利. 一种变步长LMS自适应滤波算法及分析[J]. 电子学报, 2001, 29(8): 1094–1097. doi: 10.3321/j.issn:0372-2112.2001.08.023 GAO Ying and XIE Shengli. A variable step size LMS adaptive filtering algorithm and its analysis[J]. Acta Electronica Sinica, 2001, 29(8): 1094–1097. doi: 10.3321/j.issn:0372-2112.2001.08.023
[4]	樊宽刚, 邱海云. 基于Sigmoid框架的非负最小均方算法[J]. 电子与信息学报, 2021, 43(2): 349–355. doi: 10.11999/JEIT200018 FAN Kuan’gang and QIU Haiyun. Robust nonnegative least mean square algorithm based on sigmoid framework[J]. Journal of Electronics &Information Technology, 2021, 43(2): 349–355. doi: 10.11999/JEIT200018
[5]	PEREZ F L, DE SOUZA F D C, and SEARA R. An improved mean-square weight deviation-proportionate gain algorithm based on error autocorrelation[J]. Signal Processing, 2014, 94: 503–513. doi: 10.1016/j.sigpro.2013.06.030
[6]	JIN Danqi, CHEN Jie, RICHARD C, et al. Model-driven online parameter adjustment for zero-attracting LMS[J]. Signal Processing, 2018, 152: 373–383. doi: 10.1016/j.sigpro.2018.06.020
[7]	BERSHAD N J, WEN Fuxi, and SO H C. Comments on “fractional LMS algorithm”[J]. Signal Processing, 2017, 133: 219–226. doi: 10.1016/j.sigpro.2016.11.009
[8]	SHI Long, ZHAO Haiquan, WANG Wenyuan, et al. Combined regularization parameter for normalized LMS algorithm and its performance analysis[J]. Signal Processing, 2019, 162: 75–82. doi: 10.1016/j.sigpro.2019.04.014
[9]	AHN D C, LEE J W, SHIN S J, et al. A new robust variable weighting coefficients diffusion LMS algorithm[J]. Signal Processing, 2017, 131: 300–306. doi: 10.1016/j.sigpro.2016.08.023
[10]	CHENG Songsong, WEI Yiheng, CHEN Yuquan, et al. A universal modified LMS algorithm with iteration order hybrid switching[J]. ISA Transactions, 2017, 67: 67–75. doi: 10.1016/j.isatra.2016.11.019
[11]	YANG Feiran and YANG Jun. Mean-square performance of the modified frequency-domain block LMS algorithm[J]. Signal Processing, 2019, 163: 18–25. doi: 10.1016/j.sigpro.2019.04.030
[12]	杨鹏程, 吕晓德, 柴致海, 等. 基于频域分块RDS-LMS算法的机载外辐射源雷达杂波对消[J]. 电子与信息学报, 2017, 39(10): 2302–2310. doi: 10.11999/JEIT170190 YANG Pengcheng, LÜ Xiaode, CHAI Zhihai, et al. Clutter cancellation for airborne passive radar based on frequency-domain block RDS-LMS algorithm[J]. Journal of Electronics &Information Technology, 2017, 39(10): 2302–2310. doi: 10.11999/JEIT170190
[13]	SADIGH A N, TAHERINIA A H, and YAZDI H S. Analysis of robust recursive least squares: Convergence and tracking[J]. Signal Processing, 2020, 171: 107482. doi: 10.1016/j.sigpro.2020.107482
[14]	赵海全, 李磊. 一种抗冲击噪声的对数总体最小二乘自适应滤波算法[J]. 电子与信息学报, 2021, 43(2): 284–288. doi: 10.11999/JEIT200344 ZHAO Haiquan and LI Lei. A logarithmic total least squares adaptive filtering algorithm for impulsive noise suppression[J]. Journal of Electronics &Information Technology, 2021, 43(2): 284–288. doi: 10.11999/JEIT200344
[15]	EWEDA E. A new approach for analyzing the limiting behavior of the normalized LMS algorithm under weak assumptions[J]. Signal Processing, 2009, 89(11): 2143–2151. doi: 10.1016/j.sigpro.2009.04.040
[16]	ZHANG Sheng, ZHANG Jiashu, and SO H C. Mean square deviation analysis of LMS and NLMS algorithms with white reference inputs[J]. Signal Processing, 2017, 131: 20–26. doi: 10.1016/j.sigpro.2016.07.027
[17]	BERMUDEZ J C M, BERSHAD N J, and EWEDA E. Stochastic analysis of the LMS algorithm for cyclostationary colored Gaussian inputs[J]. Signal Processing, 2019, 160: 127–136. doi: 10.1016/j.sigpro.2019.02.018