Sparse adaptive filtering algorithm based on generalized maximum Versoria criterion

doi:10.11772/j.issn.1001-9081.2020121982

Journal of Computer Applications ›› 2021, Vol. 41 ›› Issue (11): 3325-3331.DOI: 10.11772/j.issn.1001-9081.2020121982

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Sparse adaptive filtering algorithm based on generalized maximum Versoria criterion

Yuefa OU¹, Mingkun YANG²(), Dejun MU³, Jie KE², Wentao MA⁴

^1.College of Naval Architecture and Ocean Engineering，Beibu Gulf University，Qinzhou Guangxi 535011，China
^2.School of Computer Science and Engineering，Guilin University of Aerospace Technology，Guilin Guangxi 541004，China
^3.School of Cybersecurity，Northwestern Polytechnical University，Xi’an Shaanxi 710072，China
^4.School of Electrical Engineering，Xi’an University of Technology，Xi’an Shaanxi 710048，China

Received:2020-12-16 Revised:2021-05-02 Accepted:2021-08-03 Online:2021-05-02 Published:2021-11-10
Contact: Mingkun YANG
About author:OU Yuefa，born in 1982，M. S.，senior engineer. His research interests include computer software， cloud computing， intelligent manufacturing
YANG Mingkun，born in 1981，M. S.，lecturer. His research interests include network information security， control theory and application
MU Dejun，born in 1963，Ph. D.，professor. His research interests include network information security，control theory and application
KE Jie，born in 1977，engineer. His research interests include computer network architecture，internet of things engineering
MA Wentao，born in 1979，Ph. D.，associate professor. His research interests include adaptive signal processing.
Supported by:
the National Natural Science Foundation of China(61976175);the Start Project of Introducing High-Level Talents into Beibu Gulf University in 2019(2019KYQD03);the Undergraduate Teaching Reform Engineering Project of Guangxi Colleges and Universities in 2018(2018JGB327);the Key Project of Undergraduate Teaching Reform of Qinzhou University in 2018(18JGZ012)

基于广义最大Versoria准则的稀疏自适应滤波算法

欧跃发¹, 杨鸣坤²(), 慕德俊³, 柯捷², 马文涛⁴

^1.北部湾大学机械与船舶海洋工程学院，广西钦州 535011
^2.桂林航天工业学院计算机科学与工程学院，广西桂林 541004
^3.西北工业大学网络空间安全学院，西安 710072
^4.西安理工大学电气工程学院，西安 710048

通讯作者: 杨鸣坤
作者简介:欧跃发（1982—），男，广西桂林人，高级工程师，硕士，主要研究方向：计算机软件、云计算、智能制造
杨鸣坤（1981—），男，陕西西安人，讲师，硕士，主要研究方向：网络信息安全、控制理论与应用
慕德俊（1963—）男，山东荣成人，教授，博士，主要研究方向：网络信息安全、控制理论与应用
柯捷（1977—），男，江西九江人，工程师，主要研究方向：计算机网络体系结构、物联网工程
马文涛（1979—），陕西宝鸡人，副教授，博士，主要研究方向：自适应信号处理。
基金资助:
国家自然科学基金资助项目(61976175);2019年北部湾大学引进高层次人才科研启动项目(2019KYQD03);2018年度广西高等教育本科教学改革工程项目(2018JGB327);2018年度钦州学院本科教改重点项目(18JGZ012)

Abstract

Abstract:

The traditional sparse adaptive filtering has the problems of poor steady-state performance and even unable to converge in impulse noise interface environment. In order to solve the problems and improve the accuracy of sparse parameter identification without increasing too much computational cost， a sparse adaptive filtering algorithm based on Generalized Maximum Versoria Criterion （GMVC） was proposed， namely the GMVC with CIM constraints （CIMGMVC）. Firstly， the generalized Versoria function was employed as the learning criterion， which contained the reciprocal form of the error p-order moment. And thus the purpose of suppressing impulse noise was able to be achieved because the GMVC would approach to 0 when the error caused by the impulse interference was very large. Then， a novel cost function was constructed by combining the Correntropy Induced Metric （CIM） used as the sparse penalty constraint and the GMVC， where the CIM was based on the Gaussian probability density function， and it was able to be infinitely close to $l 0$ -norm when the appropriate kernel width was selected. Finally， the CIMGMVC algorithm was derived by using the gradient method， and the mean square convergence of the proposed algorithm was analyzed. The simulation was performed on Matlab platform， and the $α$ -stable distribution model was used to generate impulse noise. Experimental results show that， the proposed CIMGMVC algorithm can effectively suppress the interference of non-Gaussian impulse noise， it has the better robustness than the traditional sparse adaptive filtering， and has the steady-state error lower than the GMVC algorithm.

Key words: adaptive filtering, Maximum Versoria Criterion (MVC), sparse parameter estimation, Correntropy Induced Metric (CIM), non-Gaussian noise interference

摘要：

针对脉冲噪声干扰环境下传统稀疏自适应滤波稳态性能差，甚至无法收敛等问题，同时为提高稀疏参数辨识的精度的同时不增加过多计算代价，提出了一种基于广义最大Versoria准则（GMVC）的稀疏自适应滤波算法——带有CIM约束的GMVC（CIMGMVC）。首先，利用广义Versoria函数作为学习准则，其包含误差p阶矩的倒数形式，当脉冲干扰出现导致误差非常大时，GMVC将趋近于0，从而达到抑制脉冲噪声的目的。其次，将互相关熵诱导维度（CIM）作为稀疏惩罚约束和GMVC相结合来构建新代价函数，其中的CIM以高斯概率密度函数为基础，当选择合适核宽度时，可无限逼近于 $l 0$ -范数。最后，应用梯度法推导出CIMGMVC算法，并分析了所提算法的均方收敛性。在Matlab平台上采用 $α$ -stable分布模型产生脉冲噪声进行仿真，实验结果表明所提出的CIMGMVC算法能有效地抑制非高斯脉冲噪声的干扰，在稳健性方面优于传统稀疏自适应滤波，且稳态误差低于GMVC算法。

关键词: 自适应滤波, 最大Versoria准则, 稀疏参数估计, 互相关熵诱导维度, 非高斯噪声干扰

CLC Number:

TN911.72

Yuefa OU, Mingkun YANG, Dejun MU, Jie KE, Wentao MA. Sparse adaptive filtering algorithm based on generalized maximum Versoria criterion[J]. Journal of Computer Applications, 2021, 41(11): 3325-3331.

欧跃发, 杨鸣坤, 慕德俊, 柯捷, 马文涛. 基于广义最大Versoria准则的稀疏自适应滤波算法[J]. 《计算机应用》唯一官方网站, 2021, 41(11): 3325-3331.

Figures/Tables 5

Fig. 1 Comparison of convergence curves of different algorithms

Fig. 2 Comparison of steady-state performance of GMVC algorithm and CIMGMVC algorithm with different values of p

Fig. 3 Comparison of steady-state performance of GMVC algorithm and CIMGMVC algorithm with different values of α

Fig. 4 Convergence curves of CIMGMVC algorithm withdifferent values of kernel width σ

Fig. 5 Convergence curves of CIMGMVC algorithm withdifferent values of step size μ

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Sparse adaptive filtering algorithm based on generalized maximum Versoria criterion

基于广义最大Versoria准则的稀疏自适应滤波算法

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