基于q 梯度的仿射投影算法及其稳态均方收敛分析

王世元; 史春芬; 蒋云翔; 王文月; 钱国兵

doi:10.11999/JEIT171125

基于q 梯度的仿射投影算法及其稳态均方收敛分析

doi: 10.11999/JEIT171125

王世元^{1, 2, ,},
史春芬^{1, 2},
蒋云翔³,
王文月^{1, 2},
钱国兵^{1, 2}

1.
西南大学电子信息工程学院重庆 400715
2.
重庆非线性电路和智能信息处理重点实验室重庆 400715
3.
清华大学深圳研究生院深圳 518055

基金项目: 国家自然科学基金(61671389, 61701419)，中国博士后基金(2017M610583, 2017M620783)，重庆博士后科研基金(Xm2017107, Xm2017104)

详细信息

作者简介:
王世元：男，1980年生，教授，硕士生导师，研究方向为自适应信号处理、非线性滤波器设计、混沌通信系统

史春芬：女，1990年生，硕士生，研究方向为信号与信息处理

蒋云翔：男，1986年生，博士，研究方向为无线通信、无线能量信息同传、全双工通信

王文月：女，1994年生，硕士生，研究方向为信号与信息处理

钱国兵：男，1986年生，讲师，研究方向为自适应信号处理

通讯作者:
王世元　 wsy@swu.edu.cn

中图分类号: TN911.72
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出版历程
- 收稿日期: 2017-11-28
- 修回日期: 2018-06-14
- 网络出版日期: 2018-07-30
- 刊出日期: 2018-10-01

q -affine Projection Algorithm and Its Steady-state Mean Square Convergence Analysis

Shiyuan WANG^{1, 2
, ,},
Chunfen SHI^{1, 2},
Yunxiang JIANG³,
Wenyue WANG^{1, 2},
Guobing QIAN^{1, 2}

1.
College of Electronic and Information Engineering, Southwest University, Chongqing 400715, China
2.
Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, Chongqing 400715, China
3.
Graduate School at Shenzhen of Tsinghua University, Shenzhen 518055, China

Funds: The National Natural Science Foundation of China (61671389, 61701419), China Postdoctoral Science Foundation Funded Project (2017M610583, 2017M620783), Chongqing Postdoctoral Science Foundation Special Funded Project (Xm2017107, Xm2017104)

摘要

摘要: q梯度是基于q微分的广义梯度。为了进一步提高仿射投影算法(APA)的滤波性能，该文基于最小均方误差准则将q梯度应用于APA进而产生一种新的q-APA，在高斯噪声环境下选择合适的q值可以取得理想的滤波性能。通过理论分析，提出了保证算法收敛的充分条件，并计算出表征滤波性能的稳态额外均方误差(EMSE)。除此之外，为了进一步提高算法的滤波性能，提出一个变q的APA(V-q-APA)。在高斯噪声环境下，将q-APA和V-q-APA应用于系统辨识中。仿真结果表明：与传统的APA和变q的最小化均方(V-q-LMS)算法相比，q-APA和V-q-APA均具有更好的滤波性能。
- 信号处理 /
- q微分 /
- 误差准则 /
- 仿射投影算法 /
- 均方收敛分析
Abstract: The q-gradient is a generalized gradient based on the q-derivative concept. To improve the filtering performance of the Affine Projection Algorithm (APA), the q-gradient is applied to APA based on the minimum of the recent mean square errors, generating a novel q-Affine Projection Algorithm (q-APA). The q-APA with appropriate setting of q achieves desirable filtering performance in the presence of Gaussian noises. A sufficient condition for guaranteeing convergence of the proposed q-APA is also presented, and its steady-state Excess Mean Square Error (EMSE) of q-APA is obtained theoretically to evaluate the filtering performance. In addition, the Variable q-APA (V-q-APA) is developed to improve further the filtering performance. Simulations in the context of system identification demonstrate the superior filtering performance of the proposed algorithms compared with APA and Variable q-Least Mean Square (V-q-LMS) algorithm in the presence of Gaussian noise.
- Signal processing /
- q-derivative /
- Error criterion /
- Affine Projection Algorithm (APA) /
- Mean square convergence analysis

HTML全文

图 1 高斯噪声环境下q-APA算法的理论和仿真

下载: 全尺寸图片幻灯片

图 2 V-q-APA算法和其他不同算法的学习曲线

下载: 全尺寸图片幻灯片

表 1 基于100次蒙特卡罗仿真的各个算法的性能比较

算法	MSE	时间(s)
APA	0.0835	10.0802
q-APA (q=10)	0.0951	10.9385
q-APA (q=0.01)	0.0819	10.9385
V-q-LMS	0.0825	15.0982
V-q-APA	0.0820	15.8802
RLS	0.0818	12.0637

下载: 导出CSV

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