基于Rayleigh商的次子空间准则跟踪函数

徐中英; 高迎彬; 孔祥玉; 杜伯阳

doi:10.11959/j.issn.1000-436x.2019216

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基于Rayleigh商的次子空间准则跟踪函数

学术论文 | 更新时间：2024-06-05

- 基于Rayleigh商的次子空间准则跟踪函数
- Novel criterion function for minor subspace tracking based on Rayleigh quotient
- 通信学报 2019年40卷第11期页码：38-44
- 作者机构：
  
  火箭军工程大学控制工程系，陕西西安 710025
- 作者简介：
  
  [ "徐中英（1978- ），男，江苏徐州人，博士，火箭军工程大学讲师，主要研究方向为信号处理。" ]
  [ "高迎彬（1986- ），男，河北安平人，博士，火箭军工程大学工程师，主要研究方向为自适应信号处理。" ]
  [ "孔祥玉（1967- ），男，山西洪洞人，博士，火箭军工程大学教授，主要研究方向为信号处理、故障诊断等。" ]
  [ "杜伯阳（1990- ），男，山东滨州人，火箭军工程大学博士生，主要研究方向为系统特征提取。" ]
- 基金信息：
  
  国家自然科学基金资助项目(61673387);国家自然科学基金资助项目(61374120)
- DOI：10.11959/j.issn.1000-436x.2019216
  中图分类号： TP391
- 网络出版日期：2019-11，
  
  纸质出版日期：2019-11-25
- 稿件说明：
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徐中英, 高迎彬, 孔祥玉, 等. 基于Rayleigh商的次子空间准则跟踪函数[J]. 通信学报, 2019,40(11):38-44.

Zhongying XU, Yingbin GAO, Xiangyu KONG, et al. Novel criterion function for minor subspace tracking based on Rayleigh quotient[J]. Journal on communications, 2019, 40(11): 38-44.
徐中英, 高迎彬, 孔祥玉, 等. 基于Rayleigh商的次子空间准则跟踪函数[J]. 通信学报, 2019,40(11):38-44. DOI： 10.11959/j.issn.1000-436x.2019216.

Zhongying XU, Yingbin GAO, Xiangyu KONG, et al. Novel criterion function for minor subspace tracking based on Rayleigh quotient[J]. Journal on communications, 2019, 40(11): 38-44. DOI： 10.11959/j.issn.1000-436x.2019216.

摘要

针对次子空间信息准则函数缺乏的问题，通过对Rayleigh商函数添加惩罚项提出了新型的准则函数。平稳点分析表明，当且仅当神经网络权矩阵收敛到次子空间的一组基时，准则函数达到全局极大值。采用梯度上升法推导出一个新型的次子空间跟踪算法，并分析了算法的全局收敛性。仿真实验和实例应用验证了准则函数和导出算法的正确性。

Abstract

Aiming at the lack of information criterion functions of sub subspace

a novel criterion function was proposed by adding a penalty term to the Rayleigh quotient.Through analyzing the properties of all the stable points

it was proven that the criterion function exhibited the global maximum attained if and only if the weight matrices span the minor subspace.A minor subspace tracking algorithm was derived by gradient ascending method and its global convergence analysis was also accomplished.Numerical simulations and real application verifies the correctness of the criterion function and derived algorithm.

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Keywords

references

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