恒虚警检测信源数的方法

doi:10.12305/j.issn.1001-506X.2022.01.01

系统工程与电子技术 ›› 2022, Vol. 44 ›› Issue (1): 1-9.doi: 10.12305/j.issn.1001-506X.2022.01.01

• 电子技术 • 下一篇

恒虚警检测信源数的方法

张一迪, 王悦斌, 王培志, 杨沁, 陆起涌, 张建秋*, 李旦

复旦大学信息科学与工程学院, 上海 200433

收稿日期:2020-06-29 出版日期:2022-01-01 发布日期:2022-01-19
通讯作者: 张建秋
作者简介:张一迪(1993—), 男, 硕士研究生, 主要研究方向为信号处理及其应用|王悦斌(1993—), 男, 博士研究生, 主要研究方向为信号处理及其应用|王培志(1995—), 男, 硕士研究生, 主要研究方向为信号处理在视频中的应用|杨沁(1996—), 男, 硕士研究生, 主要研究方向为信号处理在视频中的应用|陆起涌(1966—), 男, 教授, 硕士, 主要研究方向为嵌入式系统软硬件设计、工业控制与自动化、物联网应用、大数据分析等|张建秋(1962—), 男, 教授, 博士, 主要研究方向为信号处理及其在通信、控制、测量、图像和雷达中的应用|李旦(1982—), 男, 副教授, 博士, 主要研究方向为信号处理及其在超声、测量、图像和雷达中的应用
基金资助:
国家自然科学基金(11827808);国家自然科学基金(11974082);上海市科技创新行动计划社会发展科技领域项目(19DZ1205805);上海航天科技创新基金;珠海复旦创新研究院资助项目

A method for detecting the number of signal sources with constant false alarm

Yidi ZHANG, Yuebin WANG, Peizhi WANG, Qin YANG, Qiyong LU, Jianqiu ZHANG*, Dan LI

School of Information Science and Technology, Fudan University, Shanghai 200433, China

Received:2020-06-29 Online:2022-01-01 Published:2022-01-19
Contact: Jianqiu ZHANG

摘要/Abstract

摘要：

提出了一种恒虚警检测信源数的方法, 该方法通过定义一个由观测协方差矩阵相邻特征值之差统计量构成的五维矢量序列, 并利用K均值(K-means)聚类算法将所定义的五维矢量序列分成两类, 且视为信号和噪声子空间。当将噪声子空间所对应的特征值序列描述成一个统计分布, 并通过期望最大(expectation maximization, EM)算法估计出这个统计分布时, 奈曼-皮尔逊(Neyman-Pearson, NP)假设检验就可利用这个分布来对信源数进行恒虚警检测。为了降低提出算法的计算复杂度, 也给出了一个近似的NP假设检验方法。数值仿真结果在验证提出方法有效性的同时, 也表明其优于其他方法。

关键词: 信源数检测, 恒虚警率, 期望最大算法, K均值, 聚类

Abstract:

A new method with a given constant false alarm rate for detecting signal source numbers is proposed. A five-dimension vector with the statistics of the eigenvalue differences of an observation covariance matrix is first defined. Then, the K-means clustering algorithm is used to divide these vectors into two classes. which are respectively regarded as the signal and noises subspaces of the eigenvalues corresponding to the five-dimension vectors. When the eigenvalues of noise are expressed as a probability distribution with a Gaussian mixture one known to be able to describe any probability distribution, the expectation maximization (EM) algorithm can be utilized to estimate the distribution. By means of the estimated distribution, the Neyman-Pearson (NP) hypothesis test is exploited to do source number detection with a given constant false alarm rate. Moreover, an approximated NP hypothesis, where the noise eigenvalue distribution is assumed Gaussian one regardless of the actual one, is given in order to reduce the computation complexity of the proposed method. Numerical simulation results verify the effectiveness of the proposed method while its superiority over the methods reported in literature is shown.

Key words: signal source number detection, constant false alarm rate, expectation-maximization (EM) algorithm, K-means, clustering

中图分类号:

TP957

张一迪, 王悦斌, 王培志, 杨沁, 陆起涌, 张建秋, 李旦. 恒虚警检测信源数的方法[J]. 系统工程与电子技术, 2022, 44(1): 1-9.

Yidi ZHANG, Yuebin WANG, Peizhi WANG, Qin YANG, Qiyong LU, Jianqiu ZHANG, Dan LI. A method for detecting the number of signal sources with constant false alarm[J]. Systems Engineering and Electronics, 2022, 44(1): 1-9.

图/表 8

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高斯混合分布	虚警率
高斯混合分布	0.01	0.05	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	0.99
c=2	0.007	0.058	0.111	0.211	0.311	0.407	0.493	0.572	0.654	0.752	0.899	1.000
c=3	0.006	0.056	0.108	0.209	0.306	0.406	0.507	0.584	0.665	0.757	0.891	1.000
c=5	0.005	0.056	0.108	0.208	0.306	0.406	0.502	0.592	0.674	0.763	0.886	1.000
c=10	0.005	0.055	0.108	0.206	0.305	0.404	0.503	0.595	0.681	0.768	0.884	1.000

SNR/dB	虚警率
SNR/dB	0.01	0.05	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	0.99
0	0.005	0.055	0.108	0.208	0.307	0.406	0.503	0.591	0.675	0.763	0.886	1.000
10	0.012	0.050	0.098	0.203	0.308	0.409	0.505	0.592	0.673	0.763	0.888	1.000
30	0.031	0.050	0.102	0.211	0.316	0.412	0.496	0.576	0.657	0.755	0.901	1.000

SNR/dB	虚警率
SNR/dB	0.01	0.05	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	0.99
0	0.019	0.076	0.128	0.213	0.289	0.364	0.442	0.526	0.624	0.754	0.950	1.000
10	0.032	0.070	0.112	0.189	0.264	0.342	0.424	0.516	0.626	0.776	0.974	1.000
30	0.033	0.033	0.037	0.066	0.067	0.099	0.206	0.516	0.992	1.000	1.000	1.000

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恒虚警检测信源数的方法

A method for detecting the number of signal sources with constant false alarm

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