1. 西北工业大学 航海学院， 西安 710072; 2. 陕西科技大学 电气与信息工程学院, 西安 710021
Source Number Estimation Based on Joint Probability Density Function of the Sample Eigenvectors
GUO Tuo1,2,WANG Yingmin1,ZHANG Lichen11. School of Marine Science and Technology, Northwestern Polytechnical University, Xi’an 710072, China; 2. College of Electrical and Information Engineering, Shaanxi University of Science and Technology, Xi’an 710021, China
摘要/Abstract
摘要： 针对传统信源数估计算法如基于Akaike信息论准则方法、最小描述长度准则方法及盖氏圆盘方法等存在低信噪比时性能下降甚至完全不能正确估计信源个数的问题，提出一种基于协方差矩阵特征向量之夹角联合密度函数的信源数估计方法.该方法采用样本协方差矩阵特征分解后噪声子空间的一特征向量与其他特征向量求夹角余弦，然后求这些特征向量之夹角余弦的联合概率密度函数值，最后将两相邻密度函数值相除与阈值比较确定信源个数.数值模拟与水池实验表明该方法在低信噪比时性能远远好于以往算法，在阵列信号处理中具有一定的应用价值.
关键词: 特征向量夹角余弦, 联合概率密度函数, 阵列信号处理, 信源个数估计
Abstract: Correctly estimating the number of sources is a necessary condition for the majority of high-resolution spatial spectrum estimation algorithm. Source number estimations such as the criteria based on Akaike information theory (AIC), minimum description length (MDL) criterion, and Gerschgorin disk criterion (GDE) may lead to performance degradation, or even cannot correctly work in the low SNR. A novel source number estimation method based on joint probability density function of cosine of the angle between sample eigenvectors is proposed. Firstly, in noise subspace the cosine values between an eigenvector and other eigenvectors are obtained by the sample covariance matrix decomposition. Then the joint probability density function value of these vector angle cosine is determined. At last, two divided adjacent values of the density function is compared with a threshold value for determining the source number. Numerical simulation and tank experimental verification show that the performance of the proposed method is far better than that of the conventional algorithms mentioned above.
Key words: array signal processing, source number estimation, eigenvector angle cosine, joint probability density function
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