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.
GUO Tuo1,2,WANG Yingmin1,ZHANG Lichen1
. Source Number Estimation Based on Joint Probability
Density Function of the Sample Eigenvectors[J]. Journal of Shanghai Jiaotong University, 2018
, 52(4)
: 469
-473
.
DOI: 10.16183/j.cnki.jsjtu.2018.04.012
［1］YANG X P, LI S, HU X N, et al. Improved MDL method for estimation of source number at subarray level［J］. IEEE Electronics Letters, 2015, 52(1): 85-86.
［2］HUANG L, LONG T, MAO E, et al. MMSE-based MDL method for robust estimation of number of sources without eigendecomposition［J］. IEEE Tran-sactions on Signal Processing, 2009, 57(10): 4135-4142.
［3］LIU Y, HANG Z, LI J, et al. Blind source enume-ration based on Gerschgorin Disk Estimator and virtual array extension［C］∥2016 8th International Conference on Wireless Communications & Signal Processing. Yangzhou: IEEE, 2016: 1-4.
［4］金芳晓, 邱天爽, 王鹏, 等. 基于l1稀疏正则化的信源个数估计新算法［J］. 通信学报, 2016, 37(10): 1-6.
JIN Fangxiao, QIU Tianshuang, WANG Peng, et al. New source number estimation algorithm based on l1 sparse regularization［J］. Journal on Communications, 2016, 37(10): 1-6.
［5］GUIMARES D A, SOARES P M, Souza R A A D. An empirical method for estimating the number of signal sources［J］. IEEE Latin America Transactions, 2015, 13(7): 2057-2064.
［6］LU Z H, ABDELHAK M Z. Source enumeration in array processing using a two-step test［J］. IEEE Transactions on Signal Processing, 2015, 63(10): 2718-2727.
［7］黄青华, 张翼飞, 刘凯. 一种新的基于EEF准则的空间声源个数估计算法［J］. 电子学报, 2016, 44(3): 687-692.
HUANG Qinghua, ZHANG Yifei, LIU Kai. A novel spatial acoustic source enumeration algorithm based on EEF criterion［J］. Acta Electronica Sinica, 2016, 44(3): 687-692.
［8］吴娜, 司伟建, 焦淑红, 等. 基于去特征处理的信源数估计算法［J］. 系统工程与电子技术, 2015, 37(3): 509-514.
WU Na, SI Weijian, JIAO Shuhong, et al. New source number estimation method based on feature eliminated process［J］. Journal of Systems Engineering and Electronics, 2015, 37(3): 509-514.
［9］QUIJANO J E, ZURK L M. An eigenvector-based test for local stationarity applied to array processing［J］. The Journal of the Acoustical Society of America, 2014, 135(6): EL277-EL283.
［10］JUNG S, SEN A, MARRON J S. Boundary behavior in high dimension low sample size asymptotics of PCA［J］. Journal of Multivariate Analysis, 2012, 109(4): 190-203.
［11］赵闪, 孙长瑜, 陈新华, 等. 一种改进的被动合成孔径算法用于舰船辐射噪声检测［J］. 电子与信息学报, 2013, 35(2): 426-431.
ZHAO Shan, SUN Changyu, CHEN Xinhua, et al. An improved passive synthetic aperture sonar algorithm application for detecting of the ship radiated noise［J］. Journal of Electronics and Information Technology, 2013, 35(2): 426-431.
