An information theoretic criterion for source number detection using the eigenvalues modified by Gerschgorin radius

Abstract

AIC method shows good performance in low SNR but gives over-estimation for target number, while MDL can obtain consistent estimation in high SNR but shows bad performance in low SNR. In this paper, a new method for detecting the source number is proposed to take a good compromise between the AIC and the MDL, which bases on Gerschgorinpsilas disk theorem and information theoretic criterion. The method takes a Gerschgorin transform to the covariance matrix of the samples. According to that both the eigenvalues and the Gerschgorin radius have valuable information in distinguishing signal and noise, new eigenvalues modified by the Gerschgorin radius are then introduced to AIC with a new penalty function. Theoretical analysis indicates that the number estimation acquired by the modified AIC (MAIC) method is almost consistent estimation of the number of targets. MAIC method overcomes the drawback of AIC in inconsistent estimation for target number, Simulation and experimental results show the MAIC method is a robust multi-target detecting algorithm.