An information criterion for source number detection with the eigenvalues modified by Gerschgorin radii

A new method for detecting the source number is proposed based on Gerschgorin disk theorem and information criterion. With this method, we first take a Gerschgorin transform to the covariance matrix of data samples. Then according to the fact that both the eigenvalues and the Gerschgorin radii have valuable information in distinguishing signal and noise, new eigenvalues modified by the Gerschgorin radii are introduced to Akaike information criterion (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. The MAIC method overcomes the drawback of AIC in inconsistent estimation for target number. Computer simulations and lake experimental results show that the MAIC method is a robust multi-target detection algorithm with good performance either under low SNR or high SNR.