Detection of the source number by the Gerschgorin disks

The inclusion regions of the eigenvalues enable us to work out efficient criteria for the estimation of the number of sinusoids. To exploit those regions, it is necessary first to transform the covariance matrix. That is why we put forward a transformation based on an approximation of the eigenvalues and eigenvectors, so as to obtain the radii and the centers of the Gerschgorin disks, the disks being the studied inclusion regions. We show that the introduction of information concerning the radii and the centers in the detection criteria improves their performances tremendously. A new criterion using the Euclidean distance (and called GDE_dist) is also suggested.