The source number estimation based on Gerschgorin radii

The GDE criterion is based on the estimation of the Gerschgorin disks' radii where the disks are separated in two distinct sets: one associated to the signal sources, the other related to the noise. We aim at modifying that criterion into a new one called SGDE by using the sum of the disks' radii. Besides, the SGDE criterion is modified with a simple deflation on the sum of the Gerschgorin radii to obtain a better estimation with sources of different power. We also suggest applying a deflation method to the covariance matrix before using the criteria based on the Gerschgorin radii. The transformed Gerschgorin radii can be connected to the least-squares through the transformed cross-correlation vector. So, two new criteria are put forward on the same principle as the SGDE criterion. These criteria can be applied in many situations: coloured or white noise, sources of different power.