New criteria based on Gerschgorin radii for source number estimation

In the spectral analysis of short data signals composed of sinusoids or exponentials, the source number estimation is a crucial problem for the performances of the high resolution methods (MUSIC, ESPRIT, etc.)· Indeed, for those methods, we must truncate the covariance matrix in signal and noise subspaces. That truncation depends on the estimation of the source number. So, we propose new criteria based on the Gerschgorin disks that can be applied in many situations : white noise, colored noise, signals with few samples and sources with different powers. For the last point, we put forward a simple deflation method associated to our criteria that improves the source number estimation. The Gerschgorin radii can be connected to the Least-Squares through the transformed cross-correlation vector to produce new criteria. Different simulations are carried out to compare the performances of those new criteria with other criteria such as AIC and MDL.