Source number estimators using Gerschgorin radii

We introduce the effective uses of the Gerschgorin radii of the unitary transformed covariance matrix for source number detection. The proposed log-likelihood function for developing the detection criteria combines the Gerschgorin radii to the AIC and minimum description length (MDL) and improves their detection performances for Gaussian and white noise processes. It is verified that the Gerschgorin AIC (GAIC) criterion yields a consistent estimate of source number and the Gerschgorin MDL (GMDL) criterion does not tend to under-estimate the source number at small or moderate data samples. Furthermore, the detection performances of the criteria can be further improved through the suggested rotation and averaging