A Gerschgorin-Kullback criterion for source number detection in nonuniform noise and small samples

We consider the problem of source number estimation in the presence of unknown spatially nonuniform noise and small size data samples. Gerschgorin's theorem is used to derive a goodness-of-fit function which incorporates the inequality of the noise powers. To this function, is added a penalty function which takes into account the finite sample size, based on a measure of Kullback's symmetric divergence. The combination results in an information theoretic criterion for automatic source number estimation. Performance of the new criterion is assessed through simulations and it is shown that the method is powerful in a nonuniform noise environment.