In this paper, we introduce the effective uses of Gerschgorin radii of the unitary transformed covariance matrix for source number estimation. There are two approaches, likelihood and heuristic, used for developing the detection criteria. The likelihood approach combines the Gerschgorin radii to the well-known source number detectors and improves their detection performances for Gaussian and white noise processes. It is verified that the Gerschgorin likelihood estimators (GLE) are consistent. The Gerschgorin AIC yields a consistent estimate and the Gerschgorin MDL criterion does not tend to underestimate at small or moderate data samples. The heuristic approach applying the Gerschgorin disk estimator (GDE) developed from the projection concept, overcomes the problem in cases of small data samples, an unknown noise model, and data dependency. Furthermore, the detection performances of both approaches through the suggested rotations and averaging can be further improved. Finally, the proposed and existing criteria are evaluated in various conditions by using simulated and measured experimental data.
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