Source number estimation with Gerschgorin radii by reduced-rank covariance matrix

This paper presents a new method through the equivalence reduced rank of the covariance to estimate the number of the sources, where the Gerschgorin radiis do not derectly get from the unitary transformation of the covariance matrix but by many times. It is named as the reduced rank covariance method by using the partial covariance matrix to replace the whole covariance matrix. And through this way we can estimate the source number more than once, which is much different form the traditional Gerschgorin radii method. We proposed a new detection criteria to decide the number in this paper. After the circulation we give each estimation a different weight and then take the average of the estimations to obtain the number of the sources which enables us to accurately estimate the source number. The analysis is verified by simulation results, even for closely spaced sources.