Source number estimation for minimum redundancy arrays with Gerschgorin disk estimator

Abstract

Source number estimation for minimum redundancy arrays (MRAs) is considered in this paper. When the manifold ambiguity is present, the dimension of signal subspace of conventional covariance matrix will be reduced. Therefore Akaike's information criterion (AIC) and minimum description length (MDL) approaches based on the conventional covariance matrix can not provide the correct estimation. In conventional MRA configuration, manifold ambiguities can be eliminated by augmenting the covariance matrix. However, the conventional AIC and MDL based on the augmented covariance matrix are still not able to estimate the source number correctly, due to the fluctuation of the noise eigenvalues of the augmented covariance matrix. The Gerschgorin disk estimator (GDE) based on the augmented covariance matrix is proposed in this paper. Because the noise eigenvectors of augmented covariance matrix are orthogonal to the signal subspace spanned by steering vectors, GDE can give a correct estimation. By numerical simulation we can see that GDE based on the augmented covariance matrix has a good performance.