High resolution spectral method for spatial discrimination of closely spaced correlated sources

The precision on the estimation of the angles of arrival of plane waves on a linear array of N sensors is altered either when the angular separation between sources is small, or when the sources are correlated. This may be connected to the ill conditionning of the covariance matrix in such conditions. This last point is discussed in the case of two sources: the expression of the eigenvalues is derived and we demonstrate how the use of spatial averaging may be used to improve the robustness of the estimation. The influence of the noise on estimation is then considered. The average distribution of the noise eigenvalues for finite time estimation is derived and used for a test on the number of sources. The perturbation on the signal eigenvectors is then computed and used to get the variance on the estimation of source locations.