Detection–estimation of multi-rank Gaussian sources using expected likelihood

We consider the problem of detection–estimation (resolution) of a number of sources impinging upon an antenna array, where the covariance matrix of each source has a limited signal eigen-subspace, spanned by a known linear subspace. In general, the direction of arrival (DoA) and the subspace rank of each source is not known a priori and must be estimated, along with detection of the total number of such sources. We introduce the application of a GLRT-based (“expected likelihood” (EL)) detection–estimation framework to this problem in conjunction with a novel “multi-rank MUSIC” technique for initial DoA estimation.