Joint Source Estimation and Localization

The estimation of directions of arrival is formulated as the decomposition of a 3-way array into a sum of rank-one terms, which is possible when the receive array enjoys some geometrical structure. The main advantage is that this decomposition is essentially unique under mild assumptions, if computed exactly. The drawback is that a low-rank approximation does not always exist. Therefore, a constraint is first introduced that ensures the existence of the latter best approximate. Then Cramér-Rao bounds are derived for localization parameters and source signals, assuming the others are nuisance parameters; some inaccuracies found in the literature are pointed out. Performances are eventually compared with reference algorithms such as ESPRIT, in the presence of additive Gaussian noise, with possibly non circular distribution. Index Terms multi-way array, tensor decomposition, source localization, antenna array processing, low-rank approximation, complex Cramer-Rao bounds I