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 coherence constraint is introduced that ensures the existence of the latter best approximate, which allows to localize and estimate closely located or highly correlated sources. 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 unconstrained reference algorithms such as ESPRIT, in the presence of additive complex Gaussian noise, with possibly noncircular distribution.