Sufficient conditions for the unique localization of distributed sources

The array output for a distributed source can be approximated by the superposition of the array response to a large number of closely spaced point sources. In the limit, a distributed source corresponds to an infinite number of point sources. In this approximation, the number of free parameters increases with the number of point sources. In this paper, we show that if the point sources (approximation of a distributed source) are related through some parametric constraints, then for any observation at the array output, almost surely, there is a unique solution for the localization problem, provided that the dimensionality of the parameter space satisfies a certain bound. We show this for both coherently and incoherently distributed sources.