On unique localization of multiple sources by passive sensor arrays

Necessary and sufficient conditions are derived for the unique localization of narrowband sources having the same known center frequency by passive sensor arrays. The conditions specify the maximum number of sources that can be uniquely localized by a general array that satisfies some mild geometric constraints. The conditions are expressed in terms of the number of sensors and the rank of the correlation matrix of the sources. Two different conditions are presented. The first guarantees uniqueness for every batch of sampled data. The second, which is weaker, guarantees uniqueness for almost every batch of sampled data, with the exception of a set of batches of measure zero. It is shown that a condition that is slightly weaker than the second one is also necessary