Optimum localization of multiple sources by passive arrays

The maximum likelihood (ML) estimator of the location of multiple sources and the corresponding Cramer-Rao lower bound on the error covariance matrix are derived. The derivation is carried out for the general case of correlated sources so that multipath propagation is included as a special case. It is shown that the ML processor consists of a bank of beam-formers, each focused to a different source, followed by a variable matrix-filter that is controlled by the assumed location of the sources. In the special case of uncorrelated sources and very low signal-to-noise ratio this processor reduces to an aggregate of ML processors for a single source with each processor matched to a different source. Iterative algorithms for the actual computation of the ML estimator are also presented.