Maximum likelihood localization of wideband sources

The Gaussian and deterministic maximum likelihood (ML) direction of arrival (DOA) estimates are examined for several cases of a-priori noise statistics. The structures of the Gaussian and the deterministic log-likelihood functions are compared, and it is shown that, for unknown noise spectrum, both estimators minimize the entropy of the measurements. It is also shown that the Gaussian log-likelihood function includes an additional term, which is the entropy of the projection of the measurements onto the signal subspace. General conditions under which the deterministic ML estimate is also an extremum of the Gaussian likelihood function are derived, and it is shown that the asymptotic (large K) limit of these conditions guarantees equal asymptotic performances. It is also shown that the asymptotic performance is not affected by prior knowledge of the noise spectrum