ASYMPTOTIC RESULTS FOR MAXIMUM-LIKELIHOOD-ESTIMATION WITH AN ARRAY OF SENSORS

It is well known that in many cases the maximum likelihood (ML) estimator is consistent and asymptotically normal with covariance equal to the inverse of the Fisher's information matrix. It does not follow, though, that the covariance of the ML estimator approaches the Cramer-Rao lower bound as the sample size increases. However, it is possible to draw such a conclusion for the adaptive array problem in which direction of arrival and signal magnitude are being estimated. Proofs of w-asymptotic efficiency (which comes with a convergence-of-moments condition) and strong consistency (almost-sure convergence) of the ML estimator are given. Strong consistency is also proved for a popular quasi-ML estimator.