MAXIMUM-LIKELIHOOD NARROW-BAND DIRECTION FINDING AND THE EM ALGORITHM

We have derived generalized expectation-maximization (EM) algorithms for the maximum-likelihood estimation of the directions of arrival of multiple narrow-band signals in noise. Both deterministic and stochastic signal models are considered. The algorithm for the deterministic model yields estimates of the signal amplitudes, while for the stochastic model it yields estimates of the powers of the signals. Both algorithms have the properties that their limit points are stable and satisfy the necessary maximizer conditions for maximum-likelihood estimators. It is shown via simulation that the maximum-likelihood method allows for the resolution of the directions of arrival of signals at angular separation and noise levels for which other high resolution methods will not work. Algorithm convergence does depend on initial conditions; however, convergence to a global maximum has been observed in simulation when the initial estimates are within a significant fraction of one beamwidth (componentwise) of this maximum. Simulations also show that the incorporation of prior knowledge on signal structure under the deterministic model has a significant impact on the angle estimator performance. © 1990 IEEE