A thorough derivation of the Expectation Maximization (EM) algorithm, which is an iterative numerical method of Maximum Likelihood (ML) estimation, is presented for the case of estimating direction of arrivals of unknown deterministic wide-band signals incident from different directions onto a passive array. For the rec^uired signal estimation, alternative regularized least squares estimation techniques are proposed with significant improvement over the standard least squares techniques. Also, for the angle of arrival estimation of a large number of signals, a tree structured EM algorithm is proposed and compared with the conventional EM approach. Extensive simulation results are presented for comparison of the proposed algorithms with the current high-resolution methods of wide-band direction finding. In order to handle efficiently the case of available parametric prior models on the received waveforms, the required modifications are also given.