On non-uniqueness of stochastic ML estimation of DOA and its best solution

This paper addresses the issue of uniqueness of stochastic or unconditional maximum likelihood (SML) estimation for directions-of-arrival (DOA) finding. Global search techniques for the SML estimation fail to find DOA in many cases, unlike the deterministic or conditional ML (DML) estimation. This paper reveals that its reason lies in the non-uniqueness of the SML estimation. Based on the idea that the SML local solution closest to the DML solution can be considered to be the most adequate for DOA finding, we propose an algorithm which uses a local search of the SML criterion together with the DML estimation as initialization. Finally some simulation results are shown to demonstrate the proposed algorithm is effective.