Generalized Maximum Likelihood Algorithm for Direction-of-Arrival Estimation of Coherent Sources

Abstract

The generalized maximum likelihood (GML) algorithm for direction-of-arrival estimation is proposed. Firstly, a new data model is established based on generalized steering vectors and generalized array manifold matrix. The GML algorithm is then formulated in detail. It is flexible in the sense that the arriving sources may be a mixture of multiclusters of coherent sources, the array geometry is unrestricted, and the number of sources resolved can be larger than the number of sensors. Secondly, the comparison between the GML algorithm and the conventional deterministic maximum likelihood (DML) algorithm is presented based on their respective geometrical interpretation. Subsequently, the estimation consistency of GML is proved, and the estimation variance of GML is derived. It is concluded that the performance of the GML algorithm coincides with that of the DML algorithm in the incoherent sources  case, while it improves greatly in the coherent source case. By using genetic algorithm, GML is realized, and the simulation results illustrate its improved performance compared with DML, especially in the case of multiclusters of coherent sources.