A multi-hypothesis GLRT approach to the combined source detection and direction of arrival estimation problem

The problem of detecting the number of uncorrelated narrowband signals received by an array of sensors when the direction of arrival (DOA) and power level of each source is unknown is investigated. A multi-hypothesis generalized likelihood ratio test (GLRT) approach is used, resulting in a procedure which maximizes the likelihood function with respect to the number of signals and their DOAs and powers. A tuning mechanism for controlling the tradeoff between the probability of correct detection and the probability of false alarm is obtained by imposing a constraint on the minimum allowable value for the power level estimate. A sequential search over the number of sources is used for a computationally feasible solution. Performance comparisons are made to the minimum description length (MDL) and minimum variance distortionless response (MVDR) signal detection approaches.