Efficient computation of ML DOA estimates under unknown nonuniform sensor noise powers

Abstract

This paper presents an efficient method for computing Maximum Likelihood (ML) direction-of-arrival (DOA) estimates in scenarios in which the sensor noise powers are nonuniform and unknown. The method combines the Alternating Projection (AP) algorithm for coarsely locating additional DOAs and Newton iterations for finally obtaining the ML estimates. Compared with the existing approaches, the method reduces the computational burden significantly due to the small number of Newton iterations required and to the efficient computation of each iteration. Specifically, the iterations are computed in a small number of arithmetic operations thanks to the closed-form formulas for the gradient and Hessian of the ML cost functions presented in this paper. The method’s total computational burden is of just a few mega-flops (mega floating-point operations) in typical cases. We present the method for the deterministic and stochastic ML estimators. Then, an analysis of the deterministic ML cost function’s gradient reveals an unexpected drawback: its associated estimator is either degenerate or inconsistent. Finally, we assess the method’s root-mean-square (RMS) error and computational burden numerically and compare it with other relevant estimators in the literature.