An efficient Newton-type method for the computation of ML estimators in a uniform linear array

In the problem of estimating the angles of arrival to a uniform linear array, we present an efficient method to compute Maximum Likelihood (ML) estimations, based on the Modified Variable Projection (MVP) algorithm. In contrast to methods like Iterative Quadratical Maximum Likelihood (IQML) or the Iterative Method of Direction Estimation (IMODE), it is not based on a polynomial parameterization but on directly exploiting the Vandermonde structure through analytical tools like the Fast Fourier Transform (FFT), the geometric series summation formula, and Horner´s synthetic division. The computational burden of the proposed method is significantly smaller than the burden of IMODE and of the Relaxation (RELAX) algorithm. Besides, it is shown that the computation of the ML estimation can be divided in a preliminary step in which a few FFTs are computed and an iterative step with a complexity that is independent of the array size.