Unconditional maximum likelihood approach for localization of near-field sources: Algorithm and performance analysis

Localization of near-field sources requires sophisticated estimation algorithms. In this paper, we propose an unconditional maximum likelihood method for estimating direction of arrival and angle parameters of near-field sources. However, the calculation of maximum likelihood estimation from the corresponding likelihood function results in difficult nonlinear constraint optimization problems. We therefore employed an Expectation/Maximization (EM) iterative method for obtaining maximum likelihood estimates. The most important feature of the EM algorithm is that it decomposes the observed data into its components and then estimates the parameters of each signal component separately providing computationally efficient solution to resulting optimization problem. The performance of the unconditional maximum likelihood location estimator for the near-field sources is studied based on the concentrated likelihood approach to obtain Cramér-Rao bounds. Some insights into the achievable performance of the conditional maximum likelihood algorithm is obtained by numerical evaluation of the Cramér-Rao bounds for different test cases.