EM based stochastic maximum likelihood approach for localization of near-field sources in 3-D

The goal of this paper is to estimate the locations of unknown sources in 3-D space from the data collected by a 2-D rectangular array. Various studies employing different estimation methods under near-field and far-field assumptions were presented in the past. In most of the previous studies, location estimations of sources at the same plane with the antenna array were carried out by using algorithms having constraints for various situations indeed. In this study, location estimations of sources that are placed at a different plane from the antenna array is given. In other words, locations of sources in 3-D space is estimated by using a 2-D rectangular array. Maximum likelihood (ML) method is chosen as the estimator since it has a better resolution performance than the conventional methods in the presence of less number and highly correlated source signal samples and low signal to noise ratio. Besides these superiorities, stability, asymptotic unbiasedness, asymptotic minimum variance properties as well as no restrictions on the antenna array are motivated the application of ML approach. Despite these advantages, ML estimator has computational complexity. However, this problem is tackled by the application of Expectation/Maximization (EM) iterative algorithm which converts the multidimensional search problem to one dimensional parallel search problems in order to prevent computational complexity. EM iterative algorithm is therefore adapted to the localization problem by the data (complete data) assumed to arrive to the sensors separately instead of observed data (incomplete data). Furthermore, performance of the proposed algorithm is tested by deriving Cramér-Rao bounds based on the concentrated likelihood approach. Finally, the applicability and effectiveness of the proposed algorithm is illustrated by some numerical simulations.