Expectation-maximization algorithm for direct position determination

• Published in: Signal processing Vol. 133; pp. 32 - 39
• Main Authors: Tzoreff, Elad, Weiss, Anthony J.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.04.2017
• Subjects: Direct Position Determination (DPD); Expectation Maximization (EM); Laplace Method; Time of Arrival (TOA); Time of Arrival (TOA); Direct Position Determination (DPD); Laplace Method; Expectation Maximization (EM)
• ISSN: 0165-1684; 1872-7557
• DOI: 10.1016/j.sigpro.2016.10.015

Transmitter localization is used extensively in civilian and military applications. In this paper, we focus on the Direct Position Determination (DPD) approach, based on Time of Arrival (TOA) measurements, in which the transmitter location is obtained directly, in one step, from the signals intercepted by all sensors. The DPD objective function is often non-convex and therefore finding the maximum usually require s exhaustive search, since gradient based methods usually converge to local maxima. In this paper we present an efficient technique for finding the extremum of the objective function that corresponds to the transmitter location. The proposed method is based on the Expectation-Maximization (EM) algorithm. The EM algorithm is designed to find the Maximum Likelihood (ML) estimate when the available data can be viewed as “incomplete data”, while the “complete data” is hidden in the model. By choosing the appropriate “incomplete data” we replace the high dimensional search, associated with the ML algorithm, with several sub-problems that require only one dimensional search. We demonstrate that although the EM algorithm does not guarantee a convergence to the global maximum, it does so with high probability and therefore it outperforms the common gradient-based methods. •A framework to solve TOA/TDOA based localization in the presence of nuisance parameters, using the EM algorithm.•Application of the framework to the DPD method which is usually solved using variants of exhaustive search, due to the non-convex structure of the objective function.•Demonstration by simulations that the proposed EM approach achieves the global maximum at various scenarios, and SNR levels with high probability.•Application of the EM algorithm to the traditional two step method with a closed from solution at each iteration without using derivatives (or Jacobians).•Demonstration that the algorithm is more stable than the well-known Gauss-Newton algorithm, and generally converges quickly.