Maximum Likelihood and IRLS Based Moving Source Localization with Distributed Sensors
Xudong Zhang, Fangzhou Wang, Hongbin Li, Braham Himed
Abstract
In this article, we consider the problem of estimating the location and velocity of a moving source using a distributed passive radar sensor network. We first derive the maximum likelihood estimator (MLE) using direct sensor observations, when the source signal is unknown and modeled as a deterministic process. Since the MLE obtains the source location and velocity estimates through a search process over the parameter space and is quite computationally intensive, we also developed an efficient algorithm to solve the problem using a two-step approach. The first step finds the time difference of arrival (TDOA) and frequency difference of arrival (FDOA) estimates for each sensor with respect to a reference sensor by using a two-dimensional fast Fourier transform and interpolation, while the second step employs an iterative reweighted least square (IRLS) approach with a varying weighting matrix to determine the source location and velocity. To benchmark the performance of the proposed methods, a constrained Cramér-Rao bound (CRB) for the considered source localization problem is derived. Numerical results show that the IRLS approach has a lower signal-to-noise ratio threshold phenomenon compared with several recent TDOA/FDOA-based methods, especially when the source is considerably farther away from some sensors than others, creating a larger disparity in the quality of sensors observations.