Multidimensional Scaling Analysis for Passive Moving Target Localization With TDOA and FDOA Measurements

Abstract

A new framework for positioning a moving target is introduced by utilizing time differences of arrival (TDOA) and frequency differences of arrival (FDOA) measurements collected using an array of passive sensors. It exploits the multidimensional scaling (MDS) analysis, which has been developed for data analysis in the field such as physics, geography and biology. Particularly, we present an accurate and closed-form solution for the position and velocity of a moving target. Unlike most passive target localization methods focusing on minimizing a loss function with respect to the measurement vector, the proposed method is based on the optimization of a cost function related to the scalar product matrix in the classical MDS framework. It is robust to the large measurement noise. The bias and variance of the proposed estimator is also derived. Simulation results show that the proposed estimator achieves better performance than the spherical-interpolation (SI) method and the two-step weighted least squares (WLS) approach, and it attains the Cramer-Rao lower bound at a sufficiently high noise level before the threshold effect occurs. Moreover, for the proposed estimator the threshold effect, which is a result of the nonlinear nature of the localization problem, occurs apparently later as the measurement noise increases for a near-field target.