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Academic Editor:Andrei Gurtov
National Laboratory of Radar Signal Processing, Xidian University, Xi'an 710071, China
Received 12 August 2014; Accepted 28 October 2014; 23 December 2014
This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
1. Introduction
Passive source localization using time difference of arrival (TDOA) measurements has received considerable attention and has been widely applied in target tracking [1, 2], navigation [3], sensor networks [4, 5], and wireless communications [6, 7]. In the past decades, a number of efficient algorithms such as those in [5-9] were presented for TDOA-based source localization. Nevertheless, all these works assume that the signal propagation speed is known a priori so that the obtained TDOA measurements can be converted into range differences for source positioning. In practical applications such as seismic exploration [10], tangible interface for human-computer interaction [11], and underwater acoustic [12], the propagation speed is unknown and depends strongly on the propagation medium. In this case, the unknown propagation speed needs to be estimated jointly with the source location. For this problem, Mahajan and Walworth [13] proposed an unconstrained least-squares (LS) method, in which the nonlinear TDOA measurement equations are converted into pseudolinear ones by introducing two auxiliary variables. The source location and two auxiliary variables are then jointly estimated in LS sense. Reed et al. [14] selected the LS solution as the starting value and developed a four-step method which alternately estimates the source location and propagation speed. Recently, Zheng et al. [15] proposed a three-stage approach to simultaneously compute the source location and propagation speed. Very interestingly, the accuracy of the source location and propagation speed estimates approximates the CRLB for sufficiently small noise conditions. A disadvantage of this three-stage method is that it produces two results, where only one is the true solution. Furthermore, it may generate complex solutions when finding the square root in its last stage. Annibale and Rabenstein [16] investigated the influence of a wrongly presumed propagation speed because of temperature variations on the positioning accuracy of two well-known location methods. Oyzerman and Amar [17] extended the spherical intersection (SX) technique in [5] to the joint source position and propagation speed...