An Improved Algebraic Solution for Multidimensional Scaling-Based Localization Using TDOA Measurement

In this paper, the source localization problem by utilizing time difference of arrival measurements is addressed. The weighted multidimensional scaling (MDS) is an efficient approach. However, the weighting matrix, which plays an important role in whitening residuals, lacks accuracy due to the ignoring of second-order noise terms. Thus, a considerable bias occurred in high noise region as well as poor coordinate geometry. The aim of this paper is to enhance the performance of weighted MDS method. It starts through deriving a novel weighting matrix, which considers second -order noise terms for a more precise estimation. Additionally, different from traditional methods, the derivation is presented by algebra, which is straightforward and intuitive. Secondly, the localization result is determined with a linear equation and solving in the least square sense so that accurate weighting matrix can be applied to improve the performance. According to numerical simulation results, the proposed method achieves the Cramer-Rao lower bound accuracy very well and has more noise tolerance in the presence of high error level than the existing approaches.