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Time difference of arrival (TDoA) measurement is a promising approach for target localization based on a set of nodes with known positions, with high accuracy and low complexity. Common localization algorithms include the maximum-likelihood, non-linear least-squares and weighted least-squares methods. These methods have shortcomings such as high computational complexity, requiring an initial guess position, or having difficulty in finding the optimal solution. From the point of view of geometrical analysis, this study proposes two new shrinking-circle methods (SC-1 and SC-2) to solve the TDoA-based localization problem in a two-dimensional (2-D) space. In both methods, an optimal radius is obtained by shrinking the radius with a dichotomy algorithm, and the position of the target is determined by the optimal radius. The difference of the two methods is that a distance parameter is defined in SC-1, while an error function is introduced in SC-2 to guide the localization procedure. Simulations and indoor-localization experiments based on acoustic transducers were conducted to compare the performance differences between the proposed methods, algorithms based on weighted least-squares as well as the conventional shrinking-circle method. The experimental results demonstrate that the proposed methods can realize high-precision target localization based on TDoA measurements using three nodes, and have the advantages of speed and high robustness.

Two New Shrinking-Circle Methods for Source Localization Based on TDoA Measurements