Exact solutions for the problem of source location from measured time differences of arrival

Abstract

Source location using the difference in time of arrival of a signal (TDOA) at an array of receivers is used in many fields including speaker location. Using three TDOA values from four noncollinear receivers one can, in principle, solve for the unknown source coordinates in terms of the receiver locations. However, the equations are nonlinear, and in practice signals are contaminated by noise. Practical systems often use multiple receivers for accuracy and robustness, and improved S/N, and solutions must be obtained via minimization. A new family of exact solutions, for the case of four receivers located in a plane, is presented. These solutions can be evaluated using a small number of arithmetic operations. The performance of these solutions for several practical situations is examined via simulation, and possible geometries of receiver locations suggested. For the case where multiple receivers (>4) are used, a new formulation is presented, that incorporates the present solutions, imposes additional constraints on source location, and enables use of a constrained L1 optimization procedure to achieve a robust estimate of the source location. The present estimator is compared with ones from the literature, and found to be robust and accurate, and more efficient. [Work partially supported by DARPA.]