Simultaneous mutual localization of transmitters and receivers from time difference of arrival measurements

The problem of a signal source or a signal receiver localization from time difference of arrival (TDOA) measurements is a crucial issue in many applications appearing in the fields of navigation, surveillance or wireless communication. In this paper we present the algorithm for finding a mutual location of both sources and receivers when the position of none of them is known. We derive an inequality for the numbers of sources and receivers necessary for the problem to have a unique solution. The results of conducted computer simulations and acoustic experiments illustrate the performance of the proposed algorithm as well as its sensitivity to TDOA measurement errors.