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In this paper, we propose a novel acoustic source localization method that accommodates the general scenario of multiple independent microphone arrays. The method is based on a 3-D parameter space defined by the 2-D spatial location of a source and the range difference extracted from the time difference of arrival (TDOA). In this space, the set of points that correspond to a given range lie on a circle that expand as the range increases, forming a cone whose apex is the actual location of the source. In this parameter space, the lack of synchronization between arrays results in the fact that clusters of data associated to individual arrays are free to shift along the range axis. The cone constraint, in fact, enables the realignment of such clusters while positioning the cone vertex (source location), thus resulting in a joint data re-synchronization and source localization. We also propose a novel and general analysis methodology for swiftly assessing the localization error as a function of the TDOA uncertainties, which is remarkably accurate for small localization bias. With the aid of this method, simulations and experiments on real data, we show that the cone-fitting process offers excellent localization accuracy in the scenario of multiple unsynchronized arrays, as well as in simpler single-array scenarios, also in comparison with state-of-the-art techniques. We also show that the proposed method offers the desired flexibility for adapting to arbitrary geometries of microphone clusters.