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A popular approach for 3D source localization using multiple microphones isthe steered-response power method, where the source position is directlyestimated by maximizing a function of three continuous position variables.Instead of directly estimating the source position, in this paper we propose anindirect, distance-based method for 3D source localization. Based on propertiesof Euclidean distance matrices (EDMs), we reformulate the 3D sourcelocalization problem as the minimization of a cost function of a singlevariable, namely the distance between the source and the reference microphone.Using the known microphone geometry and estimated time-differences of arrival(TDOAs) between the microphones, we show how the 3D source position can becomputed based on this variable. In addition, instead of using a single TDOAestimate per microphone pair, we propose an extension that enables to selectthe most appropriate estimate from a set of candidate TDOA estimates, which isespecially relevant in reverberant environments with strong early reflections.Experimental results for different source and microphone constellations showthat the proposed EDM-based method consistently outperforms thesteered-response power method, especially when the source is close to themicrophones.

3D Single Source Localization Based on Euclidean Distance Matrices