  A popular approach for 3D source localization using multiple microphones is
the steered-response power method, where the source position is directly
estimated by maximizing a function of three continuous position variables.
Instead of directly estimating the source position, in this paper we propose an
indirect, distance-based method for 3D source localization. Based on properties
of Euclidean distance matrices (EDMs), we reformulate the 3D source
localization problem as the minimization of a cost function of a single
variable, 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 be
computed based on this variable. In addition, instead of using a single TDOA
estimate per microphone pair, we propose an extension that enables to select
the most appropriate estimate from a set of candidate TDOA estimates, which is
especially relevant in reverberant environments with strong early reflections.
Experimental results for different source and microphone constellations show
that the proposed EDM-based method consistently outperforms the
steered-response power method, especially when the source is close to the
microphones.
