3D Single Source Localization Based on Euclidean Distance Matrices

TL;DR

This paper introduces an EDM-based indirect method for 3D source localization that reformulates the problem as a single-variable minimization, improving accuracy especially in reverberant environments.

Contribution

The paper proposes a novel distance-based approach using Euclidean distance matrices, offering an alternative to direct position estimation methods like steered-response power.

Findings

Outperforms steered-response power method in accuracy

Effective in reverberant environments with reflections

Works well with various microphone and source configurations

Abstract

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.