Microphone array positioning technique with Euclidean distance geometry

Abstract

Source localization and quantification by an acoustic array of microphones depend to a great extent on an accurate knowledge of the antenna position towards the radiating device. The present work details a methodology to determine the location of the microphones in relation to an object of study, starting from its geometric shape and that of the array, in order to reproduce an experimental configuration in any retro-propagating method. A set of reference sources are placed on several prominent locations of the device to estimate the times of flight (ToF) (and distances) between them and the microphones, connecting the array and the object together. The overall geometric configuration is thus defined by an Euclidean Distance Matrix (EDM), which is basically the matrix of squared distances between points. First, MultiDimensional Unfolding (MDU) technique is used to reconstruct the point set from distances. Second, this point set is then aligned with the device, using reference sources as anchor nodes. This orthogonal Procustes problem is solved by the Kabsch algorithm to obtain the optimal rotation and translation matrices between the coordinate system of the array and that of the object of study. The methodology is detailed, validated first by a numerical simulation of a typical experimental set-up. An experimental campaign is finally carried out to assess the robustness of the method in a typical test case.