How to localize ten microphones in one finger snap

A compelling method to calibrate the positions of microphones in an array is with sources at unknown locations. Remarkably, it is possible to reconstruct the locations of both the sources and the receivers, if their number is larger than some prescribed minimum [1, 2]. Existing methods, based on times of arrival or time differences of arrival, only exploit the direct paths between the sources and the receivers. In this proof-of-concept paper, we observe that by placing the whole setup inside a room, we can reduce the number of sources required for calibration. Moreover, our technique allows us to compute the absolute position of the microphone array in the room, as opposed to knowing it up to a rigid transformation or reflection. The key observation is that echoes correspond to virtual sources that we get “for free”. This enables endeavors such as calibrating the array using only a single source.