A closed form solution to the microphone position self-calibration problem

This paper presents a novel algorithm for the automatic 3D localization of a set of microphones in an unknown environment. Given the times of arrival at each microphone of a set of sound events, the approach simultaneously estimates the 3D positions of the sensors and the sources that have generated the events. The only assumption made is that the emission time of the sound events must be known in order to measure the time of flight for each event. A closed form solution is also proposed whenever a sound event coincides with a microphone position. Simulated and real experiments show the validity of the approach for different setups of sensors and number of events.