A bilinear approach to the position self-calibration of multiple sensors

This paper presents a novel algorithm for the automatic 3D localization of a set of sensors in an unknown environment. Given the measures of a set of time of arrival delays at each sensor, the approach simultaneously estimates the 3D position of the sensors and the sources that have generated the event. Such inference is obtained with no assumption about the sensor localization; the only assumption made is that the emission time of the sources must be known in order to evaluate the time of flight for each event. Moreover, we propose a further method that deals with the likely case of missing data in the measurements. This occurs when sensors are far apart or behind natural barriers that avoids the registration of the given event. Simulated experiments show the validity of the approach for different setups of sensors and number of events.