3D position sensing using the difference in the time-of-flights from a wave source to various receivers

3D positioning systems typically use actual time-of-flights for triangulation to determine the position of a wave source. Problems, such as inherent time delays and synchronization of the receiver/transmitter pairs are prevalent in these systems. This paper presents a novel formulation for the estimation of the coordinates of an ultrasonic wave source based on the differences in the time-of-flights (TOFs) to various receivers fixed in an inertial frame of reference. A thorough analysis of the formulation and a 1D prototype are presented. Typical applications benefiting from this technology are position sensing systems that may be used in robotics, AGV guidance and navigation, virtual reality, and vibrations