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

This paper presents a novel formulation for the estimation of the coordinat es of a wave source based on the differences in the time-of-flights from a single transmitter to various receivers fixed in three-dimensional (3-D) sp ace, The formulation is closed form,linear, and estimates the speed of soun d at every ranging operation. This leads to a robust system that is insensi tive to changes in the environmental conditions. Typical applications that will benefit from this technology are 3-D position sensing systems that may be used in robotics, navigation of autonomously guided vehicles, tracking of objects for virtual reality cells, and vibration analysis.