A Robust Method to Determine the Coordinates of a Wave Source for 3-D Position Sensing

This work addresses a method for location of a wave source by observing the wave as it reaches various observation points (receivers), or conversely, this is also a method for location of a receiver at an observation point, by probing with waves generated at various sources. The terms observing and probing imply measurement of time-of-flight (TOF) between a source (transmitter) and a receiver. Practical implications of this work include development and improvement of systems that triangulate the position of a point of interest based on TOF measurements to observation points. Typical applications to benefit from this work include 3-D digitization devices based in ultrasonic, laser, or infrared wave energy. This paper proposes a formulation for location of a wave source (receiver) using a minimum of five receivers (transmitters). It will also be shown that the proposed formulation defines a system that is inherently self-installing and self-calibrating. Also, conditions are developed to geometrically locate the observation points such that a solution to the problem is feasible, and last, a method to define an optimum geometric configuration of the observation points is provided. The case of an ultrasonic 3-D location system mounted on an autonomous vehicle is used as an example.