Tetrahedra and Relative Directions in Space, Using 2 and 3-Space Simplexes for 3-Space Localization

Abstract

This research presents a novel method of determining relative bearing and elevation measurements, to a remote signal, that is suitable for implementation on small embedded systems - potentially in a GPS denied environment. This is an important, currently open, problem in a number of areas, particularly in the field of swarm robotics, where rapid updates of positional information are of great importance. We achieve our solution by means of a tetrahedral phased array of receivers at which we measure the phase difference, or time difference of arrival, of the signal. We then perform an elegant and novel, albeit simple, series of direct calculations, on this information, in order to derive the relative bearing and elevation to the signal. This solution opens up a number of applications where rapidly updated and accurate directional awareness in 3-space is of importance and where the available processing power is limited by energy or CPU constraints.