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This research presents a novel method of determining relative bearing andelevation measurements, to a remote signal, that is suitable for implementationon small embedded systems - potentially in a GPS denied environment. This is animportant, currently open, problem in a number of areas, particularly in thefield of swarm robotics, where rapid updates of positional information are ofgreat importance. We achieve our solution by means of a tetrahedral phasedarray of receivers at which we measure the phase difference, or time differenceof arrival, of the signal. We then perform an elegant and novel, albeit simple,series of direct calculations, on this information, in order to derive therelative bearing and elevation to the signal. This solution opens up a numberof applications where rapidly updated and accurate directional awareness in3-space is of importance and where the available processing power is limited byenergy or CPU constraints.

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