Aircraft Proximity: a Synthesis of Apollonius, X-track, and Well Clear Volume Paradigms

The introduction of Unmanned Aircraft Systems (UAS) operating aerial vehicles in non-segregated airspace has sparked renewed interest into the problem of how to specify a Well-Clear Volume (WCV) for aircraft proximity. A pertinent example is the Self-Separation Volume (SSV) being developed by NASA for use in UAS Detect and Avoid (DAA) systems. To date, the generation and validation of candidate WCVs has been reliant on exhaustive simulation. Complementary research has been directed at the formalization of the Apollonius Circle paradigm in characterizing proximity for two aircraft. Recent research by Westcott, Fulton and Smith has cast the crossing-track problem in a Compromise Decision Support paradigm. In this paper the three approaches are synthesized into a single cohesive geometric model that is then used as an engineering validation tool to test the NASA SSV paradigm (a specific instance of a Well-Clear Volume). The geometric model for proximate operations is based on a Feasible Design Space that partitions into well identified geometric regions delineated by the Line of Sight (LOS) Circle and the Apollonius Circle. The LOS Circle provides insight as to the Geometric Dilution of Precision required in error analysis and also facilitates determination of the behavior of the distance at closest approach vector. The Apollonius Circle identifies, for a constant speed ratio, the locus of all possible collision points within the 2D conflict plane. The model developed in this paper facilitates a more robust geometric construction of the SSV with transparent testing and satisfaction of the operational requirements thus providing a consolidated benchmark reference for further engineering construction of WCVs.