Conformal Geometric Algebraic Description of Flight Collision Detection Algorithm Based on Cylinder Protection Zone

In order to provide sufficient reaction time for air traffic controllers and pilots, a Flight Conflict Detection Algorithm (FCDA) based on Cylindrical Protection Zone (CPZ) in the Conformal Geometric Algebra (CGA) is proposed. Initially, the CGA description of the CPZ is represented by using the CGA forms of the central circle and central axis segments of the cylinder. Then based on the inner and outer product and geometric product operations of CGA, the positional relationship of the two CPZs is judged to determine whether a flight conflict occurs or not. Subsequently, we compared the performance of flight conflict detection methods based on rectangular protection zones, spherical protection zones, and cylindrical protection zones through experiments in CGA and Euclidean space, respectively, the experimental results show that in CGA, the proposed method has a faster speed than the flight conflict method based on cuboids, and is basically equivalent to the method based on spherical protection zones. Significantly, all CGA-based methodologies demonstrated superior speed over their Euclidean space counterparts. Considering the propensity of rectangular and spherical zones to elicit false alarms due to their expansive coverage of airspace, the CGA-CPZ-FCDA method emerges as the superior choice.