Estimation of Mid-Air Collision Risk in High-Density Airspace Using Hexagonal Spatial Indexing

Civil aviation safety remains a foundational element of the modern air transport system. Each of air transportation services must be delivered in compliance with the minimum required safety levels. Contemporary safety assessment frameworks typically integrate the cumulative impact of hazardous factors on the nominal functioning of the air transport system, with detailed analyses often employing tree-structured models of risk propagation. Among all operational hazards, the risk of mid-air collision is one of the most critical, particularly given the sustained global growth in air traffic demand. Increasing aircraft density within constrained airspace volumes requires new analytical methods capable of supporting both safety assurance and efficient airspace utilization. This paper presents a comparative study of two collision-risk models suitable for airspace safety analysis. The first model explicitly incorporates three-dimensional airspace volume, while the second aggregates risk across vertical and horizontal planes. To enhance computational scalability, a hierarchical hexagonal spatial indexing system is applied for the rapid identification of potentially conflicting aircraft pairs. The resulting hybrid framework provides high-speed and accurate detection of potential conflicts, making it a valuable instrument for the modernization of air traffic management, particularly in increasingly complex environments involving both manned and unmanned aircraft. The proposed methodology is validated using ADS-B observational data from German airspace.