Toward 4-D Trajectory Management in Air Traffic Control: A Study Based on Monte Carlo Simulation and Reachability Analysis

One of the fundamental elements for the next generation in air traffic management systems, as envisioned by the Single European Sky Air Traffic Management Research Project and the Next Generation Air Transportation System Project, is 4-D trajectory management. In the contract-based air transportation system project, a novel concept of operations based on target windows (TWs) is developed. TWs are 4-D constraints imposed at different parts of the flight to increase predictability, efficiency, and safety. In this paper, we use Monte Carlo simulations and reachability analysis to evaluate some of these features of the TW concept. We start by using Monte Carlo methods to estimate the TW hitting probability and the probability of conflict. We then outline methods and computational tools based on reachability theory and highlight how they can be adapted to characterize the maneuvering freedom afforded by TWs. We also demonstrate how the reachability calculations can be used to guide conflict resolution in the presence of TW constraints. Our results indicate that TWs provide a promising balance between predictability of air traffic and maneuverability.