The safety of flights, and, in particular, separation assurance, is one of the main tasks of air traffic control (ATC). Conflict resolution refers to the process used by ATCs to prevent loss of separation. Conflict resolution involves issuing instructions to aircraft to avoid loss of safe separation between them and, at the same time, direct them to their destinations. Conflict resolution requires decision making in the face of the considerable levels of uncertainty inherent in the motion of aircraft. In this paper, a framework for conflict resolution that allows one to take into account such levels of uncertainty using a stochastic simulator is presented. The conflict resolution task is posed as the problem of optimizing an expected value criterion. It is then shown how the cost criterion can be selected to ensure an upper bound on the probability of conflict for the optimal maneuver. Optimization of the expected value resolution criterion is carried out through an iterative procedure based on Markov chain Monte Carlo. Simulation examples inspired by current ATC practice in terminal maneuvering areas and approach sectors illustrate the proposed conflict resolution strategy
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