Application of reachability analysis for stochastic hybrid systems to aircraft conflict prediction

In this paper, the problem of aircraft conflict prediction is formulated as a reachability analysis problem for a stochastic hybrid system. A switching diffusion model is introduced to predict the future positions of an aircraft following a given flight plan. The weak approximation of the switching diffusion through a Markov chain allows us to develop a numerical algorithm for computing an estimate of the probability that the aircraft enters an unsafe region of the airspace or come too close to another aircraft. Simulation results are reported to show the efficacy of the approach.