Probabilistic safety analysis in three dimensional aircraft flight

In this paper we study the problem of evaluating if the flight plan assigned to an aircraft is "safe", i.e., if it guarantees that the aircraft will neither enter any forbidden region of the airspace nor come closer than a minimum prescribed distance to another aircraft. We address the general case when the flight plan possibly involves altitude changes. The aircraft future position during the flight time is predicted based on a stochastic model that incorporates the information on the aircraft flight plan, and takes into account the presence of wind as the main source of uncertainty on the aircraft actual motion. Based on the aircraft predicted motion, we estimate the probability that an unsafe situation will occur during the aircraft flight by a stochastic approximation method. Some examples are presented to illustrate the proposed methodology for safety analysis. As expected, the examples show that the wind spatial correlation needs to be taken into account when evaluating the safety of aircraft encounters.