Aircraft conflict prediction in the presence of a spatially correlated wind field

In this paper, the problem of automated aircraft conflict prediction is studied for two-aircraft midair encounters. A model is introduced to predict the aircraft positions along some look-ahead time horizon, during which each aircraft is trying to follow a prescribed flight plan despite the presence of additive wind perturbations to its velocity. A spatial correlation structure is assumed for the wind perturbations such that the closer the two aircraft, the stronger the correlation between the perturbations to their velocities. Using this model, a method is introduced to evaluate the criticality of the encounter situation by estimating the probability of conflict, namely, the probability that the two aircraft come closer than a minimum allowed distance at some time instant during the look-ahead time horizon. The proposed method is based on the introduction of a Markov chain approximation of the stochastic processes modeling the aircraft motions. Several generalizations of the proposed approach are also discussed.