Conflict Probability Estimations Based on Geometrical and Bayesian Approaches

In this paper, we present two approaches to calculate the probability of conflict between two aircrafts in the airspace. The problem is concerned with a more general problem, that is minimizing the delay caused by airspace congestion. The long-term objective of this work is to reduce the number of potential en-route conflicts through a better assignment of flight levels (flight-level assignment problem). For this, we first need to have a reliable method for conflict probability calculation taking into account the uncertainties. Hence, we focus here on the probability conflict calculation problem and provide two approaches. In the first one, called geometrical approach, we study the distribution of minimum distance between two aircrafts and then calculate the conflict probability as the cumulative probability with respect to this distribution. The second approach is based on Bayesian network principle using Gibbs sampling.