Aircraft conflict prediction and resolution using Brownian motion

The probability of conflict between two aircraft is calculated by modeling aircraft motion as a deterministic trajectory plus a (scaled) Brownian motion perturbation. In this formalism, the probability of conflict becomes the probability that a Brownian motion escapes from a time-varying safe region. Approximate expressions for the probability of conflict are obtained in closed form for both the finite and infinite horizon cases. Based on these expressions, an autonomous algorithm is proposed for decentralized conflict resolution. The algorithm generalizes potential field ideas to path planning in a highly dynamic environment.