Conflict Detection Algorithm Based on Overall Conflict Probability and Three Dimensional Brownian Motion

With the increasing of the air traffic flow, conflict detection plays an increasingly important role in air traffic management system. A probabilistic conflict detection algorithm is proposed. Overall conflict probability in look-ahead time is calculated. The aircraft predicted trajectory is expressed as deterministic trajectory plus a Brownian motion perturbation. For the case of constant aircraft speed, conflict probability is expressed as the probability of an aircraft with Brownian motion perturbation entering a time-varying moving protection zone, the probability is approximated using coordinate transformation and Bachelier-Levy theorem. For the case of aircraft with non-constant speed, predicted trajectory can be approximated by a large enough number of constant speed segments. Conflict probability of each segment is calculated and the overall conflict probability bounds in look-ahead time are given. Compared with Monte Carlo simulations, the proposed algorithm is accurate for conflict detection and it is useful to detect and avoid conflicts in air traffic management system.