A two-stage stochastic optimization model for air traffic conflict resolution under wind uncertainty

This paper considers the air traffic conflict resolution problem in the context of wind uncertainty. Aircraft are assigned changes in airspeed to prevent conflict. The goal is to determine the optimal maneuver to balance deviation costs (e.g., fuel costs) and the probability of conflict. A two-stage recourse model is developed, in which new airspeeds are assigned in the first stage, based on expected costs due to possible corrective actions in the second stage. The second-stage considers the expected costs for any last-minute maneuvers to compensate wind modeling errors. The resulting model is solved in real-time via numerical methods, providing optimal airspeed values for the resolution of a conflict.

Introduction

There has been significant research in the fields of air traffic conflict detection and conflict resolution. A summary of results in both research areas is available in [1]. One key factor in conflict detection and resolution is the uncertainty in present and future estimations of the velocity and position vectors of aircraft. These uncertainties may be due to sensor noise (e.g., error in radar systems) or due to unpredictable disturbances such as wind. Many conflict detection algorithms account for this uncertainty [2]–[4]. On the other hand, only limited research has been done on stochastic air traffic conflict resolution [5]–[7]. Given the limited literature on conflict resolution under uncertainty, some studies concerned with developing probabilistic conflict detection models conclude by stating that there is a need to better understand and utilize conflict probability estimations in conflict resolution algorithms [8]. Hence, there is a clear need for fully developed and more complete probability based methods for conflict resolution.