Probabilistic multi-aircraft conflict detection and resolution considering wind forecast uncertainty

A probabilistic method for aircraft conflict detection and resolution considering the effects of wind forecast uncertainty is presented in this paper. The wind components are modeled as random variables, described by a joint probability density function. The probabilistic conflict detection problem is tackled using the Probabilistic Transformation Method. Two conflict indicators are used to characterize a conflict between a pair of aircraft: the distance of closest approach (which is uncertain) and the probability of conflict. The probabilistic conflict resolution consists in modifying the aircraft trajectories so that the probability of conflict between any pair of aircraft be less than a predefined safety threshold; this problem is formulated as a nonlinear programming problem subject to constraints, where the optimality criterion is the minimization of the deviation of the aircraft resolution trajectories from their nominal trajectories. The case of multiple en-route aircraft flying with constant airspeed and flight level is considered, where they follow approaching multi-segment trajectories and are affected by the same uncertain wind. The wind components are obtained from Ensemble Weather Forecasts. Numerical results are presented for a particular application where the wind components follow four-parameter beta distributions. The cost of the resolution process is analyzed, considering both cooperative and non-cooperative scenarios.