Data-Driven Probabilistic Methodology for Aircraft Conflict Detection Under Wind Uncertainty

Assuming the availability of a reliable aircraft trajectory planner, this article presents a probabilistic methodology to detect conflicts between aircraft in the cruise phase of flight in the presence of wind velocity forecasting uncertainty. This uncertainty is quantified by ensemble weather forecasts, the members of which are regarded as realizations of correlated random processes and used to derive the eastward and northward components of the wind velocity. First, the Karhunen–Loève (KL) expansion is used to obtain a series expansion of the components of the wind velocity in terms of a set of uncorrelated random variables and deterministic coefficients. Then, the uncertainty generated by these uncorrelated random variables in the outputs of the aircraft trajectory planner is quantified using the arbitrary polynomial chaos technique. Finally, the probability density function of the great circle distance between each pair of aircraft is derived from the polynomial expansions using a Gaussian kernel density estimator and used to estimate the probability of conflict. The arbitrary polynomial chaos technique allows the effects of uncertainty in complex nonlinear dynamical systems, such as those underlying aircraft trajectory planners, to be quantified with high computational efficiency, only requiring the existence of a finite number of statistical moments of the random variables of the KL expansion while avoiding any assumptions on their probability distributions. To demonstrate the effectiveness of the proposed conflict detection method, numerical experiments are conducted via an optimal control-based aircraft trajectory planner for a given wind velocity forecast represented by an ensemble prediction system.