Quantification of aircraft trajectory prediction uncertainty using polynomial chaos expansions

A novel approach to quantify the uncertainty associated with any aircraft trajectory prediction based on the application of the Polynomial Chaos (PC) theory is presented. The proposed method relies on univariate polynomial descriptions of the uncertainty sources affecting the trajectory prediction process. Those descriptions are used to build the multivariate polynomial expansions that represent the variability of the aircraft state variables along the predicted trajectory. A case study compares the results obtained by a classical Monte Carlo approach with those generated by applying the so-called arbitrary Polynomial Chaos Expansions (aPCE). The results provided herein lead to conclude that this new methodology can be used to accurately quantify trajectory prediction uncertainty with a very low computational effort, enabling the capability of computing the uncertainty of the individual trajectories of a traffic sample of thousands flights within very short time intervals.