COPTRA » Probabilistic Trajectories

Probabilistic Trajectories



  • Quantify uncertainty in the prediction of mechanical models through the exploration of applied mathematics (polynomial chaos expansion) and statistics (Gaussian process emulation)
  • Evaluation of the applicability of those identified techniques to the quantification of aircraft trajectory predictions
  • Description of a procedure for trajectory uncertainty modelling based on the most promising identified techniques in support of demand & capacity DSTs.
Description of work

To achieve the stated objectives of this work package, two tasks will be performed:

P02.01 – Establishing a basis for the work. The research and operational context for the work needs to be clarified. A baseline of Trajectory Prediction needs to be established and the specific improvements coming from Trajectory Based Operations should be identified. Based on a deterministic formulation of the aircraft motion problem, it is essential to identify and characterize the uncertainty sources affecting the prediction process. According to availability of data source, data-driven error estimation will be studied by comparing the last filed plan and actual flight trajectories. The historical 4D trajectory data set of EUROCONTROL (i.e., ALLFT+, SO6, EXP2) might provide required details on the estimation of such uncertainties. Based on that, different techniques from applied mathematics and statistics will be studied in order to evaluate their suitability for trajectory prediction uncertainty quantification.

P02.02 – Quantify trajectory prediction uncertainty. Upon the results from P02.01, a framework for quantifying the trajectory prediction uncertainty will be proposed. Such framework will allow associating uncertainty boundaries around the nominal (deterministic) values and the future projections of the aircraft state variables. The uncertainty around the state values of the aircraft highly depends on the external disturbances such as weather uncertainty, while the uncertainty in the future trajectory prediction largely depends on intent-based uncertainties. To reflect the intent uncertainties, stochastic intent sampling will be utilized in addition to the parametric uncertainty quantification. The trajectory predictions generated according to the proposed framework will be compared with real traffic samples in order to evaluate comparison. The traffic sample will be accurately represented by a trajectory prediction whereas the state variables are contained within the established uncertainty boundaries at each reporting time.


Social media & sharing icons powered by UltimatelySocial