Modelling the dispersion of aircraft trajectories using Gaussian processes

This work investigates the application of Gaussian processes to capturing the probability distribution of a set of aircraft trajectories from historical measurement data. To achieve this, all data are assumed to be generated from a probabilistic model that takes the shape of a Gaussian process. The approach to Gaussian process modelling used here is based on a linear expansion of trajectory data into set of basis functions that may be parametrized by a multivariate Gaussian distribution. The parameters are learned through maximum likelihood estimation. The resulting probabilistic model can be used for both modelling the dispersion of trajectories along the common flightpath and for generating new samples that are similar to the historical data. The performance of this approach is evaluated using three trajectory datasets; toy trajectories generated from a Gaussian distribution, sounding rocket trajectories that are generated by a stochastic rocket flight simulator and aircraft trajectories on a given departure path from Dallas Fort Worth airport, as measured by ground-based radar. The results indicate that the maximum deviation between the probabilistic model and test data obtained for the three data sets are respectively 4.9%, 7.6% and 13.1%.