Modeling 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 modeling used here is based on a linear expansion of trajectory data into a 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 modeling the dispersion of trajectories along the common flight path and for generating new samples that are similar to the historical data. The performance of this approach is evaluated using three trajectory data sets: 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 deviations between the probabilistic model and the test data obtained for the three data sets are, respectively, 4.9, 7.6, and 13.1%.