Realistic aircraft trajectory models are useful in the design and validation
of air traffic management (ATM) systems. Models of aircraft operated under
instrument flight rules (IFR) require capturing the variability inherent in how
aircraft follow standard flight procedures. The variability in aircraft
behavior varies among flight stages. In this paper, we propose a probabilistic
model that can learn the variability from the procedural data and flight tracks
collected from radar surveillance data. For each segment, a Gaussian mixture
model is used to learn the deviations of aircraft trajectories from their
procedures. Given new procedures, we can generate synthetic trajectories by
sampling a series of deviations from the trained Gaussian distributions and
reconstructing the aircraft trajectory using the deviations and the procedures.
We extend this method to capture pairwise correlations between aircraft and
show how a pairwise model can be used to generate traffic involving an
arbitrary number of aircraft. We demonstrate the proposed models on the arrival
tracks and procedures of the John F. Kennedy International Airport. The
distributional similarity between the original and the synthetic trajectory
dataset was evaluated using the Jensen-Shannon divergence between the empirical
distributions of different variables. We also provide qualitative analyses of
the synthetic trajectories generated from the models