Trajectory Clustering, Modelling, and Selection with the Focus on   Airspace Protection
  Take-off and landing are the periods of a flight where aircraft are most vulnerable to a ground based rocket attack by terrorists. While aircraft approach and depart from airports on pre-defined flight paths, there is a degree of uncertainty in the trajectory of each individual aircraft. Capturing and characterizing these deviations is important for accurate strategic planning for the defence of airports against terrorist attack. A methodology is demonstrated whereby approach and departure trajectories to a given airport are characterized statistically from historical data. It uses a two-step process of first clustering to extract the common trend, and then modelling uncertainty using Gaussian Processes (GPs). Furthermore it is shown that this approach can be used to either select probabilistic regions of airspace where trajectories are likely and - if required - can automatically generate a set of representative trajectories, or select key trajectories that are both likely and critically vulnerable. An evaluation of the methodology is demonstrated on an example data-set collected by the ground radar at an airport. The evaluation indicates that 99.8% of the calculated footprint underestimates less than 5% when replacing the original trajectory data with a set of representative trajectories. 
Willem J. Eerland and Simon Box
stat.AP