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A Complexity Indicator for 4D Flight Trajectories Based on Conflict Probability

In this paper, a complexity indicator for 4D flight trajectories is developed based on conflict probability. A 4D trajectory is modeled as piecewise linear segments connected by waypoints. The position of each aircraft is modeled as a 2D Gaussian random variable and an approximation of the conflict probability between two aircraft is deduced analytically over each segment. Based on such conflict probability, a complexity indicator is constructed for the whole trajectory. Numerical examples show that the proposed complexity indicator is able to reflect the complexity of 4D trajectories perceived by air traffic controllers.