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

TL;DR

This paper introduces a novel complexity indicator for 4D flight trajectories based on conflict probability, providing a quantitative measure that reflects the perceived complexity by air traffic controllers.

Contribution

It develops an analytical conflict probability model for 4D trajectories and constructs a complexity indicator that captures trajectory complexity.

Findings

The indicator accurately reflects perceived trajectory complexity.

Analytical conflict probability is derived for piecewise linear segments.

Numerical examples validate the effectiveness of the complexity measure.

Abstract

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.