Mathematical Models for Air Traffic Conflict and Collision Probability Estimation

Increasing traffic demands and technological developments provide novel design opportunities for future air traffic management (ATM). In order to evaluate current air traffic operations and future designs, over the past decades, several mathematical models have been proposed for air traffic conflict and collision probability estimation. However, few comparative evaluations of these models with respect to their mathematical core exist. Such comparative evaluations are particularly difficult since different authors employ different model definitions, notations, and assumptions, even when using the same modeling techniques. The aim of this paper is: 1) to present the mathematical core of the existing approaches for air traffic conflict and collision probability estimation using the same body of notations and definitions; 2) to outline the advances in estimating the probability of air traffic conflict and collision using a unified mathematical framework; 3) to various air traffic applications and their use of directed mathematical models for air traffic conflict and collision probability estimation; and 4) to provide insight into the capabilities and restrictions of the mathematical models in the evaluation of future ATM designs.