Effects of Input Data Uncertainties on an Air Traffic Control Difficulty Index

Abstract

Air traffic management (ATM) systems around the world are being modernized to accommodate shifts towards performance- and trajectory-based operations. These shifts will require new indices for safety, efficiency and complexity. The authors have been developing an index for evaluating air traffic control (ATC) difficulty that utilizes the relative positions and velocity vectors of aircraft pairs as input data. Prior to practical application of the index, it is necessary to understand the effects of input data error, i.e. errors in the positions and velocities of a pair of aircraft, on the estimated difficulty value. Two sensitivity analyses were therefore performed for a pair of aircraft cruising at constant speeds on intersecting linear tracks at the same altitude. Sensitivity analysis examines how uncertainty in inputs relates to uncertainty in outputs. Firstly, an analysis of propagation error was carried out. The formula of the propagation error at a certain point was derived based on the assumed input error, and the distribution of propagation error was investigated for all possible situations and compared with the distribution of difficulty values to clarify its characteristics. Secondly, a sensitivity analysis based on variance was carried out that evaluated the effect of each input parameter using a conditional variance value called the Sobol indices. Using a Monte Carlo method, we investigated the effect of each input parameter on the calculated difficulty value for all possible situations of aircraft pairs on intersecting trajectories. As a result, it was found that the parameter that most affects the difficulty value is the intersection angle of the trajectories.