Comparison of Horizontal Probability Estimation Methodology

-Approximation Model and Kinematical Model-

Abstract

Collision risk models are constructed on the basis of hypotheses. If their bases are frail, the calculated risk is no longer reliable. Hence we should inspect models before its application. We focus on two models developed in EUROCONTROL, the kinematical model and the approximation model. They were induced to calculate the horizontal overlap probability of the vertical collision risk formula of aircraft on crossing tracks. We make investigations into their validity in three ways.

One is a theoretical investigation. As a consequence of this investigation, we suggest that the approximation model is an approximation of the kinematical model and this approximation always provides a smaller estimate of risk than the kinematical model.

Another is a numerical calculation. We investigated the case where the model underestimates the risk significantly. We find that two estimations in two ways are almost the same in the low traffic density situation if we choose a small proximity radius; however, it is not the case in the other situations.

The other is an analysis of Japanese radar data. We determine the distribution of the distance between aircraft at the horizontal closest point of approach to ascertain validity of the approximation model. We cannot conclude that the distribution of the proximity distances follows the uniform distribution, which is the fundamental hypothesis of the approximation model.

As a consequence, we concluded that an approximation model should not been applied in Japanese air traffic situation.