Air traffic complexity and the interacting particle system method: An integrated approach for collision risk estimation

In this paper, we explore the possibility of using air traffic complexity metrics to accelerate the Interacting Particle System (IPS) method for collision risk estimation. Collision risk estimation is an essential task to assess the performance and impact of, e.g., possible modifications of the current air traffic management system or new operational concepts. The standard Monte Carlo approach to probability estimation requires a number of simulations that scales as the inverse of the probability to be estimated. This makes it impracticable for estimating the probability of a rare event such as a collision, and calls for ad-hoc solutions. In the IPS method, the collision risk is estimated as the product of the conditional probabilities of an increasing sequence of conditionally not-so-rare events, where aircraft get at progressively smaller distances one from the other. Additional computational saving can be obtained by adopting importance sampling techniques where initial aircraft configurations that are more prone to lead to a collision are favored. The idea that we pursue in this paper is to select those configurations by using some complexity metric. In particular, we propose to combine IPS with a probabilistic complexity metric that explicitly accounts for the uncertainty affecting the aircraft motion. Preliminary results obtained by applying this integrated approach to a free flight scenario are presented in the paper.