Algorithms for Uncertainty Analysis of an Air Traffic Management System

Abstract

In this paper, we develop algorithms to analyze an uncertain air traffic management (ATM) system that is based on Menon et al.’s pioneer work in modeling the national airspace system (NAS) using an Eulerian framework. 1 In that work, the entire U.S. airspace is divided into many sub-elements. Prediction of air traffic through each element, which is described by the dynamic evolution of aircraft count, is modeled as a deterministic linear system. However, it is commonly accepted that air traffic systems contain significant uncertainties. 2,3 There is an emerging need from NASA of evaluating the current ATM system performance in the presence of uncertainties. The statistic properties of uncertainties due to weather and delay, etc., are typically difficult to be quantified in a detailed and meaningful way. 4,5 In this work, we explore an alternative way that is to analyze and simulate the worst-case system performance given the measurements or predictions of outer bounds or confidential bounds on parameters and inputs in the Eulerian air traffic flow model. We develop an algorithm to compute the tightest bounds on the states that predict the air traffic flow using interval analysis. We also analyze sensitivity of the ATM systems with respect to their parameter and input uncertainties. The proposed algorithm reduces the exponential computational time using the brutal force algorithms to a polynomial computational time. Thus, our algorithm could be efficiently applied t o the large-scale air traffic systems. Simulation shows the potential of application of the proposed algorithm to the current ATM systems.