Air traffic complexity map based on non linear dynamical systems

This paper presents a new air traffic complexity metric based on non-linear dynamical systems. The goal of this metric is to identify any trajectory organisation in the traffic pattern in order to quantify the associated control difficulty. Many others works have proposed metrics in the past, but they usually identify one feature of the complexity and were not able to address any pattern organization. A full vector field can be summarized by the equation of a dynamical system which describe and control the evolution of a given state vector (~X = [x; y; z]T ). The key idea of our work is to find a dynamical system which modelizes a vector field as close as possible to the observations given by the aircraft positions (and speeds). Two approaches are then presented. The first one is based on a linear dynamical system and produces an aggregate complexity metric. The second one, which is the main part of this paper, uses a non-linear dynamical system modeling which fits the observations without error. Such a modeling enables to identify high (low) complexity areas on a map and addresses trajectory segments instead of vector field which is more relevant for the air traffic management application (the air controller sees speed vectors on his screen but works on trajectory segments in his mind in order to produce resolution scenario (past and future). A collocation technique has been used to speed up the computation of the associated complexity metric in order to address large areas with many aircraft. Such a metric is very adapted to compare different traffic situations for any scale (sector or country).