AIR TRAFFIC COMPLEXITY THROUGH LOCAL COVARIANCE IN THE CONTEXT OF LARGE AREAS OF OPERATIONS

Georges Mykoniatis (1) , D Dohy

1 ENAC - Ecole Nationale de l'Aviation Civile

The notion of air traffic complexity has many facets and can be related to workload, which is a perception of a given situation by a human controller or to disorder, which is intrinsic. The present work falls within the second category and aims at computing the level of organization in a neighborhood of a point on the earth. It is based on a two steps approach: in the first one, a smooth time-dependent vector field is inferred from the sampled traffic using local linear models. Since positions are measured on a sphere, some special care must be taken as it is not a vector space. Using the Levi-Civita connection and its associated parallel transport, a local linear model can be defined in the tangent space at any point. The time evolution is captured through the kernel function that take the form of a product with one term being time dependent. In a second phase, the underlying dynamical is characterized at each point using a symmetric positive definite matrix. Thanks to the Riemannian manifold structure of the set of such matrices, a complexity indicator is then defined.

Mots clés: Air traffic complexity; spatial data; manifold valued images; covariance function estimation; nonparametric estimation; simulation

Domaines: Optimisation et contrôle [math.OC]

Georges Mykoniatis, D Dohy. AIR TRAFFIC COMPLEXITY THROUGH LOCAL COVARIANCE IN THE CONTEXT OF LARGE AREAS OF OPERATIONS. 9th International Conference on Experiments/Process/System Modeling/Simulation/Optimization, Jul 2021, Athens, Greece. ⟨hal-03313081⟩