Air Traffic Complexity Map Based on Linear Dynamical Systems

This paper presents a new air traffic complexity metric based on linear dynamical systems, of which the goal is to quantify the intrinsic complexity of a set of aircraft trajectories. Previous works have demonstrated that the structure and organization of air traffic are essential factors in the perception of the complexity of an air traffic situation. Usually, they were not able to explicitly address trajectory pattern organization. The new metric, by identifying the organization properties of trajectories in a traffic pattern, captures some of the key factors involved in ATC complexity. The key idea of this work is to find a linear dynamical system which fits a vector field as closely as possible to the observations given by the aircraft positions and speeds. This approach produces an aggregate complexity metric that enables one to identify high (low) complexity regions of the airspace and compare their relative complexity. The metric is very appropriate to compare different traffic situations for any scale (sector or country) by associating a complexity index to each trajectory sample in the airspace. For instance, to compute the complexity for a sector, one must just sum-up the complexity for trajectory samples intersecting such a sector. This computation can also be extended in the time dimension in order to estimate the average complexity in a given airspace for a period of time.