Abstract
This article presents a survey of some metrics that can be used on geometric curve spaces which can be defined using samples points, known as landmarks, or by taking a space of immersions or embeddings and quotienting out by a group of diffeomorphisms in order to get rid of the influence of the parametrization. Finding the right metric for a class of problems is an active topic of research, with a special emphasis on applications related to computer vision or shape recognition. Similar problems arise in the field of air traffic management where the analysis of aircraft trajectories is one of the most basic issues. Despite its importance, only a few studies have been conducted on the subject, mainly due to the lack of suitable frameworks. The use of some of the shape spaces for representing aircraft flight paths, along with an example of trajectory classification will be given in the second part of the article.
Highlights
Based on recent studies [4], traffic in Europe is expected to grow on an average yearly rate of 2.6%, yielding a net increase of 2 million flights per year at the 2020 horizon
Finding metrics in geometric spaces of curves is an active area of research, mainly with applications to shape recognition and computer vision in mind
Within the frame of air traffic management, a similar problem arises, that is the analysis of aircraft trajectories
Summary
Based on recent studies [4], traffic in Europe is expected to grow on an average yearly rate of 2.6%, yielding a net increase of 2 million flights per year at the 2020 horizon. One of the main changes that the air traffic management (ATM) system will undergo is a switch from airspace based to trajectory based operations with a delegation of the separation task to the crews. Within this framework, trajectories become the basic object of ATM, changing the way air traffic controllers will be working. The FMS will broadcast its new flight path, the pertinence of the information becomes lower In such a case, an efficient trajectory predictor will help ATC controllers or even automated systems to anticipate conflicts with a sufficient level of confidence. Using spaces of curves to get a sound prediction is a promising axis of research, that is expected to be investigated in a near future
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
