A1515
Title: Regression on a Lie group: Model and statistical properties
Authors: Florence Nicol - ENAC (France)
Johan Aubray - ENAC (France) [presenting]
Anne Francoise Yao - Universite Clermont Auvergne/LMBP (France)
Abstract: The focus is on the problem of geodesic regression in a Lie group, with the aim of estimating the position of a mobile from noise-measured positions. In the context of air traffic management (ATM), estimating the position of aircraft or a drone can be a complex task, as the data cannot be processed with the usual statistical tools, as in the case of data belonging to a Euclidean space. This regression problem has been previously tackled by modeling the evolution of a mobile (position and orientation) in the Special Euclidean group SE(3). The geodesic that best fits the measurements of a mobile's trajectory in the Riemannian least-squares sense was calculated using the Levi-Civita connection. We study the statistical properties of intrinsic estimators of geodesic regression.
