Polynomial Regression on Lie Groups and Application to SE(3)

被引:0
|
作者
Aubray, Johan [1 ]
Nicol, Florence [1 ]
机构
[1] Univ Toulouse, Ecole Natl Aviat Civile, 7, Ave Edouard Belin, F-31400 Toulouse, France
关键词
Lie groups; SE(n); regression; Riemannian manifolds; affine connection; linear connection; air traffic management; KALMAN FILTER;
D O I
10.3390/e26100825
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
In this paper, we address the problem of estimating the position of a mobile such as a drone from noisy position measurements using the framework of Lie groups. To model the motion of a rigid body, the relevant Lie group happens to be the Special Euclidean group SE(n), with n=2 or 3. Our work was carried out using a previously used parametric framework which derived equations for geodesic regression and polynomial regression on Riemannian manifolds. Based on this approach, our goal was to implement this technique in the Lie group SE(3) context. Given a set of noisy points in SE(3) representing measurements on the trajectory of a mobile, one wants to find the geodesic that best fits those points in a Riemannian least squares sense. Finally, applications to simulated data are proposed to illustrate this work. The limitations of such a method and future perspectives are discussed.
引用
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页数:21
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