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.
机构:
Univ Torino, Dipartimento Matemat G Peano, Via Carlo Alberto 10, I-10123 Turin, ItalyUniv Torino, Dipartimento Matemat G Peano, Via Carlo Alberto 10, I-10123 Turin, Italy
Vezzoni, Luigi
Yang, Bo
论文数: 0引用数: 0
h-index: 0
机构:
Xiamen Univ, Sch Math Sci, Xiamen 361005, Fujian, Peoples R ChinaUniv Torino, Dipartimento Matemat G Peano, Via Carlo Alberto 10, I-10123 Turin, Italy
Yang, Bo
Zheng, Fangyang
论文数: 0引用数: 0
h-index: 0
机构:
Ohio State Univ, Dept Math, 231 West 18th Ave, Columbus, OH 43210 USAUniv Torino, Dipartimento Matemat G Peano, Via Carlo Alberto 10, I-10123 Turin, Italy