Conference
Geodesic regression on SE(3): Application to estimation of positions of a mobile
| العنوان: | Geodesic regression on SE(3): Application to estimation of positions of a mobile |
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| المؤلفون: | Aubray, Johan, Nicol, Florence, Puechmorel, Stéphane |
| المساهمون: | Ecole Nationale de l'Aviation Civile (ENAC), Université de Toulouse (UT), HTW Berlin, University of Applied Sciences |
| المصدر: | 16th International Conference of the ERCIM WG on Computational and Methodological Statistics (CMStatistics 2023) https://hal.science/hal-04361643 16th International Conference of the ERCIM WG on Computational and Methodological Statistics (CMStatistics 2023), HTW Berlin, University of Applied Sciences, Dec 2023, Berlin (Germany), Germany |
| بيانات النشر: | HAL CCSD |
| سنة النشر: | 2023 |
| المجموعة: | ENAC: HAL (Ecole Nationale de l’Aviation Civile) |
| مصطلحات موضوعية: | Manifold, Se(3), Lie groups and Lie algebras, Riemannian Manifolds, Smoothing, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG] |
| جغرافية الموضوع: | Berlin (Germany), Germany |
| الوصف: | International audience ; We address the problem of estimating the position of a mobile such as a drone from noisy position measurements. To model the motion of a rigid body, rather than considering trajectories in the state space as is usually done in functional data analysis, the framework of differential geometry is used. More precisely, the trajectory of the mobile is modelled as a Lie group-valued curve. The relevant Lie group for poses of a rigid object happens to be the Special Euclidean group SE(n), with n = 2 or 3. This work takes place in a parametric framework which extends linear regression in an Euclidean space to geodesic regression in a Riemannian manifold. This method was later on extended to higher order polynomials on Riemannian manifolds, and explicitly written in SO(3). Based on this approach, our goal is to implement this technique to 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. A more general mathematical formulation is established by using differential forms. Finally, applications to simulated data are proposed to illustrate this work. The limitations of such a method and future perspectives are discussed. |
| نوع الوثيقة: | conference object |
| اللغة: | English |
| Relation: | hal-04361643; https://hal.science/hal-04361643 |
| الاتاحة: | https://hal.science/hal-04361643 |
| رقم الانضمام: | edsbas.639AFB1C |
| قاعدة البيانات: | BASE |
| الوصف غير متاح. |