The article presents a bundle framework for nonlinear observer design on a manifold with a a Lie group action. The group action on the manifold decomposes the manifold to a quotient structure and an orbit space, and the problem of observer design for the entire system gets decomposed to a design over the orbit (the group space) and a design over the quotient space. The emphasis throughout the article is on presenting an overarching geometric structure; the special case when the group action is free is given special emphasis. Gradient based observer design on a Lie group is given explicit attention. The concepts developed are illustrated by applying them on well known examples, which include the action of $ {\mathop{\mathbb{SO}(3)}} $ on $ \mathbb{R}^3 \setminus \{0\} $ and the simultaneous localisation and mapping (SLAM) problem.

中文翻译：

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具有对称性的光滑流形上观测器设计的束框架

本文提出了一个用于在具有李群作用的流形上进行非线性观测器设计的捆绑框架。流形上的群作用将流形分解为商结构和轨道空间，整个系统的观测器设计问题分解为轨道（群空间）上的设计和商空间上的设计。整篇文章的重点是呈现总体几何结构；特别强调集体行动是自由的特殊情况。基于梯度的李群观测器设计得到了明确的关注。开发的概念通过将它们应用于众所周知的例子来说明，其中包括 $ {\mathop{\mathbb{SO}(3)}} $ 对 $ \mathbb{R}^3 \setminus \{0\} 的作用$ 和同时定位和映射 (SLAM) 问题。