论文标题
导航问题的几何形状
The Geometry of Navigation Problems
论文作者
论文摘要
尽管已经提出了许多利用现有谎言组结构的作品进行状态估计，尤其是不变的扩展卡尔曼过滤器（IEKF），但很少有论文解决了允许将给定系统施放到不变性过滤框架的组结构的构建。在本文中，我们介绍了一大批系统，其中包括大多数问题，涉及实践中遇到的导航车辆。对于那些系统，我们引入了一种新颖的方法，该方法系统地为状态空间提供了一个组结构，包括诸如偏见之类的身体框架向量。我们使用它来得出具有类似于线性观察者或过滤器的属性的观察者。拟议的统一和多功能框架涵盖了IEKF已被证明成功的所有系统，改善了最先进的“不完美” IEKF，以实现具有传感器偏见的惯性导航，并允许解决新颖的示例，例如GNSS天线杆杆组的估计。
While many works exploiting an existing Lie group structure have been proposed for state estimation, in particular the Invariant Extended Kalman Filter (IEKF), few papers address the construction of a group structure that allows casting a given system into the framework of invariant filtering. In this paper we introduce a large class of systems encompassing most problems involving a navigating vehicle encountered in practice. For those systems we introduce a novel methodology that systematically provides a group structure for the state space, including vectors of the body frame such as biases. We use it to derive observers having properties akin to those of linear observers or filters. The proposed unifying and versatile framework encompasses all systems where IEKF has proved successful, improves state-of-the art "imperfect" IEKF for inertial navigation with sensor biases, and allows addressing novel examples, like GNSS antenna lever arm estimation.
