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 IEKF framework, namely making the dynamics group affine and the observations invariant. 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.
翻译:虽然为国家估算提出了许多利用现有的Lie小组结构的工程,特别是常态扩展卡尔曼过滤器(IEKF),但很少有文件涉及能够将某一系统投入IEKF框架的集团结构的构建,即使动态组成形和观测成形。在本文中,我们引入了一大批系统,涵盖在实践中遇到的多数涉及导航飞行器的问题。对于这些系统,我们引入了一种新的方法,系统地为国家空间提供一个群结构,包括身体框架的矢量,如偏差。我们用它来获取与线性观察器或过滤器相似的观察者。拟议的统一和多功能框架涵盖了IEKF已证明成功的所有系统,改进了具有传感器偏差的惯性导航“不合格”IEKEKF的最新系统,并允许处理新的例子,如全球导航卫星系统天线杆杆估计。