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.
翻译:虽然已提议进行许多利用现有的Lie小组结构的工程,特别是常态扩展卡尔曼过滤器(IEKF),以进行国家估计,但很少有文件涉及建造一个可以将某一系统投入惯性过滤框架的集团结构,在本文中,我们引入了一大批系统,涵盖在实践中遇到的大多数导航飞行器问题。对于这些系统,我们引入了一种新颖的方法,系统地为国家空间提供一个群落结构,包括诸如偏差等身体框架的矢量。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化框架涵盖了国际电算法已经证明成功的所有系统,改进了具有传感器偏差的惯性“不完善”IEKEKF的先进“不完善”系统,并允许处理全球导航卫星系统天线杆臂估计等新颖的例子。