The Geometry of Navigation Problems

• 成果类型: Article
• 署名作者: Barrau, Axel; Bonnabel, Silvere
• 署名单位: Safran S.A.; Universite PSL; MINES ParisTech
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3144328
• 发表日期: 2023
• 页码: 689-704
• 关键词: Observers; Simultaneous localization and mapping; Kalman filters; Vehicle dynamics; Inertial navigation; CONVERGENCE; Manipulators; Aircraft navigation; Autonomous Vehicles; geometry; nonlinear filters; observers; State estimation

摘要

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 article, 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.