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Article Dans Une Revue IEEE Transactions on Automatic Control Année : 2023

The Geometry of Navigation Problems

Axel Barrau
Silvere Bonnabel

Résumé

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.

Dates et versions

hal-04387351 , version 1 (11-01-2024)

Identifiants

Citer

Axel Barrau, Silvere Bonnabel. The Geometry of Navigation Problems. IEEE Transactions on Automatic Control, 2023, 68 (2), pp.689-704. ⟨10.1109/TAC.2022.3144328⟩. ⟨hal-04387351⟩
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