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arXiv · 2410.03846

A General Nonlinear Observer Design for Inertial Navigation Systems with Almost Global Stability Guarantees

Sifeddine Benahmed·Tarek Hamel·Soulaimane Berkane
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Abstract

This paper studies nonlinear observer design for rigid-body extended pose estimation using inertial measurements and generic exteroceptive sensing. The estimation problem is formulated as a cascade architecture that separates translational dynamics from rotational kinematics while preserving the geometric constraint of attitude evolution on $SO(3)$. By embedding the inertial navigation model into a Linear Time-Varying (LTV) representation, we construct an observer composed of a Kalman-Bucy-type estimator for translational states and an auxiliary unconstrained attitude variable, coupled with a nonlinear geometric reconstruction filter evolving on $SO(3)$. The cascade interconnection is analyzed within a nonlinear systems framework. We prove that uniform observability of the LTV subsystem guarantees almost global asymptotic stability of the overall nonlinear observer. For a benchmark GPS landmark aided configuration, explicit sufficient conditions on admissible trajectories are derived to ensure uniform observability. Simulation results illustrate the effectiveness of the proposed estimation framework.

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Sifeddine Benahmed, Tarek Hamel, Soulaimane Berkane. 2024-10-04. A General Nonlinear Observer Design for Inertial Navigation Systems with Almost Global Stability Guarantees. https://arxiv.org/abs/2410.03846

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