A General Nonlinear Observer Design for Inertial Navigation Systems with Almost Global Stability Guarantees
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866908821077622784 |
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| author | Benahmed, Sifeddine Hamel, Tarek Berkane, Soulaimane |
| author_facet | Benahmed, Sifeddine Hamel, Tarek Berkane, Soulaimane |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_03846 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A General Nonlinear Observer Design for Inertial Navigation Systems with Almost Global Stability Guarantees Benahmed, Sifeddine Hamel, Tarek Berkane, Soulaimane Systems and Control 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. |
| title | A General Nonlinear Observer Design for Inertial Navigation Systems with Almost Global Stability Guarantees |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2410.03846 |