Equivalence of Left- and Right-Invariant Extended Kalman Filters on Matrix Lie Groups
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915318201319424 |
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| author | Maurer, Finn G. Basso, Erlend A. Schmidt-Didlaukies, Henrik M. Bryne, Torleiv H. |
| author_facet | Maurer, Finn G. Basso, Erlend A. Schmidt-Didlaukies, Henrik M. Bryne, Torleiv H. |
| contents | This paper derives the extended Kalman filter (EKF) for continuous-time systems on matrix Lie groups observed through discrete-time measurements. By modeling the system noise on the Lie algebra and adopting a Stratonovich interpretation for the stochastic differential equation (SDE), we ensure that solutions remain on the manifold. The derivation of the filter follows classical EKF principles, naturally integrating a necessary full-order covariance reset post-measurement update. A key contribution is proving that this full-order covariance reset guarantees that the Lie-group-valued state estimate is invariant to whether a left- or right-invariant error definition is used in the EKF. Monte Carlo simulations of the aided inertial navigation problem validate the invariance property and confirm its absence when employing reduced-order covariance resets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_01514 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Equivalence of Left- and Right-Invariant Extended Kalman Filters on Matrix Lie Groups Maurer, Finn G. Basso, Erlend A. Schmidt-Didlaukies, Henrik M. Bryne, Torleiv H. Systems and Control This paper derives the extended Kalman filter (EKF) for continuous-time systems on matrix Lie groups observed through discrete-time measurements. By modeling the system noise on the Lie algebra and adopting a Stratonovich interpretation for the stochastic differential equation (SDE), we ensure that solutions remain on the manifold. The derivation of the filter follows classical EKF principles, naturally integrating a necessary full-order covariance reset post-measurement update. A key contribution is proving that this full-order covariance reset guarantees that the Lie-group-valued state estimate is invariant to whether a left- or right-invariant error definition is used in the EKF. Monte Carlo simulations of the aided inertial navigation problem validate the invariance property and confirm its absence when employing reduced-order covariance resets. |
| title | Equivalence of Left- and Right-Invariant Extended Kalman Filters on Matrix Lie Groups |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2506.01514 |