Nonexistence of finite-dimensional estimation algebras on closed smooth manifolds
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912069158174720 |
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| author | Kang, Jiayi Salmon, Andrew Yau, Stephen Shing-Toung |
| author_facet | Kang, Jiayi Salmon, Andrew Yau, Stephen Shing-Toung |
| contents | Estimation algebras have been extensively studied in Euclidean space, where finite-dimensional estimation algebras form the foundation of the Kalman and Benes filters, and have contributed to the discovery of many other finite-dimensional filters. This work extends the theory of estimation algebras to filtering problems on Riemannian manifolds in continuous time. Our main result demonstrates that, with non-constant observation functions, the estimation algebra associated with the system on closed Riemannian manifolds is infinite-dimensional. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_08689 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nonexistence of finite-dimensional estimation algebras on closed smooth manifolds Kang, Jiayi Salmon, Andrew Yau, Stephen Shing-Toung Optimization and Control Probability 93E11, 60G35 Estimation algebras have been extensively studied in Euclidean space, where finite-dimensional estimation algebras form the foundation of the Kalman and Benes filters, and have contributed to the discovery of many other finite-dimensional filters. This work extends the theory of estimation algebras to filtering problems on Riemannian manifolds in continuous time. Our main result demonstrates that, with non-constant observation functions, the estimation algebra associated with the system on closed Riemannian manifolds is infinite-dimensional. |
| title | Nonexistence of finite-dimensional estimation algebras on closed smooth manifolds |
| topic | Optimization and Control Probability 93E11, 60G35 |
| url | https://arxiv.org/abs/2410.08689 |