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arXiv · 2410.08689

Nonexistence of finite-dimensional estimation algebras on closed smooth manifolds

Jiayi Kang·Andrew Salmon·Stephen Shing-Toung Yau
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Abstract

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.

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Jiayi Kang, Andrew Salmon, Stephen Shing-Toung Yau. 2024-10-11. Nonexistence of finite-dimensional estimation algebras on closed smooth manifolds. https://arxiv.org/abs/2410.08689

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