Nonexistence of finite-dimensional estimation algebras on closed smooth manifolds
Optimization and Control
2024-10-14 v1 Probability
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.
Cite
@article{arxiv.2410.08689,
title = {Nonexistence of finite-dimensional estimation algebras on closed smooth manifolds},
author = {Jiayi Kang and Andrew Salmon and Stephen Shing-Toung Yau},
journal= {arXiv preprint arXiv:2410.08689},
year = {2024}
}
Comments
6 pages, submitted to IEEE Transaction on Automatic Control