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Long-time asymptotics of the filtering distribution for partially observed chaotic dynamical systems
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Sanz-Alonso, Daniel and Stuart, A. M. (2015) Long-time asymptotics of the filtering distribution for partially observed chaotic dynamical systems. SIAM/ASA Journal on Uncertainty Quantification, 3 (1). pp. 1200-1220. doi:10.1137/140997336 ISSN 2166-2525.
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Official URL: http://dx.doi.org/10.1137/140997336
Abstract
The filtering distribution is a time-evolving probability distribution on the state of a dynamical system given noisy observations. We study the large-time asymptotics of this probability distribution for discrete-time, randomly initialized signals that evolve according to a deterministic map Ψ. The observations are assumed to comprise a low-dimensional projection of the signal, given by an operator P, subject to additive noise. We address the question of whether these observations contain sufficient information to accurately reconstruct the signal. In a general framework, we establish conditions on Ψ and P under which the filtering distributions concentrate around the signal in the small-noise, long-time asymptotic regime. Linear systems, the Lorenz ’63 and ’96 models, and the Navier–Stokes equation on a two-dimensional torus are within the scope of the theory. Our main findings come as a by-product of computable bounds, of independent interest, for suboptimal filters based on new variants of the 3DVAR filtering algorithm
| Item Type: | Journal Article | ||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
| Library of Congress Subject Headings (LCSH): | Chaotic behavior in systems | ||||||||
| Journal or Publication Title: | SIAM/ASA Journal on Uncertainty Quantification | ||||||||
| Publisher: | SIAM | ||||||||
| ISSN: | 2166-2525 | ||||||||
| Official Date: | 10 December 2015 | ||||||||
| Dates: |
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| Volume: | 3 | ||||||||
| Number: | 1 | ||||||||
| Page Range: | pp. 1200-1220 | ||||||||
| DOI: | 10.1137/140997336 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||||||
| Date of first compliant deposit: | 13 January 2016 | ||||||||
| Date of first compliant Open Access: | 18 February 2016 | ||||||||
| Adapted As: |
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