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Analysis of the 3DVAR filter for the partially observed Lorenz'63 model
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Stuart, A. M., Shukla, Abhishek and Law, Kody J. H. (2013) Analysis of the 3DVAR filter for the partially observed Lorenz'63 model. Discrete and Continuous Dynamical Systems, Volume 34 (Number 3). pp. 1061-1078. doi:10.3934/dcds.2014.34.1061 ISSN 1078-0947.
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Official URL: http://dx.doi.org/10.3934/dcds.2014.34.1061
Abstract
Abstract: The problem of effectively combining data with a mathematical model constitutes a major challenge in applied mathematics. It is particular challenging for high-dimensional dynamical systems where data is received sequentially in time and the objective is to estimate the system state in an on-line fashion; this situation arises, for example, in weather forecasting. The sequential particle filter is then impractical and ad hoc filters, which employ some form of Gaussian approximation, are widely used. Prototypical of these ad hoc filters is the 3DVAR method. The goal of this paper is to analyze the 3DVAR method, using the Lorenz '63 model to exemplify the key ideas. The situation where the data is partial and noisy is studied, and both discrete time and continuous time data streams are considered. The theory demonstrates how the widely used technique of variance inflation acts to stabilize the filter, and hence leads to asymptotic accuracy.
Item Type: | Journal Article | ||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
Journal or Publication Title: | Discrete and Continuous Dynamical Systems | ||||||
Publisher: | American Institute of Mathematical Sciences | ||||||
ISSN: | 1078-0947 | ||||||
Official Date: | August 2013 | ||||||
Dates: |
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Volume: | Volume 34 | ||||||
Number: | Number 3 | ||||||
Page Range: | pp. 1061-1078 | ||||||
DOI: | 10.3934/dcds.2014.34.1061 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Access rights to Published version: | Restricted or Subscription Access |
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