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Analysis of the ensemble Kalman filter for inverse problems
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Schillings, Claudia and Stuart, A. M. (2017) Analysis of the ensemble Kalman filter for inverse problems. SIAM Journal on Numerical Analysis, 55 (3). pp. 1264-1290. doi:10.1137/16M105959X ISSN 0036-1429.
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WRAP-analysis-ensemble-filter-inverse-problems-Stuart-2017.pdf - Accepted Version - Requires a PDF viewer. Download (1496Kb) | Preview |
Official URL: http://dx.doi.org/10.1137/16M105959X
Abstract
The ensemble Kalman filter (EnKF) is a widely used methodology for state estimation in partially, noisily observed dynamical systems and for parameter estimation in inverse problems. Despite its widespread use in the geophysical sciences, and its gradual adoption in many other areas of application, analysis of the method is in its infancy. Furthermore, much of the existing analysis deals with the large ensemble limit, far from the regime in which the method is typically used. The goal of this paper is to analyze the method when applied to inverse problems with fixed ensemble size. A continuous time limit is derived and the long-time behavior of the resulting dynamical system is studied. Most of the rigorous analysis is confined to the linear forward problem, where we demonstrate that the continuous time limit of the EnKF corresponds to a set of gradient flows for the data misfit in each ensemble member, coupled through a common preconditioner which is the empirical covariance matrix of the ensemble. Numerical results demonstrate that the conclusions of the analysis extend beyond the linear inverse problem setting. Numerical experiments are also given which demonstrate the benefits of various extensions of the basic methodology.
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): | Kalman filtering, Inverse problems (Differential equations), Bayesian statistical decision theory, Differentiable dynamical systems | ||||||||||||
Journal or Publication Title: | SIAM Journal on Numerical Analysis | ||||||||||||
Publisher: | Society for Industrial and Applied Mathematics | ||||||||||||
ISSN: | 0036-1429 | ||||||||||||
Official Date: | 25 May 2017 | ||||||||||||
Dates: |
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Volume: | 55 | ||||||||||||
Number: | 3 | ||||||||||||
Page Range: | pp. 1264-1290 | ||||||||||||
DOI: | 10.1137/16M105959X | ||||||||||||
Status: | Peer Reviewed | ||||||||||||
Publication Status: | Published | ||||||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||||||
Date of first compliant deposit: | 8 December 2017 | ||||||||||||
Date of first compliant Open Access: | 8 December 2017 | ||||||||||||
RIOXX Funder/Project Grant: |
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