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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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
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:	Date Event 25 May 2017 Published 18 November 2016 Accepted
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:	Project/Grant ID RIOXX Funder Name Funder ID EQUIP Engineering and Physical Sciences Research Council http://dx.doi.org/10.13039/501100000266 UNSPECIFIED Defense Advanced Research Projects Agency http://dx.doi.org/10.13039/100000185 UNSPECIFIED Office of Naval Research http://dx.doi.org/10.13039/100000006

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