411
Views
43
CrossRef citations to date
0
Altmetric
Original Articles

Convergence analysis of ensemble Kalman inversion: the linear, noisy case

&
Pages 107-123 | Received 25 Feb 2017, Accepted 26 Sep 2017, Published online: 15 Oct 2017

References

  • Law K, Stuart A, Zygalakis K. Data assimilation: a mathematical introduction. Switzerland: Springer International Publishing; 2015.
  • Ghil M, Cohn J, Tavantzis SE, et al. Application of estimation theory to numerical weather prediction. In: Bengtsson L, Ghil M, K{\"a}ll{\’e}n E, editors. Dynamic meteorology: data assimilation methods. New York (NY): Springer; 1981. p. 139–224.
  • Evensen G. Data assimilation: the ensemble Kalman filter. Secaucus (NJ): Springer-Verlag New York; 2006.
  • Evensen G. The ensemble Kalman filter: theoretical formulation and practical implementation. Ocean Dyn. 2003;53:343–367.
  • Evensen G, Van Leeuwen P. Assimilation of geosat altimeter data for the agulhas current using the ensemble Kalman filter with a quasi-geostrophic model. Mon Weather. 1996;128:85–96.
  • Houtekamer P, Mitchell H. A sequential ensemble Kalman filter for atmospheric data assimilation. Mon Weather Rev. 2001;129:123–137.
  • Oliver D, Reynolds A, Liu N. Inverse theory for petroleum reservoir characterization and history matching. Cambridge: Cambridge University Press; 2008.
  • Iglesias M, Law K, Stuart A. Ensemble Kalman methods for inverse problems. Inverse Prob. 2013;29:045001.
  • Li G, Reynolds A. An iterative ensemble Kalman filter for data assimilation. In: SPE Annual Technical Conference and Exhibition. Anaheim, CA; 2007.
  • Schillings C, Stuart A. Analysis of the ensemble Kalman filter for inverse problems. SIAM Numer Anal. 2017;55(3):1264–1290.
  • Bergemann K, Reich S. A localization technique for ensemble Kalman filters. Quart J R Meteorol Soc. 2010;136:701–707.
  • Stuart AM. Inverse problems: a Bayesian perspective. Acta Numer. 2010;19:451–559.
  • Dashti M, Stuart AM. The Bayesian approach to inverse problems. In: Ghanem R, Higdon D, Owhadi H, editors. Handbook of uncertainty quantification. Switzerland: Springer International Publishing; 2015.
  • Reich S, Cotter C. Probabilistic forecasting and Bayesian data assimilation. Cambridge: Cambridge University Press; 2015.
  • Kelly D, Law K, Stuart A. Well-posedness and accuracy of the ensemble Kalman filter in discrete and continuous time. Nonlinearity. 2014;27:2579.
  • Tong XT, Majda AJ, Kelly D. Nonlinear stability and ergodicity of ensemble based Kalman filters. Nonlinearity. 2016;29:657.
  • Tong XT, Majda AJ, Kelly D. Nonlinear stability of the ensemble Kalman filter with adaptive covariance inflation. 2015, arXiv:1507.08319.
  • Kelly D, Majda AJ, Tong XT. Concrete ensemble Kalman filters with rigorous catastrophic filter divergence. Proc Nat Acad Sci. 2015;112:10589–10594.
  • de Wiljes J, Reich S, Stannat W. Long-time stability and accuracy of the ensemble Kalman-Bucy filter for fully observed processes and small measurement noise. 2016, arXiv e-prints.
  • Bergemann K, Reich S. A mollified ensemble Kalman filter. Quart J R Meteorol Soc. 2010;136:1636–1643.
  • Reich S. A dynamical systems framework for intermittent data assimilation. BIT Numer Math. 2011;51:235–249.
  • Kwiatkowski E, Mandel J. Convergence of the square root ensemble Kalman filter in the large ensemble limit. SIAM/ASA J Uncert Quant. 2015;3:1–17.
  • Gratton S, Mandel J, et al. On the convergence of a non-linear ensemble Kalman smoother. 2014, arXiv preprint arXiv:1411.4608.
  • Ernst O, Sprungk B, Starkloff H. Analysis of the ensemble and polynomial chaos Kalman filters in Bayesian inverse problems. 2015, arXiv preprint arXiv:1504.03529.
  • Iglesias M. Iterative regularization for ensemble data assimilation in reservoir models. Comput Geosci. 2014;1–36.
  • Iglesias MA. A regularizing iterative ensemble Kalman method for pde-constrained inverse problems. 2015, arXiv preprint arXiv:1505.03876.
  • Engl H, Hanke M, Neubauer A. Regularization of inverse problems. Vol. 375. The Netherlands: Springer Science & Business Media; 1996.
  • Kaipio J, Somersalo E. Statistical inverse problems: discretization, model reduction and inverse crimes. J Comput Appl Math. 2007;198:493–504.
  • Blanchard G, Mathé P. Discrepancy principle for statistical inverse problems with application to conjugate gradient iteration. Inverse Prob. 2012;19(1):177–212.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.