Abo Bibliothek: Guest
Digitales Portal Digitale Bibliothek eBooks Zeitschriften Referenzen und Berichte Forschungssammlungen
International Journal for Uncertainty Quantification
Impact-faktor: 3.259 5-jähriger Impact-Faktor: 2.547 SJR: 0.417 SNIP: 0.8 CiteScore™: 1.52

ISSN Druckformat: 2152-5080
ISSN Online: 2152-5099

Offener Zugang

International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.2012003889
pages 357-370

AN ENSEMBLE KALMAN FILTER USING THE CONJUGATE GRADIENT SAMPLER

Johnathan M. Bardsley
Department of Mathematical Sciences, The University of Montana, Missoula, Montana 59812-0864, USA
Antti Solonen
Lappeenranta University of Technology, Laboratory of Applied Mathematics
Albert Parker
Center for Biofilm Engineering, Montana State University, Bozeman, Montana, 59717, USA
Heikki Haario
Department of Mathematics and Physics, Lappeenranta University of Technology; Finnish Meteorological Institute, Helsinki, Finland
Marylesa Howard
Department of Mathematical Sciences, University of Montana, Missoula, Montana, 59812

ABSTRAKT

The ensemble Kalman filter (EnKF) is a technique for dynamic state estimation. EnKF approximates the standard extended Kalman filter (EKF) by creating an ensemble of model states whose mean and empirical covariance are then used within the EKF formulas. The technique has a number of advantages for large-scale, nonlinear problems. First, large-scale covariance matrices required within EKF are replaced by low-rank and low-storage approximations, making implementation of EnKF more efficient. Moreover, for a nonlinear state space model, implementation of EKF requires the associated tangent linear and adjoint codes, while implementation of EnKF does not. However, for EnKF to be effective, the choice of the ensemble members is extremely important. In this paper, we show how to use the conjugate gradient (CG) method, and the recently introduced CG sampler, to create the ensemble members at each filtering step. This requires the use of a variational formulation of EKF. The effectiveness of the method is demonstrated on both a large-scale linear, and a small-scale, nonlinear, chaotic problem. In our examples, the CG-EnKF performs better than the standard EnKF, especially when the ensemble size is small.


Articles with similar content:

OPTIMIZATION-BASED SAMPLING IN ENSEMBLE KALMAN FILTERING
International Journal for Uncertainty Quantification, Vol.4, 2014, issue 4
Alexander Bibov, Heikki Haario, Antti Solonen, Johnathan M. Bardsley
On One Method of Successive Construction of Orthogonal Transformation Matrices
Journal of Automation and Information Sciences, Vol.37, 2005, issue 2
Olga F. Garashchenko, Nikolay Fedorovich Kirichenko
AN ERROR SUBSPACE PERSPECTIVE ON DATA ASSIMILATION
International Journal for Uncertainty Quantification, Vol.5, 2015, issue 6
Haiyan Cheng, Adrian Sandu
Numerical Solution to Some Inverse Problems for Elliptic Systems Using Pseudoinverse Matrices
Journal of Automation and Information Sciences, Vol.43, 2011, issue 7
Ivan V. Sergienko, Vasiliy S. Deineka
BAYESIAN MULTISCALE FINITE ELEMENT METHODS. MODELING MISSING SUBGRID INFORMATION PROBABILISTICALLY
International Journal for Multiscale Computational Engineering, Vol.15, 2017, issue 2
Wing Tat Leung, B. Mallick, Yalchin Efendiev, N. Guha, V. H. Hoang, S. W. Cheung