Compressed state Kalman filter for large systems

Advances in Water Resources

Volumn 76, Issue , 2015, Pages 120-126

  Kitanidis, Peter K ^a  

^a Stanford University   (United States)

Author keywords

Bayesian analysis; Geostatistics; Kalman filter; Probability; Statistics

Indexed keywords

APPROXIMATION THEORY; COMPUTATIONAL METHODS; COVARIANCE MATRIX; KALMAN FILTERS; LINEAR SYSTEMS; MATRIX ALGEBRA; PROBABILITY; STATISTICS;

BAYESIAN ANALYSIS; COMPUTATIONAL RESULTS; GEO-STATISTICS; LOW RANK APPROXIMATIONS; RECURSIVE FILTERS; SOLUTE CONCENTRATIONS; STATE-COVARIANCE MATRIX; TRANSITION MATRICES;

JACOBIAN MATRICES;

BAYESIAN ANALYSIS; FORWARD MODELING; GEOSTATISTICS; KALMAN FILTER; NUMERICAL MODEL; PROBABILITY; STATISTICAL ANALYSIS;

EID: 84922647531     PISSN: 03091708     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.advwatres.2014.12.010     Document Type: Article

References (26)

1. Kalman R.E., Bucy R.S. New results in linear filtering and prediction theory. J Basic Eng Trans ASME Ser D 1961, 83(3):95-108. 10.1115/1.3658902.
2. Liu G., Chen Y., Zhang D. Investigation of flow and transport processes at the made site using ensemble Kalman filter. Adv Water Resour 2008, 31:975-986. 10.1016/j.advwatres.2008.03.006.
3. Chatterjee A., Michalak A.M., Anderson J.L., Mueller K.L., Yadav V. Toward reliable ensemble Kalman filter estimates of CO2 fluxes. J Geophys Res Atmos 2012, 117(D22):D22306. 10.1029/2012jd018176.
4. Jafarpour B., McLaughlin D.B. Reservoir characterization with the discrete cosine transform. SPE J 2009, 14(01):182-201. 10.2118/106453-PA.
5. Kurtz W., Franssen H.J.H., Vereecken H. Identification of time-variant river bed properties with the ensemble Kalman filter. Water Resour Res 2012, 48:W10534. 10.1029/2011wr011743.
6. Reichle R.H., McLaughlin D.B., Entekhabi D. Hydrologic data assimilation with the ensemble Kalman filter. Mon Weather Rev 2002, 130(1):103-114. 10.1175/1520-0493(2002) 1300103:hdawte2.0.co;2.
7. Lee J., Kitanidis P.K. Large-scale hydraulic tomography and joint inversion of head and tracer data using the principal component geostatistical approach (pcga). Water Resour Res 2014, 50(7):5410-5427. 10.1002/2014wr015483.
8. Ng G.-H.C., McLaughlin D., Entekhabi D., Ahanin A. The role of model dynamics in ensemble Kalman filter performance for chaotic systems. Tellus A 2011, 63(5):958-977. 10.1111/j.1600-0870.2011.00539.x.
9. Evensen G. Sequential data assimilation with a non-linear quasi-geostrophic model using Monte Carlo methods to forecast error statistics. J Geophys Res 1994, 99(C5):10.143-10.162. 10.1029/94JC00572.
10. Burgers G., Jan van Leeuwen P., Evensen G. Analysis scheme in the ensemble Kalman filter. Mon Weather Rev 1998, 126(6):1719-1724. 10.1175/1520-0493.
11. Evensen G. The ensemble Kalman filter: theoretical formulation and practical implementation. Ocean Dyn 2003, 53:343-367. 10.1007/s10236-003-0036-9.
12. Evensen G. Data Assimilation: The Ensemble Kalman Filter 2006, Springer.
13. Gu Y., Oliver D.S. An iterative ensemble Kalman filter for multiphase fluid flow data assimilation. SPE J 2007, 438-446. 10.2118/108438-PA.
14. Pham D.T., Verron J., Roubaud M.C. Singular evolutive Kalman filter with EOF initialization for data assimilation in oceanography. J Mar Syst 1997, 16:323-340. 10.1016/S0924-7963(97)00109-7.
15. Pham D.T., Verron J., Gourdeau L. Singular evolutive Kalman filters for data assimilation in oceanography. C R Acad Sci Paris 1998, 326:255-260.
16. Brasseur P., Ballabrera-Poy J., Verron J. Assimilation of altimetric observations in a primitive equation model of the gulf stream using a singular evolutive extended Kalman filter. J Mar Sys 1999, 22(4):269-294. 10.1016/S0924-7963(99)00044-5.
17. Hoteit I, Pham D.-T, Blum J, A simplified reduced order Kalman filtering and application to altimetric data assimilation in tropical pacific, J Mar Syst 36 (1-2). http://dx.doi.org/10.1016/S0924-7963(02)00129-X. doi:10.1016/S0924-7963(02)00129-X.
18. Cressie N., Shi T., Kang E. Fixed rank filtering for spatio-temporal data. J Comput Graph Stat 2010, 19(3):724-745. 10.1198/jcgs.2010.09051.
19. Fong W., Darve E. The black-box fast multipole method. J Comput Phys 2009, 228(23):8712-8725. 10.1016/j.jcp.2009.08.031.
20. Saibaba A.K., Ambikasaran S., Li J.Y., Kitanidis P.K., Darve E.F. Application of hierarchical matrices to linear inverse problems in geostatistics. Oil Gas Sci Technol 2012, 67(5):857-875. 10.2516/ogst/2012064.
21. Grewal M.S., Andrews A.P. Kalman Theory and Practice 1993, Prentice-Hall, Englewood Cliffs, NJ.
22. Trefethen L.N., Bau D. Numerical Linear Algebra. SIAM 1997.
23. Nowak W., Tenkleve S., Cirpka O. Efficient computation of linearized cross-covariance and auto-covariance matrices of interdependent quantities. Math Geol 2003, 35(1):53-66. 10.1023/A:1022365112368.
24. Ambikasaran S., Li J., Kitanidis P., Darve E. Large-scale stochastic linear inversion using hierarchical matrices. Comput Geosci 2013, 17(6):913-927. 10.1007/s10596-013-9364-0.
25. Halko N., Martinsson P.G., Tropp J.A. Finding structure with randomness: probabilistic algorithms for constructing approximate matrix decompositions. SIAM Rev 2011, 53(2):217-288. 10.1137/090771806.
26. Strang G. The discrete cosine transform. SIAM Rev 1999, 41(1):135-147. 10.1137/S0036144598336745.