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Volumn 14, Issue 4, 2010, Pages 721-744

A stochastic collocation based Kalman filter for data assimilation

Author keywords

Data assimilation; Ensemble Kalman filter; Stochastic collocation; Uncertainty quantification

Indexed keywords

COVARIANCE ANALYSIS; DATA ASSIMILATION; ENSEMBLE FORECASTING; ESTIMATION METHOD; HYDRAULIC CONDUCTIVITY; KALMAN FILTER; MONTE CARLO ANALYSIS; MULTIPHASE FLOW; NUMERICAL METHOD; STOCHASTICITY;

EID: 77955919808     PISSN: 14200597     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10596-010-9183-5     Document Type: Article
Times cited : (42)

References (37)
  • 5
    • 0018435192 scopus 로고
    • Asymptotic-behavior of the extended kalman filter as a parameter estimator for linear-systems
    • Ljung, L.: Asymptotic-behavior of the extended kalman filter as a parameter estimator for linear-systems. IEEE Trans. Autom. Control. 24, 36-50 (1979).
    • (1979) IEEE Trans. Autom. Control. , vol.24 , pp. 36-50
    • Ljung, L.1
  • 6
    • 0028193070 scopus 로고
    • Sequential data assimilation with a nonlinear quasi-geostrophic model using monte-carlo methods to forecast error statistics
    • Evensen, G.: Sequential data assimilation with a nonlinear quasi-geostrophic model using monte-carlo methods to forecast error statistics. J. Geophys. Res. 99, 10143-10162 (1994).
    • (1994) J. Geophys. Res. , vol.99 , pp. 10143-10162
    • Evensen, G.1
  • 7
    • 0031742114 scopus 로고    scopus 로고
    • A singular evolutive extended Kalman filter for data assimilation in oceanography
    • Pham, D. T., Verron, J., Roubaud, M. C.: A singular evolutive extended Kalman filter for data assimilation in oceanography. J. Mar. Syst. 16, 323-340 (1998).
    • (1998) J. Mar. Syst. , vol.16 , pp. 323-340
    • Pham, D.T.1    Verron, J.2    Roubaud, M.C.3
  • 8
    • 0036704805 scopus 로고    scopus 로고
    • An integrated approach to hydrologic data assimilation: Interpolation, smoothing, and filtering
    • McLaughlin, D.: An integrated approach to hydrologic data assimilation: interpolation, smoothing, and filtering. Adv. Water Resour. 25, 1275-1286 (2002).
    • (2002) Adv. Water Resour. , vol.25 , pp. 1275-1286
    • McLaughlin, D.1
  • 9
    • 33746216685 scopus 로고    scopus 로고
    • Data assimilation for transient flow in geologic formations via ensemble Kalman filter
    • Chen, Y., Zhang, D. X.: Data assimilation for transient flow in geologic formations via ensemble Kalman filter. Adv. Water Resour. 29, 1107-1122 (2006).
    • (2006) Adv. Water Resour. , vol.29 , pp. 1107-1122
    • Chen, Y.1    Zhang, D.X.2
  • 10
    • 17744366835 scopus 로고    scopus 로고
    • Reservoir monitoring and continuous model updating using ensemble Kalman filter
    • Naevdal, G., Johnsen, L. M., Aanonsen, S. I., Vefring, E. H.: Reservoir monitoring and continuous model updating using ensemble Kalman filter. SPE J. 10, 66-74 (2005).
    • (2005) SPE J. , vol.10 , pp. 66-74
    • Naevdal, G.1    Johnsen, L.M.2    Aanonsen, S.I.3    Vefring, E.H.4
  • 11
    • 20444479133 scopus 로고    scopus 로고
    • Ensemble Kalman filter for automatic history matching of geologic facies
    • Liu, N., Oliver, D. S.: Ensemble Kalman filter for automatic history matching of geologic facies. J. Pet. Sci. Eng. 47, 147-161 (2005).
    • (2005) J. Pet. Sci. Eng. , vol.47 , pp. 147-161
    • Liu, N.1    Oliver, D.S.2
  • 12
    • 22544460244 scopus 로고    scopus 로고
    • History matching of the PUNQ-S3 reservoir model using the ensemble Kalman filter
    • Gu, Y. Q., Oliver, D. S.: History matching of the PUNQ-S3 reservoir model using the ensemble Kalman filter. SPE J. 10, 217-224 (2005).
    • (2005) SPE J. , vol.10 , pp. 217-224
    • Gu, Y.Q.1    Oliver, D.S.2
  • 13
    • 35448939588 scopus 로고    scopus 로고
    • Assessing the uncertainty in reservoir description and performance predictions with the ensemble Kalman filter
    • Zafari, M., Reynolds, A. C.: Assessing the uncertainty in reservoir description and performance predictions with the ensemble Kalman filter. SPE J. 12, 382-391 (2007).
    • (2007) SPE J. , vol.12 , pp. 382-391
    • Zafari, M.1    Reynolds, A.C.2
  • 14
    • 0036646009 scopus 로고    scopus 로고
    • Ensemble data assimilation without perturbed observations
    • Whitaker, J. S., Hamill, T. M.: Ensemble data assimilation without perturbed observations. Mon. Weather Rev. 130, 1913-1924 (2002).
    • (2002) Mon. Weather Rev. , vol.130 , pp. 1913-1924
    • Whitaker, J.S.1    Hamill, T.M.2
  • 15
    • 0032024819 scopus 로고    scopus 로고
    • Data assimilation using an ensemble Kalman filter technique
    • Houtekamer, P. L., Mitchell, H. L.: Data assimilation using an ensemble Kalman filter technique. Mon. Weather Rev. 126, 796-811 (1998).
    • (1998) Mon. Weather Rev. , vol.126 , pp. 796-811
    • Houtekamer, P.L.1    Mitchell, H.L.2
  • 16
    • 66849101595 scopus 로고    scopus 로고
    • The ensemble Kalman filter for combined state and parameter estimation
    • Evensen, G.: The ensemble Kalman filter for combined state and parameter estimation. IEEE Control. Syst. Mag. 29, 83-104 (2009).
    • (2009) IEEE Control. Syst. Mag. , vol.29 , pp. 83-104
    • Evensen, G.1
  • 18
    • 0037249229 scopus 로고    scopus 로고
    • The Wiener-Askey polynomial chaos for stochastic differential equations
    • Xiu, D. B., Karniadakis, G. E.: The Wiener-Askey polynomial chaos for stochastic differential equations. Siam. J. Sci. Comput. 24, 619-644 (2002).
    • (2002) Siam. J. Sci. Comput. , vol.24 , pp. 619-644
    • Xiu, D.B.1    Karniadakis, G.E.2
  • 19
    • 34248523110 scopus 로고    scopus 로고
    • Stochastic spectral methods for efficient Bayesian solution of inverse problems
    • Marzouk, Y. M., Najm, H. N., Rahn, L. A.: Stochastic spectral methods for efficient Bayesian solution of inverse problems. J. Comput. Phys. 224, 560-586 (2007).
    • (2007) J. Comput. Phys. , vol.224 , pp. 560-586
    • Marzouk, Y.M.1    Najm, H.N.2    Rahn, L.A.3
  • 20
    • 77955922097 scopus 로고    scopus 로고
    • Saad, G. A.: Stochastic Data Assimilation with Application to Multi-Phase Flow and Health Monitoring Problems. PhD thesis, University of Southern California, Los Angeles (2007).
  • 21
    • 34247278161 scopus 로고    scopus 로고
    • Dynamic reservoir data assimilation with an efficient, dimension-reduced Kalman filter
    • Zhang, D. X., Lu, Z. M., Chen, Y.: Dynamic reservoir data assimilation with an efficient, dimension-reduced Kalman filter. SPE J. 12, 108-117 (2007).
    • (2007) SPE J. , vol.12 , pp. 108-117
    • Zhang, D.X.1    Lu, Z.M.2    Chen, Y.3
  • 22
    • 0031392891 scopus 로고    scopus 로고
    • An efficient method for parametric uncertainty analysis of numerical geophysical models
    • Tatang, M. A., Pan, W. W., Prinn, R. G., McRae, G. J.: An efficient method for parametric uncertainty analysis of numerical geophysical models. J. Geophys. Res. 102, 21925-21932 (1997).
    • (1997) J. Geophys. Res. , vol.102 , pp. 21925-21932
    • Tatang, M.A.1    Pan, W.W.2    Prinn, R.G.3    McRae, G.J.4
  • 23
    • 35948933092 scopus 로고    scopus 로고
    • Probabilistic collocation method for flow in porous media: Comparisons with other stochastic methods
    • Li, H., Zhang, D. X.: Probabilistic collocation method for flow in porous media: comparisons with other stochastic methods. Water Resour. Res. 43, W9409 (2007).
    • (2007) Water Resour. Res. , vol.43
    • Li, H.1    Zhang, D.X.2
  • 24
    • 58749090528 scopus 로고    scopus 로고
    • Probabilistic collocation method for unconfined flow in heterogeneous media
    • Shi, L. S., Yang, J. H., Zhang, D. X., Li, H.: Probabilistic collocation method for unconfined flow in heterogeneous media. J. Hydrol. 365, 4-10 (2009).
    • (2009) J. Hydrol. , vol.365 , pp. 4-10
    • Shi, L.S.1    Yang, J.H.2    Zhang, D.X.3    Li, H.4
  • 25
    • 33646577797 scopus 로고    scopus 로고
    • High-order collocation methods for differential equations with random inputs
    • Xiu, D. B., Hesthaven, J. S.: High-order collocation methods for differential equations with random inputs. Siam. J. Sci. Comput. 27, 1118-1139 (2005).
    • (2005) Siam. J. Sci. Comput. , vol.27 , pp. 1118-1139
    • Xiu, D.B.1    Hesthaven, J.S.2
  • 26
    • 34548216854 scopus 로고    scopus 로고
    • A stochastic collocation method for elliptic partial differential equations with random input data
    • Babuska, I., Nobile, F., Tempone, R.: A stochastic collocation method for elliptic partial differential equations with random input data. Siam J. Numer. Anal. 45, 1005-1034 (2007).
    • (2007) Siam J. Numer. Anal. , vol.45 , pp. 1005-1034
    • Babuska, I.1    Nobile, F.2    Tempone, R.3
  • 27
    • 67650935289 scopus 로고    scopus 로고
    • A comparative study of stochastic collocation methods for flow in spatially correlated random fields
    • Chang, H. B., Zhang, D. X.: A comparative study of stochastic collocation methods for flow in spatially correlated random fields. Commun. Comput. Phys. 6, 509-535 (2009).
    • (2009) Commun. Comput. Phys. , vol.6 , pp. 509-535
    • Chang, H.B.1    Zhang, D.X.2
  • 28
    • 40849151822 scopus 로고    scopus 로고
    • A scalable framework for the solution of stochastic inverse problems using a sparse grid collocation approach
    • Zabaras, N., Ganapathysubramanian, B.: A scalable framework for the solution of stochastic inverse problems using a sparse grid collocation approach. J. Comput. Phys. 227, 4697-4735 (2008).
    • (2008) J. Comput. Phys. , vol.227 , pp. 4697-4735
    • Zabaras, N.1    Ganapathysubramanian, B.2
  • 29
    • 46149110946 scopus 로고    scopus 로고
    • Kernel principal component analysis for efficient, differentiable parameterization of multipoint geostatistics
    • Sarma, P., Durlofsky, L. J., Aziz, K.: Kernel principal component analysis for efficient, differentiable parameterization of multipoint geostatistics. Math. Geosci. 40, 3-32 (2008).
    • (2008) Math. Geosci. , vol.40 , pp. 3-32
    • Sarma, P.1    Durlofsky, L.J.2    Aziz, K.3
  • 30
    • 49749130443 scopus 로고    scopus 로고
    • Numerical integration formulas of degree two
    • Xiu, D. B.: Numerical integration formulas of degree two. Appl. Numer. Math. 58, 1515-1520 (2008).
    • (2008) Appl. Numer. Math. , vol.58 , pp. 1515-1520
    • Xiu, D.B.1
  • 31
    • 61549132041 scopus 로고    scopus 로고
    • Improved initial sampling for the ensemble Kalman filter
    • Chen, Y., Oliver, D. S.: Improved initial sampling for the ensemble Kalman filter. Computat. Geosci. 13, 13-26 (2009).
    • (2009) Computat. Geosci. , vol.13 , pp. 13-26
    • Chen, Y.1    Oliver, D.S.2
  • 32
    • 76349104633 scopus 로고    scopus 로고
    • Efficient and accurate quantification of uncertainty for multiphase flow with probabilistic collocation method
    • Li, H., Zhang, D. X.: Efficient and accurate quantification of uncertainty for multiphase flow with probabilistic collocation method. SPE J. 14, 665-679 (2009).
    • (2009) SPE J. , vol.14 , pp. 665-679
    • Li, H.1    Zhang, D.X.2
  • 33
    • 77955926920 scopus 로고    scopus 로고
    • Sarma, P., Durlofsky, L. J., Aziz, K.: Efficient closed-loop production optimization under uncertainty. SPE paper 94241 (2005).
  • 34
    • 0036472444 scopus 로고    scopus 로고
    • Polynomial chaos decomposition for simulation of non-Gaussian non-stationary stochastic processes
    • Sakamoto, S., Ghanem, R.: Polynomial chaos decomposition for simulation of non-Gaussian non-stationary stochastic processes. ASCE J. Eng. Mech. 128, 190-201 (2002).
    • (2002) ASCE J. Eng. Mech. , vol.128 , pp. 190-201
    • Sakamoto, S.1    Ghanem, R.2
  • 35
    • 63249112668 scopus 로고    scopus 로고
    • Solving elliptic problems with non-Gaussian spatially-dependent random coefficients
    • Wan, X., Karniadakis, G. E.: Solving elliptic problems with non-Gaussian spatially-dependent random coefficients. Comput. Meth. Appl. Mech. Eng. 198, 1985-1995 (2009).
    • (2009) Comput. Meth. Appl. Mech. Eng. , vol.198 , pp. 1985-1995
    • Wan, X.1    Karniadakis, G.E.2
  • 36
    • 77955927586 scopus 로고    scopus 로고
    • Sarma, P., Chen, W. H.: Generalization of the ensemble Kalman filter using kernels for non-gaussian random fields. SPE paper 119177 (2009).
  • 37
    • 70349770723 scopus 로고    scopus 로고
    • Stochastic analysis of unsaturated flow with probabilistic collocation method
    • Li, W. X., Lu, Z. M., Zhang, D. X.: Stochastic analysis of unsaturated flow with probabilistic collocation method. Water Resour. Res. 45, W08425 (2009).
    • (2009) Water Resour. Res. , vol.45
    • Li, W.X.1    Lu, Z.M.2    Zhang, D.X.3


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