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Fast and accurate parameter estimation by means of a semi-implicit extended Kalman filter

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Author: Gryzlov, A. · Leskens, M. · Mudde, R.F.
Publisher: Institute of Electrical and Electronics Engineers Inc.
Institution: TNO Industrie en Techniek
Source:2009 10th European Control Conference, ECC 2009, 23 August 2009 through 26 August 2009, 1925-1930
Identifier: 531907
ISBN: 9783952417393
Article number: 7074685
Keywords: Covariance matrix · Extended Kalman filters · Kalman filters · Porous materials · Error covariance matrix · Explicit time integration scheme · One dimensional problems · Parameter estimators · Permeability distribution · Permeability estimation · Time-integration scheme · Unconditionally stable · Parameter estimation


An assessment of the time-integration scheme impact on results of data assimilation based on the extended Kalman filter approach is performed. The use of the implicit Euler scheme, which is unconditionally stable for the whole range of time steps both for the model and covariance update, results in a less accurate estimation of permeability distribution, which can be overcome using a parameter estimator based on the explicit Euler scheme. However, the latter strongly limits the maximum time step, which can be used, and leads to inappropriate simulation time. The alternative can be found using a semi-implicit estimator, where a model is updated using the implicit Euler scheme, whereas the propagation of the error covariance matrix in time is based on the explicit time integration scheme. This hybrid approach combines the accuracy of the conventional Kalman filtering with the robustness of the implicit forward modelling. The proposed algorithm is successfully applied for the solution of the one-dimensional problem of permeability estimation in a porous medium for a single phase oil flow. © 2009 EUCA.