Fast and accurate parameter estimation by means of a semi-implicit extended Kalman filter
TNO Industrie en Techniek
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.
To reference this document use:
Extended Kalman filters
Error covariance matrix
Explicit time integration scheme
One dimensional problems
Institute of Electrical and Electronics Engineers Inc.
2009 10th European Control Conference, ECC 2009, 23 August 2009 through 26 August 2009, 1925-1930