A semi-implicit approach for fast parameter estimation by means of the extended Kalman filter

An assessment is performed of the impact of the time-integration scheme on data assimilation based on the extended Kalman filter approach. The usage of the implicit Euler scheme, which leads to unconditionally stable model updates for the whole range of time steps, results in a less accurate estimation of model parameters, which can be overcome using a parameter estimator based on the explicit Euler scheme. However, the latter limits the maximum time step which may lead to an unacceptable increase in computational load. 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. The improved properties of the proposed algorithm are demonstrated on a one-dimensional problem of permeability estimation in a porous medium for a single phase oil flow. (C) 2011 Elsevier Ltd. All rights reserved.