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Andreas S. Stordal Hans A. Karlsen Geir Nævdal Hans J. Skaug Brice Vallès 《Computational Geosciences》2011,15(2):293-305
The nonlinear filtering problem occurs in many scientific areas. Sequential Monte Carlo solutions with the correct asymptotic
behavior such as particle filters exist, but they are computationally too expensive when working with high-dimensional systems.
The ensemble Kalman filter (EnKF) is a more robust method that has shown promising results with a small sample size, but the
samples are not guaranteed to come from the true posterior distribution. By approximating the model error with a Gaussian
distribution, one may represent the posterior distribution as a sum of Gaussian kernels. The resulting Gaussian mixture filter
has the advantage of both a local Kalman type correction and the weighting/resampling step of a particle filter. The Gaussian
mixture approximation relies on a bandwidth parameter which often has to be kept quite large in order to avoid a weight collapse
in high dimensions. As a result, the Kalman correction is too large to capture highly non-Gaussian posterior distributions.
In this paper, we have extended the Gaussian mixture filter (Hoteit et al., Mon Weather Rev 136:317–334, 2008) and also made the connection to particle filters more transparent. In particular, we introduce a tuning parameter for the
importance weights. In the last part of the paper, we have performed a simulation experiment with the Lorenz40 model where
our method has been compared to the EnKF and a full implementation of a particle filter. The results clearly indicate that
the new method has advantages compared to the standard EnKF. 相似文献
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Andreas S. Stordal Randi Valestrand Hans Arnfinn Karlsen Geir N?vdal Hans Julius Skaug 《Computational Geosciences》2012,16(2):467-482
Over the last years, the ensemble Kalman filter (EnKF) has become a very popular tool for history matching petroleum reservoirs.
EnKF is an alternative to more traditional history matching techniques as it is computationally fast and easy to implement.
Instead of seeking one best model estimate, EnKF is a Monte Carlo method that represents the solution with an ensemble of
state vectors. Lately, several ensemble-based methods have been proposed to improve upon the solution produced by EnKF. In
this paper, we compare EnKF with one of the most recently proposed methods, the adaptive Gaussian mixture filter (AGM), on
a 2D synthetic reservoir and the Punq-S3 test case. AGM was introduced to loosen up the requirement of a Gaussian prior distribution
as implicitly formulated in EnKF. By combining ideas from particle filters with EnKF, AGM extends the low-rank kernel particle
Kalman filter. The simulation study shows that while both methods match the historical data well, AGM is better at preserving
the geostatistics of the prior distribution. Further, AGM also produces estimated fields that have a higher empirical correlation
with the reference field than the corresponding fields obtained with EnKF. 相似文献
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