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Computational Geosciences

, Volume 16, Issue 3, pp 837–852 | Cite as

Shrinked (1 − α) ensemble Kalman filter and α Gaussian mixture filter

  • Javad RezaieEmail author
  • Jo Eidsvik
Original Paper

Abstract

State estimation in high dimensional systems remains a challenging part of real time analysis. The ensemble Kalman filter addresses this challenge by using Gaussian approximations constructed from a number of samples. This method has been a large success in many applications. Unfortunately, for some cases, Gaussian approximations are no longer valid, and the filter does not work so well. In this paper, we use the idea of the ensemble Kalman filter together with the more theoretically valid particle filter. We outline a Gaussian mixture approach based on shrinking the predicted samples to overcome sample degeneracy, while maintaining non-Gaussian nature. A tuning parameter determines the degree of shrinkage. The computational cost is similar to the ensemble Kalman filter. We compare several filtering methods on three different cases: a target tracking model, the Lorenz 40 model, and a reservoir simulation example conditional on seismic and electromagnetic data.

Keywords

Sequential updating Filtering EnKF Reservoir simulation Statistics 

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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Department of Mathematical SciencesNorwegian University of Science and TechnologyTrondheimNorway

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