Definition
The ensemble Kalman filter (EnKF) is an evolution of the Kalman filter for its application to nonlinear state-transition systems with a further extension to serve as a powerful parameter inversion method. Its main purpose is to improve the estimates of the system state as observations are acquired. As the Kalman filter, the EnKF is based on two steps, forecasting and updating (or filtering). During the forecasting step, the state of the system is forecasted on the basis of the latest state estimate; then, forecasts are compared with observations and a correction is made to the state (and possibly to the parameters of the state equation) that will serve as the basis for the next forecast.
The Kalman filter was developed by Kalman (1960) for the purpose of improving the trajectory estimation of spacecrafts and missiles and one of its very first implementations was in the Apollo program. The Kalman filter, as developed by Kalman, had a great success when it was first proposed...
This is a preview of subscription content, log in via an institution to check access.
References
Evensen G (1994) Sequential data assimilation with a nonlinear quasi- geostrophic model using Monte Carlo methods to forecast error statistics. Journal of Geophysical Research 99(C5):10143–10162
Jazwinski AH (1970) Stochastic Processes and Filtering Theory. Academic Press
Kalman RE (1960) A new approach to linear filtering and prediction problems. Journal of Basic Engineering 82:35–45
Wen XH, Chen WH (2007) Some practical issues on real-time reservoir model updating using ensemble Kalman filter. SPE Journal 12(02):156–166
Xu T, Gómez-Hernández JJ (2018) Simultaneous identification of a con- taminant source and hydraulic conductivity via the restart normal-score ensemble Kalman filter. Advances in Water Resources 112:106–123
Zhou H, Gómez-Hernández J, Hendricks Franssen H, Li L (2011) An approach to handling non-gaussianity of parameters and state variables in ensemble Kalman filtering. Advances in Water Resources 34(7):844–864
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this entry
Cite this entry
Gómez-Hernández, J.J. (2021). Ensemble Kalman Filtering. In: Daya Sagar, B.S., Cheng, Q., McKinley, J., Agterberg, F. (eds) Encyclopedia of Mathematical Geosciences. Encyclopedia of Earth Sciences Series. Springer, Cham. https://doi.org/10.1007/978-3-030-26050-7_101-1
Download citation
DOI: https://doi.org/10.1007/978-3-030-26050-7_101-1
Received:
Accepted:
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-26050-7
Online ISBN: 978-3-030-26050-7
eBook Packages: Springer Reference Earth and Environm. ScienceReference Module Physical and Materials ScienceReference Module Earth and Environmental Sciences