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The ensemble Kalman filter and its relations to other nonlinear filters

Michael Roth, Carsten Fritsche, Gustaf Hendeby, Fredrik Gustafison
2015 2015 23rd European Signal Processing Conference (EUSIPCO)  
Furthermore, its application to nonlinear problems is compared to sigma point Kalman filters and the particle filter, so as to reveal new insights and improvements for high-dimensional filtering algorithms  ...  The Ensemble Kalman filter (EnKF) is a standard algorithm in oceanography and meteorology, where it has got thousands of citations.  ...  Sec. 3 shows how the EnKF can be applied to nonlinear systems, and establishes relations to sigma point Kalman filters and the particle filter.  ... 
doi:10.1109/eusipco.2015.7362581 dblp:conf/eusipco/RothFHG15 fatcat:zmjsusuolrby7dvdl52eja6uoi

Forecasting: it is not about statistics, it is about dynamics

K. Judd, T. Stemler
2009 Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences  
It is argued that more often than not the tracking and forecasting of nonlinear systems has more to do with the nonlinear dynamics that Lorenz considered than it has to do with statistics that Kalman considered  ...  A position with which both Lorenz and Kalman would appear to agree. Of course, in general these tasks may be done better by nonlinear filters.  ...  The authors also acknowledge the support of Leonard Smith and the London School of Economics.  ... 
doi:10.1098/rsta.2009.0195 pmid:19948555 fatcat:7qjttba63zcazglwpf3p3jhkky

Linear versus Nonlinear Filtering with Scale-Selective Corrections for Balanced Dynamics in a Simple Atmospheric Model

Aneesh C. Subramanian, Ibrahim Hoteit, Bruce Cornuelle, Arthur J. Miller, Hajoon Song
2012 Journal of the Atmospheric Sciences  
This paper investigates the role of the linear analysis step of the ensemble Kalman filters (EnKF) in disrupting the balanced dynamics in a simple atmospheric model and compares it to a fully nonlinear  ...  The PFs perform significantly better in the fully coupled nonlinear model where fast and slow variables modulate each other.  ...  We thank the two referees for their careful reviews and important comments that significantly improved the manuscript.  ... 
doi:10.1175/jas-d-11-0332.1 fatcat:b4vk26qs45dytgd4v3qyq3vhgu

A Non-Gaussian Ensemble Filter Update for Data Assimilation

Jeffrey L. Anderson
2010 Monthly Weather Review  
A deterministic square root ensemble Kalman filter and a stochastic perturbed observation ensemble Kalman filter are used for data assimilation in both linear and nonlinear single variable dynamical systems  ...  For the linear system, the deterministic filter is simply a method for computing the Kalman filter and is optimal while the stochastic filter has suboptimal performance due to sampling error.  ...  The author thanks Andy Majda, Chris Snyder, Stephen Anderson, Doug Nychka, Thomas Bengtsson, and Peter Bickell for their insights on ensemble and particle filters.  ... 
doi:10.1175/2010mwr3253.1 fatcat:t5wjslck3rb7vgw7gjehrmtu4y

A Local Least Squares Framework for Ensemble Filtering

Jeffrey L. Anderson
2003 Monthly Weather Review  
A more general class of methods including these ensemble Kalman filter methods is derived starting from the nonlinear filtering problem.  ...  In general, these methods have been derived from the Kalman filter and have been known as ensemble Kalman filters.  ...  The author is grateful to Chris Snyder, Jim Hansen, Jeff Whitaker, Tom Hamill, Joe Tribbia, and Ron Errico for ongoing discussions of en-  ... 
doi:10.1175/1520-0493(2003)131<0634:allsff>2.0.co;2 fatcat:7mdimc4nyzbtzdb2qz4flz43vq

Sequential Data Assimilation for Nonlinear Dynamics: The Ensemble Kalman Filter [chapter]

Geir Evensen
2002 Ocean Forecasting  
Another major problem of the Kalman filter is related to the storage and compu- tation of the error covariance matrix.  ...  Sequential Data Assimilation for Nonlinear Dynamics: The Ensemble Kalman Filter 105 6.3 Ensemble Kalman Filter The ensemble Kalman filter as proposed by Evensen (1994b) is now introduced.  ... 
doi:10.1007/978-3-662-22648-3_6 fatcat:svllxkjulvcxfa2vti2clhjtey

A comparison of assimilation results from the ensemble Kalman Filter and a reduced-rank extended Kalman Filter

X. Zang, P. Malanotte-Rizzoli
2003 Nonlinear Processes in Geophysics  
The goal of this study is to compare the performances of the ensemble Kalman filter and a reduced-rank extended Kalman filter when applied to different dynamic regimes.  ...  For the high viscosity case, both the reducedrank extended Kalman filter and the ensemble Kalman filter are able to significantly reduce the analysis error and their performances are similar.  ...  The computations were performed on the NCAR's parallel machines. Special thanks go to M. Buehner and J. Hansen for discussions. Comments from reviewers helped to improve our presentation.  ... 
doi:10.5194/npg-10-477-2003 fatcat:zsaef3uvorcjtc5rmogtf4kvna

Beating the Uncertainties: Ensemble Forecasting and Ensemble-Based Data Assimilation in Modern Numerical Weather Prediction

Hailing Zhang, Zhaoxia Pu
2010 Advances in Meteorology  
Recent developments in ensemble forecasting and ensemble-based data assimilation have proved that there are promising ways to beat the forecast uncertainties in NWP.  ...  Due to inadequate observations, our limited understanding of the physical processes of the atmosphere, and the chaotic nature of atmospheric flow, uncertainties always exist in modern numerical weather  ...  Acknowledgments The authors are grateful to three anonymous reviewers for their review comments that were helpful in improving this manuscript. This study is supported by U. S.  ... 
doi:10.1155/2010/432160 fatcat:c5qlafhlqffszhxw4r2ahpx3vu

Efficient State Estimation for Gas Pipeline Networks via Low-Rank Approximations [article]

Nadine Stahl, Nicole Marheineke
2021 arXiv   pre-print
For state estimation we propose to combine these low-rank models with Kalman filtering and show the advantages of this procedure to established low-rank Kalman filters in terms of efficiency and quality  ...  In this paper we investigate the performance of projection-based low-rank approximations in Kalman filtering.  ...  Ensemble Kalman Filter Additionally to the projection-based approaches, we consider the Ensemble Kalman Filter (EnKF) for comparison reasons in Sec. 4, as it is probably the most used Kalman filter variant  ... 
arXiv:2007.15988v2 fatcat:lc5dba6dwfd5vem7dwdwwdq54u

Advanced Data Assimilation for Strongly Nonlinear Dynamics

Geir Evensen
1997 Monthly Weather Review  
The ensemble Kalman filter is used for sequential data assimilation and the recently proposed ensemble smoother method and a gradient descent method are used to minimize two different weak constraint formulations  ...  The problems associated with the use of an approximate tangent linear model when solving the Euler-Lagrange equations, or when the extended Kalman filter is used, are eliminated when using these methods  ...  This work was supported by the Norwegian Research Council.  ... 
doi:10.1175/1520-0493(1997)125<1342:adafsn>2.0.co;2 fatcat:arh7z7kt75ccjpnztdgsoqr4oy

The Ensemble Kalman filter: a signal processing perspective

Michael Roth, Gustaf Hendeby, Carsten Fritsche, Fredrik Gustafsson
2017 EURASIP Journal on Advances in Signal Processing  
The ensemble Kalman filter (EnKF) is a Monte Carlo based implementation of the Kalman filter (KF) for extremely high-dimensional, possibly nonlinear and non-Gaussian state estimation problems.  ...  Algorithmic challenges and required extensions of the EnKF are provided, as well as relations to sigma-point KF and particle filters.  ...  Acknowledgements This work was supported by the project Scalable Kalman Filters granted by the Swedish Research Council (VR). The authors declare that they have no competing interests.  ... 
doi:10.1186/s13634-017-0492-x fatcat:aop4isxsfrgqpbzvg5w7mvrsdy

Nonlinearity in Data Assimilation Applications: A Practical Method for Analysis

M. Verlaan, A. W. Heemink
2001 Monthly Weather Review  
applying a second-order (or higher order) Kalman filter or an ensemble Kalman filter.  ...  It is based on computation of the first neglected term in a "Taylor" series expansion of the errors introduced by an extended Kalman filter, and can be computed at very little cost when one is already  ...  For strongly nonlinear problems the ensemble Kalman filter is preferable for its higher accuracy.  ... 
doi:10.1175/1520-0493(2001)129<1578:nidaaa>2.0.co;2 fatcat:5ca7wgcjebaazd6vheimc5nvmu

Analysis of SST images by weighted Ensemble Transform Kalman Filter

Sai Subrahmanyam Gorthi, Sebastien Beyou, Etienne Memin
2011 2011 IEEE International Geoscience and Remote Sensing Symposium  
The contribution of this paper lies in proposing a novel, robust and simple approach based on Weighted Ensemble Transform Kalman filter (WETKF) data assimilation technique for the analysis of real SST  ...  images, that may contain coast regions or large areas of missing data due to the cloud cover.  ...  Ensemble Transform Kalman filter (ETKF) is an ensemble implementation of the well known recursive Kalman filter (KF), similar to the Ensemble Kalman Filter [3] , which minimizes the mean square error  ... 
doi:10.1109/igarss.2011.6050049 dblp:conf/igarss/GorthiBM11 fatcat:eyxyn2uconfxlonsp4rr6pt2tq

Sequential data assimilation with multiple nonlinear models and applications to subsurface flow

Lun Yang, Akil Narayan, Peng Wang
2017 Journal of Computational Physics  
Based on an earlier study of Multi-model Kalman filter, we propose a novel framework to assimilate multiple models with observation data for nonlinear systems, using extended Kalman filter, ensemble Kalman  ...  Over the years, data assimilation techniques, such as the Kalman filter, have become essential tools for improved system estimation by incorporating both models forecast and measurement; but its potential  ...  Further extensions to address nonlinear systems, such as the extended Kalman filter [12, 18] , the ensemble Kalman filter [10, 11] and other variants [1, 2, 6, 35, 40] , have also been proposed and  ... 
doi:10.1016/j.jcp.2017.06.026 fatcat:zi3zrjbxgjeybbs5gydkqmxvei

Particle Kalman Filtering: A Nonlinear Bayesian Framework for Ensemble Kalman Filters*

Ibrahim Hoteit, Xiaodong Luo, Dinh-Tuan Pham
2012 Monthly Weather Review  
We show that this filter is an algorithm in between the Kalman filter and the particle filter, and therefore is referred to as the particle Kalman filter (PKF).  ...  The resulting filter is similar to the particle filter, but is different from it in that, the standard weight-type correction in the particle filter is complemented by the Kalman-type correction with the  ...  We thank the three anonymous reviewers for their valuable comments and suggestions.  ... 
doi:10.1175/2011mwr3640.1 fatcat:igrcslirenbz3enyy3eygo263y
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