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The Ensemble Kalman filter: a signal processing perspective
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-1971-4295
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
2017 (English)In: EURASIP Journal on Advances in Signal Processing, ISSN 1687-6172, E-ISSN 1687-6180, article id 56Article, review/survey (Refereed) Published
Abstract [en]

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. Its ability to handle state dimensions in the order of millions has made the EnKF a popular algorithm in different geoscientific disciplines. Despite a similarly vital need for scalable algorithms in signal processing, e.g., to make sense of the ever increasing amount of sensor data, the EnKF is hardly discussed in our field. This self-contained review is aimed at signal processing researchers and provides all the knowledge to get started with the EnKF. The algorithm is derived in a KF framework, without the often encountered geoscientific terminology. Algorithmic challenges and required extensions of the EnKF are provided, as well as relations to sigma point KF and particle filters. The relevant EnKF literature is summarized in an extensive survey and unique simulation examples, including popular benchmark problems, complement the theory with practical insights. The signal processing perspective highlights new directions of research and facilitates the exchange of potentially beneficial ideas, both for the EnKF and high-dimensional nonlinear and non-Gaussian filtering in general.

Place, publisher, year, edition, pages
SPRINGER INTERNATIONAL PUBLISHING AG , 2017. article id 56
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:liu:diva-139901DOI: 10.1186/s13634-017-0492-xISI: 000406890100001OAI: oai:DiVA.org:liu-139901DiVA, id: diva2:1135767
Note

Funding Agencies|project Scalable Kalman Filters - Swedish Research Council

Available from: 2017-08-24 Created: 2017-08-24 Last updated: 2018-02-09
In thesis
1. Advanced Kalman Filtering Approaches to Bayesian State Estimation
Open this publication in new window or tab >>Advanced Kalman Filtering Approaches to Bayesian State Estimation
2017 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Bayesian state estimation is a flexible framework to address relevant problems at the heart of existing and upcoming technologies. Application examples are obstacle tracking for driverless cars and indoor navigation using smartphone sensor data. Unfortunately, the mathematical solutions of the underlying theory cannot be translated to computer code in general. Therefore, this thesis discusses algorithms and approximations that are related to the Kalman filter (KF).

Four scientific articles and an introduction with the relevant background on Bayesian state estimation theory and algorithms are included. Two articles discuss nonlinear Kalman filters, which employ the KF measurement update in nonlinear models. The numerous variants are presented in a common framework and the employed moment approximations are analyzed. Furthermore, their application to target tracking problems is discussed. A third article analyzes the ensemble Kalman filter (EnKF), a Monte Carlo implementation of the KF that has been developed for high-dimensional geoscientific filtering problems. The EnKF is presented in a simple KF framework, including its challenges, important extensions, and relations to other filters. Whereas the aforementioned articles contribute to the understanding of existing algorithms, a fourth article devises novel filters and smoothers to address heavy-tailed noise. The development is based on Student’s t distribution and provides simple recursions in the spirit of the KF. The introduction and articles are accompanied by extensive simulation experiments.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2017. p. 81
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1832
National Category
Signal Processing Control Engineering Computational Mathematics Computer Sciences Probability Theory and Statistics
Identifiers
urn:nbn:se:liu:diva-134867 (URN)10.3384/diss.diva-134867 (DOI)9789176855782 (ISBN)
Public defence
2017-04-21, Visionen, B-huset, Campus Valla, Linköping, 10:15 (English)
Opponent
Supervisors
Available from: 2017-03-22 Created: 2017-02-27 Last updated: 2018-02-09Bibliographically approved

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Roth, MichaelHendeby, GustafFritsche, CarstenGustafsson, Fredrik
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