Asymptotic convergence of the ensemble Kalman filter

Butala, Mark D.; Yun, Jonghyun; Chen, Yuguo; Frazin, R. A.; Kamalabadi, F.

doi:10.1109/icip.2008.4711882

Cited by 14 publications

(17 citation statements)

References 5 publications

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“…This result has been established from different theoretical perspectives [26][27][28]31]. For nonlinear systems, the convergence is not as tangible.…”

Section: Asymptotic Convergence Resultsmentioning

confidence: 93%

“…Under the assumption of the structure in (27), a local analysis would amount to an EnKF update of the x 1 -and x 2 -components only, to avoid errors in x 3 .…”

Section: Localizationmentioning

confidence: 99%

“…Convergence properties for N → ∞ have been established using different theoretical analyses of the EnKF [26][27][28]. Statistical perspectives are provided in the thesis [29] and the review [30].…”

Section: Reviewmentioning

confidence: 99%

“…However, it will become clear that not all entries ofP k|k−1 must be computed. Prior knowledge of a covariance structure as in (27) is used to create an n × n matrix ρ with entries in [0, 1], and a tapered covariance (ρ •P k|k−1 ) is computed. Here, • denotes the element-wise Hadamard or Schur product [61].…”

Section: Localizationmentioning

confidence: 99%

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The Ensemble Kalman filter: a signal processing perspective

Roth

Hendeby

Fritsche

et al. 2017

EURASIP J. Adv. Signal Process.

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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.

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“…This result has been established from different theoretical perspectives [26][27][28]31]. For nonlinear systems, the convergence is not as tangible.…”

Section: Asymptotic Convergence Resultsmentioning

confidence: 93%

“…Under the assumption of the structure in (27), a local analysis would amount to an EnKF update of the x 1 -and x 2 -components only, to avoid errors in x 3 .…”

Section: Localizationmentioning

confidence: 99%

Section: Reviewmentioning

confidence: 99%

Section: Localizationmentioning

confidence: 99%

See 2 more Smart Citations

The Ensemble Kalman filter: a signal processing perspective

Roth

Hendeby

Fritsche

et al. 2017

EURASIP J. Adv. Signal Process.

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“…In particular, a result that for linear systems the EnKF converges to the KF as the number of ensemble members tends to infinity has been reported by different authors [12][13][14] rather recently.…”

Section: Introductionmentioning

confidence: 96%

The ensemble Kalman filter and its relations to other nonlinear filters

Roth

Fritsche

Hendeby

et al. 2015

2015 23rd European Signal Processing Conference (EUSIPCO)

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The Ensemble Kalman filter (EnKF) is a standard algorithm in oceanography and meteorology, where it has got thousands of citations. It is in these communities appreciated since it scales much better with state dimension n than the standard Kalman filter (KF). In short, the EnKF propagates ensembles with N state realizations instead of mean values and covariance matrices and thereby avoids the computational and storage burden of working on n × n matrices. Perhaps surprising, very little attention has been devoted to the EnKF in the signal processing community. In an attempt to change this, we present the EnKF in a Kalman filtering context. 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 in general. A simulation example shows the EnKF performance in a space debris tracking application.

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