Bridging the ensemble Kalman and particle filters

Frei, Mario; Künsch, Hans R.

doi:10.1093/biomet/ast020

Cited by 76 publications

(132 citation statements)

References 48 publications

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“…The well-known challenges, mostly related to the problem of importance sampling in high dimensions, are reviewed in [48,49]. Several recent approaches [50][51][52] were successfully tested on a popular EnKF benchmark problem [53] that is also investigated in Section 7.4. Combinations of the EnKF with the deterministic sampling of sigma point filters [5] are given in [54] and [55].…”

Section: Reviewmentioning

confidence: 99%

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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Section: Reviewmentioning

confidence: 99%

The Ensemble Kalman filter: a signal processing perspective

Roth

Hendeby

Fritsche

et al. 2017

EURASIP J. Adv. Signal Process.

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“…A similar EM-BIC approach following Tagade et al (2014) further proposed sampling directly from the posterior GM, while only matching its first moment by applying a modified Kalman update to the forecast particles. Frei and Künsch (2013a) resorted to the so-called progressive correction idea of Musso et al (2001) to propose a GM filter that allows a smooth transition, somehow tuned by a transition parameter, between the PF and the EnKF. The resulting Kalman gain involves the same formula as in the EnGMF in which the transition parameter plays the role of the bandwidth parameter.…”

Section: Other Variants Of Gaussian Mixture Filteringmentioning

confidence: 99%

Efficient Kernel-Based Ensemble Gaussian Mixture Filtering

Liu

Ait‐El‐Fquih

Hoteit

2016

Monthly Weather Review

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The Bayesian filtering problem for data assimilation is considered following the kernel-based ensemble Gaussian mixture filtering (EnGMF) approach introduced by Anderson and Anderson. In this approach, the posterior distribution of the system state is propagated with the model using the ensemble Monte Carlo method, providing a forecast ensemble that is then used to construct a prior Gaussian mixture (GM) based on the kernel density estimator. This results in two update steps: a Kalman filter (KF)-like update of the ensemble members and a particle filter (PF)-like update of the weights, followed by a resampling step to start a new forecast cycle. After formulating EnGMF for any observational operator, the influence of the bandwidth parameter of the kernel function on the covariance of the posterior distribution is analyzed. Then the focus is on two aspects: (i) the efficient implementation of EnGMF with (relatively) small ensembles, where a new deterministic resampling strategy is proposed preserving the first two moments of the posterior GM to limit the sampling error; and (ii) the analysis of the effect of the bandwidth parameter on contributions of KF and PF updates and on the weights variance. Numerical results using the Lorenz-96 model are presented to assess the behavior of EnGMF with deterministic resampling, study its sensitivity to different parameters and settings, and evaluate its performance against ensemble KFs. The proposed EnGMF approach with deterministic resampling suggests improved estimates in all tested scenarios, and is shown to require less localization and to be less sensitive to the choice of filtering parameters.

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“…As a consequence, they can benefit from each other with a combination. A similar effort towards this goal is the ensemble Kalman particle filter (EnKPF) proposed by Frei and Künsch (Frei and Künsch, 2013), which is a mixture of the stochastic EnKF and PF. However, the EAKF and SIR-PF can also be combined with the same manner, producing a new mixture filter.…”

Section: The Ensemble Adjustment Kalman Particle Filter (Eakpf)mentioning

confidence: 99%

“…The rationale behind this two-stage procedure is to achieve a compromise between ensemble diversity and systematic error due to nonGaussian feature of the prior (Frei and Künsch, 2013). The parameter γ controls the trade-off between a correct analysis and the diversity of the ensemble.…”

Section: Algorithm Of the Eakpfmentioning

confidence: 99%

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Comparison and combination of EAKF and SIR-PF in the Bayesian filter framework

Shen¹,

Zhang²,

Tang

2016

Acta Oceanol. Sin.

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Bayesian estimation theory provides a general approach for the state estimate of linear or nonlinear and Gaussian or non-Gaussian systems. In this study, we first explore two Bayesian-based methods: ensemble adjustment Kalman filter (EAKF) and sequential importance resampling particle filter (SIR-PF), using a well-known nonlinear and non-Gaussian model (Lorenz '63 model). The EAKF, which is a deterministic scheme of the ensemble Kalman filter (EnKF), performs better than the classical (stochastic) EnKF in a general framework. Comparison between the SIR-PF and the EAKF reveals that the former outperforms the latter if ensemble size is so large that can avoid the filter degeneracy, and vice versa. The impact of the probability density functions and effective ensemble sizes on assimilation performances are also explored. On the basis of comparisons between the SIR-PF and the EAKF, a mixture filter, called ensemble adjustment Kalman particle filter (EAKPF), is proposed to combine their both merits. Similar to the ensemble Kalman particle filter, which combines the stochastic EnKF and SIR-PF analysis schemes with a tuning parameter, the new mixture filter essentially provides a continuous interpolation between the EAKF and SIR-PF. The same Lorenz '63 model is used as a testbed, showing that the EAKPF is able to overcome filter degeneracy while maintaining the non-Gaussian nature, and performs better than the EAKF given limited ensemble size.

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Bridging the ensemble Kalman and particle filters

Cited by 76 publications

References 48 publications

The Ensemble Kalman filter: a signal processing perspective

The Ensemble Kalman filter: a signal processing perspective

Efficient Kernel-Based Ensemble Gaussian Mixture Filtering

Comparison and combination of EAKF and SIR-PF in the Bayesian filter framework

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