Cluster ensemble Kalman filter

Smith, Keston W.

doi:10.1111/j.1600-0870.2007.00246.x

Cited by 43 publications

(45 citation statements)

References 11 publications

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“…This idea is similar to that in Smith (2007), Luo et al (2010), and Hoteit et al (2012), who randomly sampled the particles while preserving the first two moments of the analysis pdf. First, we rewrite the sample covariance of the analysis ensemble as…”

Section: A Deterministic Resampling Proceduresmentioning

confidence: 99%

“…The particles are then resampled before applying the Kalman update to the ensemble members as in the EnKF. These algorithms use distinct clustering techniques and/or resampling strategies in the update step (e.g., Bengtsson et al 2003;Smith 2007;Sondergaard and Lermusiaux 2013). The reader may refer to Frei and Künsch (2013b) for a thorough discussion about this class of methods.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: A Deterministic Resampling Proceduresmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Efficient Kernel-Based Ensemble Gaussian Mixture Filtering

Liu

Ait‐El‐Fquih

Hoteit

2016

Monthly Weather Review

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“…This is possible, as well, by other means, for instance in the GMM-EnKF filter proposed by Smith in [29], the number of mixture components relies on the Akaie's Information Criteria (AIC)…”

Section: Gaussian Mixture Models Based Filtersmentioning

confidence: 99%

A Robust Non-Gaussian Data Assimilation Method for Highly Non-Linear Models

2018

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Abstract:In this paper, we propose an efficient EnKF implementation for non-Gaussian data assimilation based on Gaussian Mixture Models and Markov-Chain-Monte-Carlo (MCMC) methods. The proposed method works as follows: based on an ensemble of model realizations, prior errors are estimated via a Gaussian Mixture density whose parameters are approximated by means of an Expectation Maximization method. Then, by using an iterative method, observation operators are linearized about current solutions and posterior modes are estimated via a MCMC implementation. The acceptance/rejection criterion is similar to that of the Metropolis-Hastings rule. Experimental tests are performed on the Lorenz 96 model. The results show that the proposed method can decrease prior errors by several order of magnitudes in a root-mean-square-error sense for nearly sparse or dense observational networks.

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“…This idea began with the work of Alspach and Sorenson (1972). Since then, Anderson and Anderson (1999), Chen and Liu (2000), Bengtsson et al (2003), Kotecha and Djurić (2003), Smith (2007), Hoteit et al (2008), Dovera and Rossa (2011), Stordal et al (2011), Reich (2012), Frei and Künsch (2013), Sondergaard and Lermusiaux (2013a, b) and many others have developed similar approaches. In particular, all of these techniques followed from adaptations of BPF or the ensemble Kalman filter (EnKF; Evensen, 1994.…”

Section: Introductionmentioning

confidence: 99%

A potential implicit particle method for high-dimensional systems

Weir

Miller

Spitz

2013

Nonlin. Processes Geophys.

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Abstract. This paper presents a particle method designed for high-dimensional state estimation. Instead of weighing random forecasts by their distance to given observations, the method samples an ensemble of particles around an optimal solution based on the observations (i.e., it is implicit). It differs from other implicit methods because it includes the state at the previous assimilation time as part of the optimal solution (i.e., it is a lag-1 smoother). This is accomplished through the use of a mixture model for the background distribution of the previous state. In a high-dimensional, linear, Gaussian example, the mixture-based implicit particle smoother does not collapse. Furthermore, using only a small number of particles, the implicit approach is able to detect transitions in two nonlinear, multi-dimensional generalizations of a double-well. Adding a step that trains the sampled distribution to the target distribution prevents collapse during the transitions, which are strongly nonlinear events. To produce similar estimates, other approaches require many more particles.

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Cluster ensemble Kalman filter

Cited by 43 publications

References 11 publications

Efficient Kernel-Based Ensemble Gaussian Mixture Filtering

Efficient Kernel-Based Ensemble Gaussian Mixture Filtering

A Robust Non-Gaussian Data Assimilation Method for Highly Non-Linear Models

A potential implicit particle method for high-dimensional systems

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