A localization technique for ensemble Kalman filters

Bergemann, Kay; Reich, Sebastian

doi:10.1002/qj.591

Cited by 60 publications

(88 citation statements)

References 30 publications

(86 reference statements)

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“…The mean of the analyzed ensemble is computed from the standard KF analysis equation and used to obtain the analyzed ensemble. In [38], Bergemann et al present another formulation of the analysis step using ODEs. In this scheme, the analyzed ensemble is directly obtained as a solution of the ODEs over a time step.…”

Section: Ensemble Based Kalman-bucy Filtersmentioning

confidence: 99%

“…In this scheme, the analyzed ensemble is directly obtained as a solution of the ODEs over a time step. Amezcua et al [39] provide a discussion on the above approaches [37,38]. They point out that in both of these approaches the stability of the filter depends on the ratio of the forecast error covariance to the observation error covariance.…”

Section: Ensemble Based Kalman-bucy Filtersmentioning

confidence: 99%

“…The results indicate that the proposed method has better performance compared to the EnKF. In [50], Reich incorporates the Gaussian mixture prior and posterior distributions in a continuous formulation of the EnKF [38]. Initially, the expectation maximization algorithm is used to determine the parameters of the Gaussian mixture distribution from the forecast ensemble.…”

Section: Enkf With Gaussian Mixture Modelsmentioning

confidence: 99%

“…They conclude that this distance dependent reduction of covariance reduces spurious correlations and the optimal design of the correlation function strongly depends on the size of the ensemble. Bergemann et al [38] introduce covariance localization in the continuous formulation of the EnKF. They also employ the Schur product between the covariance and the correlation functions to eliminate spurious correlations.…”

Section: Covariance Localizationmentioning

confidence: 99%

“…It is shown that simultaneous estimation of the inflation factor and measurement error statistics gives better results. Reich [61] extends the inflation technique to the continuous formulation of the EnKF [38]. An additional term is introduced in the continuous analysis equations that does not affect the mean of the ensemble but causes a slight increase in the ensemble deviations.…”

Section: Inflationmentioning

confidence: 99%

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Distributed ensemble Kalman filtering

Shahid

Üstebay

Coates

2014

2014 IEEE 8th Sensor Array and Multichannel Signal Processing Workshop (SAM)

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Distributed estimation in a wireless sensor network has many advantages. It eliminates the need of the centralized knowledge of the measurement model parameters and does not have a single point of failure. Also, any sensor node can be queried to retrieve the state estimate. Furthermore, for high dimensional measurements, local processing of information also results in a significant reduction in the communication overhead.The existing distributed Kalman filtering schemes have good computational and communication efficiency, but do not work well for non-linear and non-Gaussian problems. On the other hand, the distributed particle filtering schemes handle the non-linearities well, but have a much higher computational and communication cost.In this thesis, we propose novel distributed filtering schemes based on the ensemble Kalman filter (EnKF). We consider three forms of the EnKF and express their update equations in an alternative information form. This allows us to use the randomized gossip algorithm to reach consensus on the sufficient statistics and perform local updates. The simulation results show that all three forms of the EnKF have a considerably lower computational cost compared to the particle filters. The results suggest that the proposed distributed schemes outperform the existing state-of-the-art distributed filtering schemes in two scenarios, a) linear measurement model with non-linear state dynamics, and b) high dimensional measurements (model parameters known everywhere in the network) with nonlinear measurement model and state dynamics. In both of these scenarios, the proposed schemes achieve an estimation accuracy comparable to the existing state-of-the-art schemes while significantly reducing the communication cost.ii Résumé L'estimation distribuée dans un réseau de capteurs sans fil possède plusieurs avantages. Ellé elimine le besoin d'une connaissance centralisée des paramtres du modèle de mesure et n'a pas un point de défaillance unique. Aussi, n'importe quel agent-capteur peut-être consulté pour obtenir une approximation de l'état général. De plus, pour des mesures de hautes dimensions, le calcul local d'informations résulte en une réduction significative des coûts de communication.Les implémentations courantes du filtre de Kalman sont efficaces sur les plans de la charge de calcul et de la communication mais ne le sont pas pour les problmes non-linéaires et non-gaussiens. D'un autre côté, les techniques distribuées de filtrage particulaire gèrent avec succès les cas non-linéaires mais sont coûteuses sur les plans de la charge de calcul et de la communication.Dans cette thèse, nous proposons des techniques de filtrage distribué basées sur le filtre de Kalman d'ensemble (FKEn). Nous considérons trois formes du FKEn et exprimons leurséquations de changement sous une forme alternative. Cela nous permet d'utiliser un algorithme de gossip aléatoire afin d'atteindre un consensus sur les statistiques suffisantes et calculer les changements locaux. Les résultats des simulations montrent que ...

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Section: Ensemble Based Kalman-bucy Filtersmentioning

confidence: 99%

Section: Ensemble Based Kalman-bucy Filtersmentioning

confidence: 99%

Section: Enkf With Gaussian Mixture Modelsmentioning

confidence: 99%

Section: Covariance Localizationmentioning

confidence: 99%

Section: Inflationmentioning

confidence: 99%

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Distributed ensemble Kalman filtering

Shahid

Üstebay

Coates

2014

2014 IEEE 8th Sensor Array and Multichannel Signal Processing Workshop (SAM)

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Ensemble transform Kalman–Bucy filters

Amezcua

Ide

Kalnay

et al. 2013

Quart J Royal Meteoro Soc

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Two recent works have adapted the Kalman-Bucy filter into an ensemble setting. In the first formulation, the ensemble of perturbations is updated by the solution of an ordinary differential equation (ODE) in pseudo-time, while the mean is updated as in the standard Kalman filter. In the second formulation, the full ensemble is updated in the analysis step as the solution of single set of ODEs in pseudo-time. Neither requires matrix inversions except for the frequently diagonal observation error covariance.We analyse the behaviour of the ODEs involved in these formulations. We demonstrate that they stiffen for large magnitudes of the ratio of background error to observational error variance, and that using the integration scheme proposed in both formulations can lead to failure. A numerical integration scheme that is both stable and is not computationally expensive is proposed. We develop transform-based alternatives for these Bucy-type approaches so that the integrations are computed in ensemble space where the variables are weights (of dimension equal to the ensemble size) rather than model variables.Finally, the performance of our ensemble transform Kalman-Bucy implementations is evaluated using three models: the 3-variable Lorenz 1963 model, the 40-variable Lorenz 1996 model, and a medium complexity atmospheric general circulation model known as SPEEDY. The results from all three models are encouraging and warrant further exploration of these assimilation techniques.

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A mollified ensemble Kalman filter

Bergemann

Reich

2010

Quart J Royal Meteoro Soc

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It is well recognized that discontinuous analysis increments of sequential data assimilation systems, such as ensemble Kalman filters, might lead to spurious high-frequency adjustment processes in the model dynamics. Various methods have been devised to spread out the analysis increments continuously over a fixed time interval centred about the analysis time. Among these techniques are nudging and incremental analysis updates (IAU). Here we propose another alternative, which may be viewed as a hybrid of nudging and IAU and which arises naturally from a recently proposed continuous formulation of the ensemble Kalman analysis step. A new slow-fast extension of the popular Lorenz-96 model is introduced to demonstrate the properties of the proposed mollified ensemble Kalman filter.

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A localization technique for ensemble Kalman filters

Cited by 60 publications

References 30 publications

Distributed ensemble Kalman filtering

Distributed ensemble Kalman filtering

Ensemble transform Kalman–Bucy filters

A mollified ensemble Kalman filter

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