Multimodal ensemble Kalman filtering using Gaussian mixture models

Dovera, Laura; Rossa, Ernesto Della

doi:10.1007/s10596-010-9205-3

Cited by 106 publications

(56 citation statements)

References 26 publications

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“…To relax the Gaussian assumption, two paradigms are predominant: mixture filters that approximate the forecast distribution as a mixture of Gaussian distributions (Bengtsson et al, 2003;Sun et al, 2009;Dovera & Della Rossa, 2011;Stordal et al, 2011;Hoteit et al, 2012;Rezaie & Eidsvik, 2012;Frei & Künsch, 2013), and sequential importance samplers that use the ensemble Kalman filter as a proposal distribution (Mandel & Beezley, 2009;Papadakis et al, 2010). In this article, we introduce an update scheme that blends these: a Gaussian mixture proposal obtained from an ensemble Kalman filter update based on a tempered likelihood is corrected by a particle filter update.…”

Section: Introductionmentioning

confidence: 99%

Bridging the ensemble Kalman and particle filters

2013

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SUMMARYIn many applications of Monte Carlo nonlinear filtering, the propagation step is computationally expensive, and hence the sample size is limited. With small sample sizes, the update step becomes crucial. Particle filtering suffers from the well-known problem of sample degeneracy. Ensemble Kalman filtering avoids this, at the expense of treating non-Gaussian features of the forecast distribution incorrectly. Here we introduce a procedure that makes a continuous transition indexed by γ ∈ [0, 1] between the ensemble and the particle filter update. We propose automatic choices of the parameter γ such that the update stays as close as possible to the particle filter update subject to avoiding degeneracy. In various examples, we show that this procedure leads to updates that are able to handle non-Gaussian features of the forecast sample even in high-dimensional situations.

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Section: Introductionmentioning

confidence: 99%

Bridging the ensemble Kalman and particle filters

2013

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“…Researchers have presented several methods including Gaussian mixture models, truncated pluri-Gaussian method, level set method, discrete cosine transform, and other principal component analysis methods. Dovera and Rossa (2011) proposed expressions of conditional means, covariances, and weights for Gaussian mixture models, so that the ensemble Kalman filter algorithm (EnKF) became usable in this case. Liu and Oliver (2005a, b) combined EnKF with a truncated pluri-Gaussian method for history matching of reservoir facies.…”

Section: Automatic History Matchingmentioning

confidence: 99%

A review of closed-loop reservoir management

Hou

Zhou

Zhang³

et al. 2015

Pet. Sci.

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The closed-loop reservoir management technique enables a dynamic and real-time optimal production schedule under the existing reservoir conditions to be achieved by adjusting the injection and production strategies. This is one of the most effective ways to exploit limited oil reserves more economically and efficiently. There are two steps in closed-loop reservoir management: automatic history matching and reservoir production optimization. Both of the steps are large-scale complicated optimization problems. This paper gives a general review of the two basic techniques in closed-loop reservoir management; summarizes the applications of gradient-based algorithms, gradient-free algorithms, and artificial intelligence algorithms; analyzes the characteristics and application conditions of these optimization methods; and finally discusses the emphases and directions of future research on both automatic history matching and reservoir production optimization.

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“…In [41], Dovera et al have extended the EnKF to incorporate multimodal distributions. They model the multimodal prior distributions using a Gaussian mixture.…”

Section: Enkf With Gaussian Mixture Modelsmentioning

confidence: 99%

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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Multimodal ensemble Kalman filtering using Gaussian mixture models

Cited by 106 publications

References 26 publications

Bridging the ensemble Kalman and particle filters

Bridging the ensemble Kalman and particle filters

A review of closed-loop reservoir management

Distributed ensemble Kalman filtering

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