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dc.contributor.authorStordal, Andreas Størkseneng
dc.contributor.authorKarlsen, Hans A.eng
dc.contributor.authorNævdal, Geireng
dc.contributor.authorSkaug, Hans J.eng
dc.contributor.authorVallès, Briceeng
dc.PublishedComputational Geosciences 1-13en_US
dc.description.abstractThe nonlinear filtering problem occurs in many scientific areas. Sequential Monte Carlo solutions with the correct asymptotic behavior such as particle filters exist, but they are computationally too expensive when working with high-dimensional systems. The ensemble Kalman filter (EnKF) is a more robust method that has shown promising results with a small sample size, but the samples are not guaranteed to come from the true posterior distribution. By approximating the model error with a Gaussian distribution, one may represent the posterior distribution as a sum of Gaussian kernels. The resulting Gaussian mixture filter has the advantage of both a local Kalman type correction and the weighting/resampling step of a particle filter. The Gaussian mixture approximation relies on a bandwidth parameter which often has to be kept quite large in order to avoid a weight collapse in high dimensions. As a result, the Kalman correction is too large to capture highly non-Gaussian posterior distributions. In this paper, we have extended the Gaussian mixture filter (Hoteit et al., Mon Weather Rev 136:317–334, 2008) and also made the connection to particle filters more transparent. In particular, we introduce a tuning parameter for the importance weights. In the last part of the paper, we have performed a simulation experiment with the Lorenz40 model where our method has been compared to the EnKF and a full implementation of a particle filter. The results clearly indicate that the new method has advantages compared to the standard EnKF.en_US
dc.rightsAttribution-NonCommercial CC BY-NCeng
dc.subjectNonlinear filteringeng
dc.subjectData assimilationeng
dc.subjectEnsemble Kalman filtereng
dc.subjectParticle filterseng
dc.titleBridging the ensemble Kalman filter and particle filters: the adaptive Gaussian mixture filteren_US
dc.typePeer reviewed
dc.typeJournal article
dc.rights.holderThe Author(s) 2010en_US
dc.rights.holderCopyright The Author(s) 2010. This article is published with open access at Springerlink.comen_US
dc.subject.nsiVDP::Mathematics and natural science: 400en_US

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