Bridging the ensemble Kalman filter and particle filters: the adaptive Gaussian mixture filter
TypePeer reviewed; Journal article
MetadataShow full item record
The 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.
CitationComputational Geosciences 1-13
Copyright The Author(s) 2010. This article is published with open access at Springerlink.com
The Author(s) 2010
The Author(s) 2010
Except where otherwise noted, this item's license is described as Attribution-NonCommercial CC BY-NC
Showing items related by title, author, creator and subject.
Esperås, Eirik Nymark (The University of Bergen, 2013-09-02)Ein kvantitativ og kvalitativ analyse av innhaldet på norske partileiarars facebooksider i 2012. Studien belyser Facebooks rolle som arena for politisk kommunikasjon, sjølvpresentasjon og veljardialog. Den undersøker ...Master thesis
Gurholt, Tiril Pedersen (The University of Bergen, 2013-10-11)Paper A: 2-D Visualisation of Unstable Waterflood and Polymer Flood for Displacement of Heavy Oil. Full-text not available in BORA. The published version is available at: <a href="http://dx.doi.org/10.2118/154292-ms" ...Doctoral thesis
Evensen, Geir (American Geophysical Union, 1993-05-18)The formulation of consistent boundary conditions for the quasi-geostrophic (QG) model with an extended Kaiman filter in a data assimilation scheme is discussed. To form a well-posed boundary value problem for the QG model, ...Journal article