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    Fast Kalman-like filtering for large-dimensional linear and Gaussian state-space models

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    Type
    Article
    Authors
    Ait-El-Fquih, Boujemaa
    Hoteit, Ibrahim cc
    KAUST Department
    Applied Mathematics and Computational Science Program
    Earth Fluid Modeling and Prediction Group
    Earth Science and Engineering Program
    Physical Science and Engineering (PSE) Division
    Date
    2015-08-14
    Online Publication Date
    2015-08-14
    Print Publication Date
    2015-11
    Permanent link to this record
    http://hdl.handle.net/10754/575243
    
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    Abstract
    This paper considers the filtering problem for linear and Gaussian state-space models with large dimensions, a setup in which the optimal Kalman Filter (KF) might not be applicable owing to the excessive cost of manipulating huge covariance matrices. Among the most popular alternatives that enable cheaper and reasonable computation is the Ensemble KF (EnKF), a Monte Carlo-based approximation. In this paper, we consider a class of a posteriori distributions with diagonal covariance matrices and propose fast approximate deterministic-based algorithms based on the Variational Bayesian (VB) approach. More specifically, we derive two iterative KF-like algorithms that differ in the way they operate between two successive filtering estimates; one involves a smoothing estimate and the other involves a prediction estimate. Despite its iterative nature, the prediction-based algorithm provides a computational cost that is, on the one hand, independent of the number of iterations in the limit of very large state dimensions, and on the other hand, always much smaller than the cost of the EnKF. The cost of the smoothing-based algorithm depends on the number of iterations that may, in some situations, make this algorithm slower than the EnKF. The performances of the proposed filters are studied and compared to those of the KF and EnKF through a numerical example.
    Citation
    Fast Kalman-like filtering for large-dimensional linear and Gaussian state-space models 2015:1 IEEE Transactions on Signal Processing
    Publisher
    Institute of Electrical and Electronics Engineers (IEEE)
    Journal
    IEEE Transactions on Signal Processing
    DOI
    10.1109/TSP.2015.2468674
    Additional Links
    http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=7194838
    ae974a485f413a2113503eed53cd6c53
    10.1109/TSP.2015.2468674
    Scopus Count
    Collections
    Articles; Applied Mathematics and Computational Science Program; Physical Science and Engineering (PSE) Division; Earth Science and Engineering Program

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