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

Handle URI:
http://hdl.handle.net/10754/575243
Title:
Fast Kalman-like filtering for large-dimensional linear and Gaussian state-space models
Authors:
Ait-El-Fquih, Boujemaa; Hoteit, Ibrahim ( 0000-0002-3751-4393 )
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.
KAUST Department:
Applied Mathematics and Computational Science Program
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
Issue Date:
13-Aug-2015
DOI:
10.1109/TSP.2015.2468674
Type:
Article
ISSN:
1053-587X; 1941-0476
Additional Links:
http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=7194838
Appears in Collections:
Articles; Applied Mathematics and Computational Science Program

Full metadata record

DC FieldValue Language
dc.contributor.authorAit-El-Fquih, Boujemaaen
dc.contributor.authorHoteit, Ibrahimen
dc.date.accessioned2015-08-19T12:30:46Zen
dc.date.available2015-08-19T12:30:46Zen
dc.date.issued2015-08-13en
dc.identifier.citationFast Kalman-like filtering for large-dimensional linear and Gaussian state-space models 2015:1 IEEE Transactions on Signal Processingen
dc.identifier.issn1053-587Xen
dc.identifier.issn1941-0476en
dc.identifier.doi10.1109/TSP.2015.2468674en
dc.identifier.urihttp://hdl.handle.net/10754/575243en
dc.description.abstractThis 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.en
dc.language.isoenen
dc.publisherInstitute of Electrical and Electronics Engineers (IEEE)en
dc.relation.urlhttp://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=7194838en
dc.rights(c) 2015 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.en
dc.titleFast Kalman-like filtering for large-dimensional linear and Gaussian state-space modelsen
dc.typeArticleen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.identifier.journalIEEE Transactions on Signal Processingen
dc.eprint.versionPost-printen
dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)en
kaust.authorAit-El-Fquih, Boujemaaen
kaust.authorHoteit, Ibrahimen
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