Bayesian fixed-interval smoothing algorithms in singular state-space systems

B. Ait-El-Fquih; F. Desbouvries

doi:10.1109/MLSP.2009.5306257

Bayesian fixed-interval smoothing algorithms in singular state-space systems

B. Ait-El-Fquih^*, F. Desbouvries

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Scopus citations

Abstract

Fixed-interval Bayesian smoothing in state-space systems has been addressed for a long time. However, as far as the measurement noise is concerned, only two cases have been addressed so far: the regular case, i.e. with positive definite covariance matrix; and the perfect measurement case, i.c, with zero measurement noise. In this paper we address the smoothing problem in the intermediate case where the measurement noise covariance is positive semi definite (p.s.d.) with arbitrary rank. We exploit the singularity of the model in order to transform the original state-space system into a pairwise Markov chain (PMC) with reduced state dimension. Finally, the a posteriori Markovianity of the reduced state enables us to propose a family of fixed-interval smoothing algorithms.

Original language	English (US)
Title of host publication	Machine Learning for Signal Processing XIX - Proceedings of the 2009 IEEE Signal Processing Society Workshop, MLSP 2009
DOIs	https://doi.org/10.1109/MLSP.2009.5306257
State	Published - 2009
Externally published	Yes
Event	Machine Learning for Signal Processing XIX - 2009 IEEE Signal Processing Society Workshop, MLSP 2009 - Grenoble, France Duration: Sep 2 2009 → Sep 4 2009

Publication series

Name	Machine Learning for Signal Processing XIX - Proceedings of the 2009 IEEE Signal Processing Society Workshop, MLSP 2009

Other

Other	Machine Learning for Signal Processing XIX - 2009 IEEE Signal Processing Society Workshop, MLSP 2009
Country/Territory	France
City	Grenoble
Period	09/2/09 → 09/4/09

ASJC Scopus subject areas

Human-Computer Interaction
Signal Processing
Education

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10.1109/MLSP.2009.5306257

Cite this

Ait-El-Fquih, B., & Desbouvries, F. (2009). Bayesian fixed-interval smoothing algorithms in singular state-space systems. In Machine Learning for Signal Processing XIX - Proceedings of the 2009 IEEE Signal Processing Society Workshop, MLSP 2009 Article 5306257 (Machine Learning for Signal Processing XIX - Proceedings of the 2009 IEEE Signal Processing Society Workshop, MLSP 2009). https://doi.org/10.1109/MLSP.2009.5306257

@inproceedings{37f8104abcc242a3ad385fb5e14a74a1,

title = "Bayesian fixed-interval smoothing algorithms in singular state-space systems",

abstract = "Fixed-interval Bayesian smoothing in state-space systems has been addressed for a long time. However, as far as the measurement noise is concerned, only two cases have been addressed so far: the regular case, i.e. with positive definite covariance matrix; and the perfect measurement case, i.c, with zero measurement noise. In this paper we address the smoothing problem in the intermediate case where the measurement noise covariance is positive semi definite (p.s.d.) with arbitrary rank. We exploit the singularity of the model in order to transform the original state-space system into a pairwise Markov chain (PMC) with reduced state dimension. Finally, the a posteriori Markovianity of the reduced state enables us to propose a family of fixed-interval smoothing algorithms.",

author = "B. Ait-El-Fquih and F. Desbouvries",

year = "2009",

doi = "10.1109/MLSP.2009.5306257",

language = "English (US)",

isbn = "9781424449484",

series = "Machine Learning for Signal Processing XIX - Proceedings of the 2009 IEEE Signal Processing Society Workshop, MLSP 2009",

booktitle = "Machine Learning for Signal Processing XIX - Proceedings of the 2009 IEEE Signal Processing Society Workshop, MLSP 2009",

note = "Machine Learning for Signal Processing XIX - 2009 IEEE Signal Processing Society Workshop, MLSP 2009 ; Conference date: 02-09-2009 Through 04-09-2009",

}

Ait-El-Fquih, B & Desbouvries, F 2009, Bayesian fixed-interval smoothing algorithms in singular state-space systems. in Machine Learning for Signal Processing XIX - Proceedings of the 2009 IEEE Signal Processing Society Workshop, MLSP 2009., 5306257, Machine Learning for Signal Processing XIX - Proceedings of the 2009 IEEE Signal Processing Society Workshop, MLSP 2009, Machine Learning for Signal Processing XIX - 2009 IEEE Signal Processing Society Workshop, MLSP 2009, Grenoble, France, 09/2/09. https://doi.org/10.1109/MLSP.2009.5306257

Bayesian fixed-interval smoothing algorithms in singular state-space systems. / Ait-El-Fquih, B.; Desbouvries, F.
Machine Learning for Signal Processing XIX - Proceedings of the 2009 IEEE Signal Processing Society Workshop, MLSP 2009. 2009. 5306257 (Machine Learning for Signal Processing XIX - Proceedings of the 2009 IEEE Signal Processing Society Workshop, MLSP 2009).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - Fixed-interval Bayesian smoothing in state-space systems has been addressed for a long time. However, as far as the measurement noise is concerned, only two cases have been addressed so far: the regular case, i.e. with positive definite covariance matrix; and the perfect measurement case, i.c, with zero measurement noise. In this paper we address the smoothing problem in the intermediate case where the measurement noise covariance is positive semi definite (p.s.d.) with arbitrary rank. We exploit the singularity of the model in order to transform the original state-space system into a pairwise Markov chain (PMC) with reduced state dimension. Finally, the a posteriori Markovianity of the reduced state enables us to propose a family of fixed-interval smoothing algorithms.

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Ait-El-Fquih B, Desbouvries F. Bayesian fixed-interval smoothing algorithms in singular state-space systems. In Machine Learning for Signal Processing XIX - Proceedings of the 2009 IEEE Signal Processing Society Workshop, MLSP 2009. 2009. 5306257. (Machine Learning for Signal Processing XIX - Proceedings of the 2009 IEEE Signal Processing Society Workshop, MLSP 2009). doi: 10.1109/MLSP.2009.5306257

Bayesian fixed-interval smoothing algorithms in singular state-space systems

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