Kalman filtering for triplet Markov Chains: Applications and extensions

B. Ait El Fquih; F. Desbouvries

doi:10.1109/ICASSP.2005.1416101

Kalman filtering for triplet Markov Chains: Applications and extensions

B. Ait El Fquih^*, F. Desbouvries

^*Corresponding author for this work

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

7 Scopus citations

Abstract

An important problem in signal processing consists in estimating an unobservable process x = {x_n}_n∈IN from an observed process y = {y_n}_n∈IN. In Linear Gaussian Hidden Markov Chains (LGHMC), the classical recursive solution is given by the Kalman filter. In this paper, we consider Linear Gaussian Triplet Markov Chains (LGTMC) by assuming that the triplet (x, r, y) (in which r = {r_n} _n∈IN is some additional process) is Markovian and Gaussian. We first show that this model encompasses and generalizes the classical linear stochastic dynamical models with autoregressive process and / or measurement noise. We next propose (for the regular and for the perfect-measurement cases) restoration Kalman-like algorithms for general LGTMC.

Original language	English (US)
Title of host publication	2005 IEEE ICASSP '05 - Proc. - Design and Implementation of Signal Proces.Syst.,Indust. Technol. Track,Machine Learning for Signal Proces. Signal Proces. Education, Spec. Sessions
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	IV685-IV688
ISBN (Print)	0780388747, 9780780388741
DOIs	https://doi.org/10.1109/ICASSP.2005.1416101
State	Published - 2005
Externally published	Yes
Event	2005 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP '05 - Philadelphia, PA, United States Duration: Mar 18 2005 → Mar 23 2005

Publication series

Name	ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Volume	IV
ISSN (Print)	1520-6149

Other

Other	2005 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP '05
Country/Territory	United States
City	Philadelphia, PA
Period	03/18/05 → 03/23/05

ASJC Scopus subject areas

Software
Signal Processing
Electrical and Electronic Engineering

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10.1109/ICASSP.2005.1416101

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Ait El Fquih, B., & Desbouvries, F. (2005). Kalman filtering for triplet Markov Chains: Applications and extensions. In 2005 IEEE ICASSP '05 - Proc. - Design and Implementation of Signal Proces.Syst.,Indust. Technol. Track,Machine Learning for Signal Proces. Signal Proces. Education, Spec. Sessions (pp. IV685-IV688). Article 1416101 (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings; Vol. IV). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ICASSP.2005.1416101

Ait El Fquih, B. ; Desbouvries, F. / Kalman filtering for triplet Markov Chains : Applications and extensions. 2005 IEEE ICASSP '05 - Proc. - Design and Implementation of Signal Proces.Syst.,Indust. Technol. Track,Machine Learning for Signal Proces. Signal Proces. Education, Spec. Sessions. Institute of Electrical and Electronics Engineers Inc., 2005. pp. IV685-IV688 (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings).

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abstract = "An important problem in signal processing consists in estimating an unobservable process x = {xn}n∈IN from an observed process y = {yn}n∈IN. In Linear Gaussian Hidden Markov Chains (LGHMC), the classical recursive solution is given by the Kalman filter. In this paper, we consider Linear Gaussian Triplet Markov Chains (LGTMC) by assuming that the triplet (x, r, y) (in which r = {rn} n∈IN is some additional process) is Markovian and Gaussian. We first show that this model encompasses and generalizes the classical linear stochastic dynamical models with autoregressive process and / or measurement noise. We next propose (for the regular and for the perfect-measurement cases) restoration Kalman-like algorithms for general LGTMC.",

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

year = "2005",

doi = "10.1109/ICASSP.2005.1416101",

language = "English (US)",

isbn = "0780388747",

series = "ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

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booktitle = "2005 IEEE ICASSP '05 - Proc. - Design and Implementation of Signal Proces.Syst.,Indust. Technol. Track,Machine Learning for Signal Proces. Signal Proces. Education, Spec. Sessions",

address = "United States",

note = "2005 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP '05 ; Conference date: 18-03-2005 Through 23-03-2005",

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Ait El Fquih, B & Desbouvries, F 2005, Kalman filtering for triplet Markov Chains: Applications and extensions. in 2005 IEEE ICASSP '05 - Proc. - Design and Implementation of Signal Proces.Syst.,Indust. Technol. Track,Machine Learning for Signal Proces. Signal Proces. Education, Spec. Sessions., 1416101, ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings, vol. IV, Institute of Electrical and Electronics Engineers Inc., pp. IV685-IV688, 2005 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP '05, Philadelphia, PA, United States, 03/18/05. https://doi.org/10.1109/ICASSP.2005.1416101

Kalman filtering for triplet Markov Chains: Applications and extensions. / Ait El Fquih, B.; Desbouvries, F.
2005 IEEE ICASSP '05 - Proc. - Design and Implementation of Signal Proces.Syst.,Indust. Technol. Track,Machine Learning for Signal Proces. Signal Proces. Education, Spec. Sessions. Institute of Electrical and Electronics Engineers Inc., 2005. p. IV685-IV688 1416101 (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings; Vol. IV).

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

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AU - Ait El Fquih, B.

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PY - 2005

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AB - An important problem in signal processing consists in estimating an unobservable process x = {xn}n∈IN from an observed process y = {yn}n∈IN. In Linear Gaussian Hidden Markov Chains (LGHMC), the classical recursive solution is given by the Kalman filter. In this paper, we consider Linear Gaussian Triplet Markov Chains (LGTMC) by assuming that the triplet (x, r, y) (in which r = {rn} n∈IN is some additional process) is Markovian and Gaussian. We first show that this model encompasses and generalizes the classical linear stochastic dynamical models with autoregressive process and / or measurement noise. We next propose (for the regular and for the perfect-measurement cases) restoration Kalman-like algorithms for general LGTMC.

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Ait El Fquih B, Desbouvries F. Kalman filtering for triplet Markov Chains: Applications and extensions. In 2005 IEEE ICASSP '05 - Proc. - Design and Implementation of Signal Proces.Syst.,Indust. Technol. Track,Machine Learning for Signal Proces. Signal Proces. Education, Spec. Sessions. Institute of Electrical and Electronics Engineers Inc. 2005. p. IV685-IV688. 1416101. (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings). doi: 10.1109/ICASSP.2005.1416101

Kalman filtering for triplet Markov Chains: Applications and extensions

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