Kalman filtering in triplet Markov chains

Boujemaa Ait-El-Fquih; François Desbouvries

doi:10.1109/TSP.2006.877651

Kalman filtering in triplet Markov chains

Boujemaa Ait-El-Fquih^*, François Desbouvries

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

35 Scopus citations

Abstract

Let x = {X_n}_nεIN be a hidden process, y = {Y_n}_nεIN an observed process, and r = {r_n}_nεIN some additional process. We assume that t = (x r y) is a (so-called "Triplet") vector Markov chain (TMC). We first show that the linear TMC model encompasses and generalizes, among other models, the classical state-space systems with colored process and/or measurement noise(s). We next propose restoration Kalman-like filters for arbitrary linear Gaussian (LG) TMC.

Original language	English (US)
Pages (from-to)	2957-2963
Number of pages	7
Journal	IEEE Transactions on Signal Processing
Volume	54
Issue number	8
DOIs	https://doi.org/10.1109/TSP.2006.877651
State	Published - Aug 2006
Externally published	Yes

Keywords

Bayesian signal restoration
Hidden Markov chains Kalman filtering
Markovian models
Triplet Markov chains

ASJC Scopus subject areas

Signal Processing
Electrical and Electronic Engineering

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10.1109/TSP.2006.877651

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keywords = "Bayesian signal restoration, Hidden Markov chains Kalman filtering, Markovian models, Triplet Markov chains",

author = "Boujemaa Ait-El-Fquih and Fran{\c c}ois Desbouvries",

year = "2006",

month = aug,

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T1 - Kalman filtering in triplet Markov chains

AU - Ait-El-Fquih, Boujemaa

AU - Desbouvries, François

PY - 2006/8

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AB - Let x = {Xn}nεIN be a hidden process, y = {Yn}nεIN an observed process, and r = {rn}nεIN some additional process. We assume that t = (x r y) is a (so-called "Triplet") vector Markov chain (TMC). We first show that the linear TMC model encompasses and generalizes, among other models, the classical state-space systems with colored process and/or measurement noise(s). We next propose restoration Kalman-like filters for arbitrary linear Gaussian (LG) TMC.

KW - Bayesian signal restoration

KW - Hidden Markov chains Kalman filtering

KW - Markovian models

KW - Triplet Markov chains

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M3 - Article

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EP - 2963

JO - IEEE Transactions on Signal Processing

JF - IEEE Transactions on Signal Processing

IS - 8

ER -

Kalman filtering in triplet Markov chains

Abstract

Keywords

ASJC Scopus subject areas

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