TY - GEN

T1 - Bayesian smoothing algorithms in pairwise and triplet Markov chains

AU - Ait-El-Fquih, B.

AU - Desbouvries, F.

PY - 2005/1/1

Y1 - 2005/1/1

N2 - 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), recursive solutions are given by Kalman-like Bayesian restoration algorithms. In this paper, we consider the more general framework of Linear Gaussian Triplet Markov Chains (LGTMC), i.e. of models in which the triplet (x, r, y) (where r = {rn}n∈IN is some additional process) is Markovian and Gaussian. We address fixed-interval smoothing algorithms, and we extend to LGTMC the RTS algorithm by Rauch, Tung and Striebel, as well as the Two-Filter algorithm by Mayne and Fraser and Potter.

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), recursive solutions are given by Kalman-like Bayesian restoration algorithms. In this paper, we consider the more general framework of Linear Gaussian Triplet Markov Chains (LGTMC), i.e. of models in which the triplet (x, r, y) (where r = {rn}n∈IN is some additional process) is Markovian and Gaussian. We address fixed-interval smoothing algorithms, and we extend to LGTMC the RTS algorithm by Rauch, Tung and Striebel, as well as the Two-Filter algorithm by Mayne and Fraser and Potter.

UR - http://www.scopus.com/inward/record.url?scp=33947158187&partnerID=8YFLogxK

U2 - 10.1109/ssp.2005.1628688

DO - 10.1109/ssp.2005.1628688

M3 - Conference contribution

AN - SCOPUS:33947158187

SN - 0780394046

SN - 9780780394049

T3 - IEEE Workshop on Statistical Signal Processing Proceedings

SP - 721

EP - 726

BT - 2005 IEEE/SP 13th Workshop on Statistical Signal Processing - Book of Abstracts

PB - IEEE Computer Society

T2 - 2005 IEEE/SP 13th Workshop on Statistical Signal Processing

Y2 - 17 July 2005 through 20 July 2005

ER -