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 - https://www.scopus.com/pages/publications/33947158187
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 -