SSP'05 -- Proceedings

	IEEE/SP 13th workshop on Statistical Signal Processing July, 17-20, 2005 - Bordeaux - France

Information regarding the paper

Title

Bayesian smoothing algorithms in Pairwise and Triplet Markov Chains

Author(s)

Boujemaa Ait-el-Fquih	Institut National des Télécommunications
François Desbouvries	Institut National des Télécommunications

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Abstract

An important problem in signal processing consists in estimating an unobservable process x = \{ x_n \}_{n \in \NN} from an observed process y = \{ y_n \}_{n \in \NN}. 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 = \{ r_n \}_{n \in \NN} 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.