@inproceedings{a1ca2d8643044f89b3e7de1280fc31f9,
title = "Kalman filtering for triplet Markov Chains: Applications and extensions",
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",
month = jan,
day = "1",
doi = "10.1109/ICASSP.2005.1416101",
language = "English",
isbn = "0780388747",
series = "ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
pages = "IV685--IV688",
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",
note = "2005 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP '05 ; Conference date: 18-03-2005 Through 23-03-2005",
}