Kalman filtering for triplet Markov Chains: Applications and extensions

Boujemaa Ait El Fquih*, F. Desbouvries

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

3 Scopus citations

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.

Original languageEnglish (US)
Title of host publication2005 IEEE ICASSP '05 - Proc. - Design and Implementation of Signal Proces.Syst.,Indust. Technol. Track,Machine Learning for Signal Proces. Signal Proces. Education, Spec. Sessions
PublisherInstitute of Electrical and Electronics Engineers Inc.
ISBN (Print)0780388747, 9780780388741
DOIs
StatePublished - Jan 1 2005
Event2005 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP '05 - Philadelphia, PA, United States
Duration: Mar 18 2005Mar 23 2005

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
VolumeIV
ISSN (Print)1520-6149

Other

Other2005 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP '05
CountryUnited States
CityPhiladelphia, PA
Period03/18/0503/23/05

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Electrical and Electronic Engineering

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