Exact and approximate Bayesian smoothing algorithms in partially observed Markov Chains

Boujemaa Ait El Fquih*, François Desbouvries

*Corresponding author for this work

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

3 Scopus citations

Abstract

Let x = {xn}n∈IN be a hidden process, y = {yn}n∈IN an observed process and r = {r n}n∈IN some auxiliary process. We assume that t = {tn}n∈IN with tn = (xn, r n, yn-1) is a (Triplet) Markov Chain (TMC). TMC are more general than Hidden Markov Chains (HMC) and yet enable the development of efficient restoration and parameter estimation algorithms. This paper is devoted to Bayesian smoothing algorithms for TMC. We first propose twelve algorithms for general TMC. In the Gaussian case, they reduce to a set of algorithms which includes, among other solutions, extensions to TMC of classical Kalman-like smoothing algorithms such as the RTS algorithms, the Two-Filter algorithm or the Bryson and Frazier algorithm. We finally propose particle filtering (PF) approximations for the general case.

Original languageEnglish (US)
Title of host publicationNSSPW - Nonlinear Statistical Signal Processing Workshop 2006
DOIs
StatePublished - Dec 1 2006
EventNSSPW - Nonlinear Statistical Signal Processing Workshop 2006 - Cambridge, United Kingdom
Duration: Sep 13 2006Sep 15 2006

Publication series

NameNSSPW - Nonlinear Statistical Signal Processing Workshop 2006

Other

OtherNSSPW - Nonlinear Statistical Signal Processing Workshop 2006
CountryUnited Kingdom
CityCambridge
Period09/13/0609/15/06

ASJC Scopus subject areas

  • Signal Processing
  • Statistics, Probability and Uncertainty
  • Electrical and Electronic Engineering
  • Statistics and Probability

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