Kalman filtering in triplet Markov chains

Boujemaa Ait-El-Fquih*, François Desbouvries

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

35 Scopus citations


Let x = {Xn}nεIN be a hidden process, y = {Yn}nεIN an observed process, and r = {rn}nεIN some additional process. We assume that t = (x r y) is a (so-called "Triplet") vector Markov chain (TMC). We first show that the linear TMC model encompasses and generalizes, among other models, the classical state-space systems with colored process and/or measurement noise(s). We next propose restoration Kalman-like filters for arbitrary linear Gaussian (LG) TMC.

Original languageEnglish (US)
Pages (from-to)2957-2963
Number of pages7
JournalIEEE Transactions on Signal Processing
Issue number8
StatePublished - Aug 2006
Externally publishedYes


  • Bayesian signal restoration
  • Hidden Markov chains Kalman filtering
  • Markovian models
  • Triplet Markov chains

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering


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