On Bayesian fixed-interval smoothing algorithms

Boujemaa Ait-El-Fquih*, François Desbouvries

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


In this note, we revisit fixed-interval Kalman like smoothing algorithms. We have two results. We first unify the family of existing algorithms by deriving them in a common Bayesian framework; as we shall see, all these algorithms stem from forward and/or backward Markovian properties of the state process, involve one (or two) out of four canonical probability density functions, and can be derived from the systematic use of some generic properties of Gaussian variables which we develop in a specific toolbox. On the other hand the methodology we use enables us to complete the set of existing algorithms by five new Kalman like smoothing algorithms, which is our second result.

Original languageEnglish (US)
Pages (from-to)2437-2442
Number of pages6
JournalIEEE Transactions on Automatic Control
Issue number10
StatePublished - 2008
Externally publishedYes


  • Fixed-interval Kalman smoothing algorithms
  • Hidden Markov chains (HMC)

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


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