Fixed-interval kalman smoothing algorithms in singular state-space systems

Boujemaa Ait-El-Fquih, François Desbouvries*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


Fixed-interval Bayesian smoothing in state-space systems has been addressed for a long time. However, as far as the measurement noise is concerned, only two cases have been addressed so far : the regular case, i.e., with positive definite covariance matrix; and the perfect measurement case, i.e., with zero measurement noise. In this paper we address the smoothing problem in the intermediate case where the measurement noise covariance is positive semi definite with arbitrary rank. We exploit the singularity of the model in order to transform the original state-space system into a pairwise Markov model with reduced state dimension. Finally, the a posteriori Markovianity of the reduced state enables us to propose a family of fixed-interval smoothing algorithms.

Original languageEnglish (US)
Pages (from-to)469-478
Number of pages10
JournalJournal of Signal Processing Systems
Issue number3
StatePublished - Dec 2011
Externally publishedYes


  • Bayesian restoration
  • Kalman smoothing
  • Singular systems
  • State-space systems

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Theoretical Computer Science
  • Signal Processing
  • Information Systems
  • Modeling and Simulation
  • Hardware and Architecture


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