Convergence of discrete-time Kalman filter estimate to continuous time estimate

Atte Aalto*

*Corresponding author for this work

Research output: Contribution to journalArticleResearchpeer-review

6 Citations (Scopus)


This article is concerned with the convergence of the state estimate obtained from the discrete-time Kalman filter to the continuous time estimate as the temporal discretisation is refined. The convergence follows from Martingale convergence theorem as demonstrated below; however, surprisingly, no results exist on the rate of convergence. We derive convergence rate estimates for the discrete-time Kalman filter estimate for finite and infinite dimensional systems. The proofs are based on applying the discrete-time Kalman filter on a dense numerable subset of a certain time interval [0, T].

Original languageEnglish
Pages (from-to)668-679
Number of pages12
JournalInternational Journal of Control
Issue number4
Publication statusPublished - 2 Apr 2016
Externally publishedYes


  • Kalman filter
  • infinite dimensional systems
  • sampled data
  • temporal discretisation


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