An Improved Iterative FIR State Estimator and Its Applications

Shunyi Zhao, Yuriy S. Shmaliy, Choon Ki Ahn, Lijia Luo

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)


In this paper, an iterative finite impulse response (FIR) filter is proposed for discrete time-varying state-space models, with the purpose of a new initialization strategy for the iterative FIR structure as well as consideration of possible unexpected state dynamics in a finite horizon. A compensation variable that satisfies the Gaussian property is introduced into the state equation, and its probability density function (pdf) is estimated analytically together with the pdf of state variable using the variational Bayesian inference technique. Different from the existing methods, the proposed filter exploits the FIR structure from the perspective of pdf propagation, which provides a new efficient way to use the iterative FIR filtering structure without any particular initialization scheme. Moreover, the effects of uncertainties (caused by initialization and/or possible unmodeled state dynamics) on the filtering output are loosened adaptively. Two examples of applications demonstrate that the proposed algorithm can not only provide optimal estimates when the model used perfectly matches the measurements, but can also exhibit better robustness than the Kalman filter, optimal FIR filter, maximum likelihood FIR filter, and some commonly used robust and/or adaptive Kalman filters when the underlying process suffers from unpredicted uncertainties.

Original languageEnglish
Article number8744320
Pages (from-to)1003-1012
Number of pages10
JournalIEEE Transactions on Industrial Informatics
Issue number2
Publication statusPublished - 2020 Feb


  • Finite impulse response (FIR) filter
  • Kalman filter (KF)
  • probability density function (pdf)
  • state estimation
  • variational inference

ASJC Scopus subject areas

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


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