Continuous-time optimal unbiased FIR filter for input-delayed systems

Dong Kyu Lee, Hyun Ho Kang, Jung Min Pak, Choon Ki Ahn

Research output: Contribution to journalArticlepeer-review


Most existing finite impulse response (FIR) filters are restricted to models without delays. This paper proposes an continuous-time optimal unbiased FIR filter for input-delayed systems (CTOUFFID). A new integral transformation relation was introduced to derive the FIR filter. By applying this relation, the CTOUFFID problem is represented as an optimal control problem with zero terminal state. The filter gain function is obtained by solving two coupled matrix differential equations using initial conditions. The paper also offers discussion on the horizon size and a few special cases. The main benefit of the proposed solution is that it provides the maximum likelihood estimate with no requirements for the initial values. Finally, an application with the (Formula presented.) -404 turbofan engine model is presented to demonstrate the highly robust nature of the proposed FIR filer against incomplete noise information and unspecified model uncertainties.

Original languageEnglish
Pages (from-to)1027-1042
Number of pages16
JournalInternational Journal of Robust and Nonlinear Control
Issue number2
Publication statusPublished - 2023 Jan 25

Bibliographical note

Publisher Copyright:
© 2022 John Wiley & Sons Ltd.


  • continuous time
  • input delay
  • integral transformation
  • optimal unbiased FIR filter

ASJC Scopus subject areas

  • Control and Systems Engineering
  • General Chemical Engineering
  • Biomedical Engineering
  • Aerospace Engineering
  • Mechanical Engineering
  • Industrial and Manufacturing Engineering
  • Electrical and Electronic Engineering


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