A New Unbiased FIR Filter with Improved Robustness Based on Frobenius Norm with Exponential Weight

Choon Ki Ahn, Yuriy S. Shmaliy, Shunyi Zhao

Research output: Contribution to journalArticlepeer-review

19 Citations (Scopus)


This brief proposes a new unbiased finite impulse response (FIR) filter with improved robustness for state-space models in continuous time. The FIR filter proposed in this brief is called the unbiased FIR filter based on the Frobenius norm and exponential weight (UFFFNE). A new integral cost function based on the Frobenius norm for the filter gain function with exponential weight is introduced to improve its robustness. It is shown that the UFFFNE design problem can be cast into the constrained minimum-energy optimal control problem. A new analytic expression for the gain function of the UFFFNE is also proposed. The higher robustness of the proposed UFFFNE is demonstrated through a comparison with the existing minimum variance unbiased FIR filter and the conventional Kalman-Bucy filter based on a numerical example.

Original languageEnglish
Pages (from-to)521-525
Number of pages5
JournalIEEE Transactions on Circuits and Systems II: Express Briefs
Issue number4
Publication statusPublished - 2018 Apr

Bibliographical note

Funding Information:
Manuscript received June 15, 2017; revised August 16, 2017; accepted August 31, 2017. Date of publication September 5, 2017; date of current version March 26, 2018. This work was supported by the NRF through the Ministry of Science, ICT, and Future Planning under Grant NRF-2017R1A1A1A05001325. This brief was recommended by Associate Editor H. H.-C. Iu. (Corresponding author: Choon Ki Ahn.) C. K. Ahn is with the School of Electrical Engineering, Korea University, Seoul 136-701, South Korea (e-mail: hironaka@korea.ac.kr).

Publisher Copyright:
© 2004-2012 IEEE.


  • Frobenius norm
  • continuous time
  • exponential weight
  • finite impulse response filter
  • robustness

ASJC Scopus subject areas

  • Electrical and Electronic Engineering


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