Minimum Weighted Frobenius Norm Discrete-Time FIR Filter with Embedded Unbiasedness

Sung Hyun You, Choon Ki Ahn, Yuriy S. Shmaliy, Shunyi Zhao

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)


In this brief, we propose a new receding horizon finite impulse response (FIR) filter that minimizes the weighted Frobenius norm with embedded unbiasedness in discrete-time state-space. The filter, called the discrete-time weighted Frobenius norm unbiased FIR (DTWFNUF) filter, belongs to a class of maximum likelihood estimators. The Frobenius norm is introduced and minimized as a performance criterion to the filter gain matrix. It is shown that the DTWFNUF filter design problem can be cast into the optimization problem with the equality constraint and the filter gain matrix obtained by the Lagrange multiplier method. Higher robustness of the proposed filter is demonstrated in a comparison with the Kalman filter and minimum variance unbiased FIR filter based on a numerical example of the F-404 gas turbine engine.

Original languageEnglish
Article number8305498
Pages (from-to)1284-1288
Number of pages5
JournalIEEE Transactions on Circuits and Systems II: Express Briefs
Issue number9
Publication statusPublished - 2018 Sept

Bibliographical note

Funding Information:
Manuscript received November 29, 2017; revised January 26, 2018; accepted February 9, 2018. Date of publication March 1, 2018; date of current version August 28, 2018. This work was supported in part by the National Research Foundation of Korea through the Ministry of Science, ICT, and Future Planning under Grant NRF-2017R1A1A1A05001325, and in part by the Human Resources Program in Energy Technology of the Korea Institute of Energy Technology Evaluation and Planning through the Ministry of Trade, Industry and Energy, South Korea, under Grant 20174030201820. This brief was recommended by Associate Editor L.-P. Chau. (Corresponding authors: Choon Ki Ahn; Shunyi Zhao.) S. H. You and C. K. Ahn are with the School of Electrical Engineering, Korea University, Seoul 136-701, South Korea (e-mail: [email protected]).

Publisher Copyright:
© 2018 IEEE.


  • Finite impulse response filtering
  • Lagrange multiplier
  • robustness
  • state estimation

ASJC Scopus subject areas

  • Electrical and Electronic Engineering


Dive into the research topics of 'Minimum Weighted Frobenius Norm Discrete-Time FIR Filter with Embedded Unbiasedness'. Together they form a unique fingerprint.

Cite this