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

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

doi:10.1109/TCSII.2018.2810812

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 journal › Article › peer-review

10 Citations (Scopus)

Abstract

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 language	English
Article number	8305498
Pages (from-to)	1284-1288
Number of pages	5
Journal	IEEE Transactions on Circuits and Systems II: Express Briefs
Volume	65
Issue number	9
DOIs	https://doi.org/10.1109/TCSII.2018.2810812
Publication status	Published - 2018 Sep

Keywords

Finite impulse response filtering
Lagrange multiplier
robustness
state estimation

ASJC Scopus subject areas

Electrical and Electronic Engineering

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10.1109/TCSII.2018.2810812

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title = "Minimum Weighted Frobenius Norm Discrete-Time FIR Filter with Embedded Unbiasedness",

abstract = "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.",

keywords = "Finite impulse response filtering, Lagrange multiplier, robustness, state estimation",

author = "You, {Sung Hyun} and Ahn, {Choon Ki} and Shmaliy, {Yuriy S.} and Shunyi Zhao",

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: hironaka@korea.ac.kr). Publisher Copyright: {\textcopyright} 2018 IEEE.",

year = "2018",

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N1 - 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: hironaka@korea.ac.kr). Publisher Copyright: © 2018 IEEE.

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N2 - 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.

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

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