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 journalArticle

2 Citations (Scopus)

Abstract

This paper 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 paper 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 (MVUFIR) filter and the conventional Kalman-Bucy filter based on a numerical example.

Original languageEnglish
JournalIEEE Transactions on Circuits and Systems II: Express Briefs
DOIs
Publication statusAccepted/In press - 2017 Sep 4

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FIR filters
Kalman filters
Cost functions

Keywords

  • continuous time
  • Cost function
  • Differential equations
  • exponential weight
  • finite impulse response filter
  • Finite impulse response filters
  • Frobenius norm
  • Optimal control
  • Robustness
  • robustness.
  • Uncertainty

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

Cite this

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abstract = "This paper 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 paper 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 (MVUFIR) filter and the conventional Kalman-Bucy filter based on a numerical example.",
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N2 - This paper 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 paper 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 (MVUFIR) filter and the conventional Kalman-Bucy filter based on a numerical example.

AB - This paper 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 paper 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 (MVUFIR) filter and the conventional Kalman-Bucy filter based on a numerical example.

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