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Symmetrical Augmented System of Equations for the Parameter Identification of Discrete Fractional Systems by Generalized Total Least Squares

Author

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  • Dmitriy Ivanov

    (Department of Information Systems Security, Samara National Research University, 443086 Samara, Russia
    Department of Mechatronics, Samara State University of Transport, 443066 Samara, Russia)

  • Aleksandr Zhdanov

    (Department of Applied Mathematics and Computer Science, Samara State Technical University, 443100 Samara, Russia)

Abstract

This paper is devoted to the identification of the parameters of discrete fractional systems with errors in variables. Estimates of the parameters of such systems can be obtained using generalized total least squares (GTLS). A GTLS problem can be reduced to a total least squares (TLS) problem. A total least squares problem is often ill-conditioned. To solve a TLS problem, a classical algorithm based on finding the right singular vector or an algorithm based on an augmented system of equations with complex coefficients can be applied. In this paper, a new augmented system of equations with real coefficients is proposed to solve TLS problems. A symmetrical augmented system of equations was applied to the parameter identification of discrete fractional systems. The simulation results showed that the use of the proposed symmetrical augmented system of equations can shorten the time for solving such problems. It was also shown that the proposed system can have a smaller condition number.

Suggested Citation

  • Dmitriy Ivanov & Aleksandr Zhdanov, 2021. "Symmetrical Augmented System of Equations for the Parameter Identification of Discrete Fractional Systems by Generalized Total Least Squares," Mathematics, MDPI, vol. 9(24), pages 1-13, December.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:24:p:3250-:d:703402
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    References listed on IDEAS

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    2. Reisen, Valderio Anselmo & Rodrigues, Alexandre L. & Palma, Wilfredo, 2006. "Estimation of seasonal fractionally integrated processes," Computational Statistics & Data Analysis, Elsevier, vol. 50(2), pages 568-582, January.
    3. C. W. J. Granger & Roselyne Joyeux, 1980. "An Introduction To Long‐Memory Time Series Models And Fractional Differencing," Journal of Time Series Analysis, Wiley Blackwell, vol. 1(1), pages 15-29, January.
    4. Wayne A. Woodward & Q. C. Cheng & H. L. Gray, 1998. "A k‐Factor GARMA Long‐memory Model," Journal of Time Series Analysis, Wiley Blackwell, vol. 19(4), pages 485-504, July.
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