Symmetrical Augmented System of Equations for the Parameter Identification of Discrete Fractional Systems by Generalized Total Least Squares
Д. В. Иванов, Александр Иванович Жданов
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.