Abstract
For equation-error autoregressive (EEAR) systems, this paper proposes an identification algorithm by means of the model equivalence transformation. The basic idea is to eliminate the autoregressive term in the model using the model transformation, to estimate the parameters of the converted system and further to compute the parameter estimates of the original system using the comparative coefficient way and the model equivalence principle. For comparison, the recursive generalized least squares algorithm is given simply. The simulation results verify that the proposed algorithm is effective and can produce more accurate parameter estimates.
Highlights
System modeling and system identification are the prerequisite and foundation of all control issues.System identification has a significant effect on the filtering [1,2,3], state estimation [4,5,6], system control [7,8,9] and optimization [10]
Yu et al derived the recursive identification algorithm to identify the parameters in the parameterized Hammerstein–Wiener system model [29]; Filipovic presented a robust recursive algorithm for identification of a Hammerstein model with a static nonlinear block in polynomial form and a linear block described by the ARMAX model [30]; Cao et al studied constrained two-dimensional recursive least squares identification problems for batch processes, which can improve the identification performance by incorporating a soft constraint term in the cost function to reduce the variation of the estimated parameters [31]
According to the above derivation, it is clear that the model equivalence-based recursive least squares (ME-RLS) algorithm in Equations (20)–(25) and (29)–(30) increases the complexity of computation compared with the recursive generalized least squares (RGLS) algorithm
Summary
System modeling and system identification are the prerequisite and foundation of all control issues. Liu and Lu derived the mathematical models and presented a least squares-based iterative algorithm for multi-input multirate systems with colored noises by replacing the unknown noise terms in the information vector with their estimates [32]. Xiao and Yue derived a filtering-based recursive least squares identification algorithm for nonlinear dynamical adjustment models [36]; Li developed a maximum likelihood estimation algorithm to estimate the parameters of Hammerstein nonlinear CARARMA systems by using the Newton iteration [37]; Ding presented a recursive generalized extended least squares algorithm for identifying controlled ARMA systems [28]; the basic idea is to replace the unknown terms in the information vector with their estimates.
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