Abstract
This paper is concerned with the identification problem for multivariable equation-error systems whose disturbance is an autoregressive moving average process. By means of the hierarchical identification principle and the iterative search, a hierarchical least-squares-based iterative (HLSI) identification algorithm is derived and a least-squares-based iterative (LSI) identification algorithm is given for comparison. Furthermore, a hierarchical multi-innovation least-squares-based iterative (HMILSI) identification algorithm is proposed using the multi-innovation theory. Compared with the LSI algorithm, the HLSI algorithm has smaller computational burden and can give more accurate parameter estimates and the HMILSI algorithm can track time-varying parameters. Finally, a simulation example is provided to verify the effectiveness of the proposed algorithms.
Highlights
With the development of modern industry, multivariable systems have provided rich possibilities to system modeling and process control [1,2]
Considering that the least-squares algorithms have high estimation accuracy and rapid convergence [40–42], this paper focuses on the parameter identification problem of multivariable equation-error systems with autoregressive moving average noise process and presents iterative identification algorithms using the hierarchical identification principle and the multi-innovation method
A decomposition least-squares-based iterative identification algorithm is derived for multivariable equation-error autoregressive moving average systems by using the hierarchical identification principle
Summary
With the development of modern industry, multivariable systems have provided rich possibilities to system modeling and process control [1,2]. A filtering based multi-innovation gradient estimation algorithm has been proposed for nonlinear dynamical systems [18]. An adaptive filtering based multi-innovation stochastic gradient algorithm was derived for bilinear systems with colored noise and can give small parameter estimation errors as the innovation length increases [21]. Using the hierarchical identification principle and the multi-innovation identification theory, some algorithms have been proposed to track the parameters of nonlinear systems and multivariable systems [38,39]. Considering that the least-squares algorithms have high estimation accuracy and rapid convergence [40–42], this paper focuses on the parameter identification problem of multivariable equation-error systems with autoregressive moving average noise process and presents iterative identification algorithms using the hierarchical identification principle and the multi-innovation method. A decomposition least-squares-based iterative identification algorithm is derived for multivariable equation-error autoregressive moving average systems by using the hierarchical identification principle.
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