Circuits, Systems, and Signal Processing

, Volume 38, Issue 7, pp 2971–2991 | Cite as

Decomposition- and Gradient-Based Iterative Identification Algorithms for Multivariable Systems Using the Multi-innovation Theory

  • Lijuan WanEmail author
  • Feng DingEmail author


This paper is concerned with the identification problem for multivariable equation-error systems with autoregressive moving average noise using the hierarchical identification principle and the multi-innovation identification theory. We propose a hierarchical gradient-based iterative (HGI) identification algorithm and give a gradient-based iterative (GI) identification algorithm for comparison. Meanwhile, the multi-innovation theory is used to derive the hierarchical multi-innovation gradient-based iterative (HMIGI) identification algorithm. The analysis shows that the HGI algorithm has smaller computational burden and can give more accurate parameter estimates than the GI algorithm and the HMIGI algorithm can track time-varying parameters. Finally, a simulation example is provided to verify the effectiveness of the proposed algorithms.


Gradient search Multivariable system Iterative identification Hierarchical principle Multi-innovation theory Parameter estimation 



This work was supported by the National Natural Science Foundation of China (Nos. 61873111, 61803049), the Natural Science Foundation of Shandong Province (ZR201702170236) and the Natural Science Fundamental Research Project of Colleges and Universities in Jiangsu Province (No. 17KJB120001).


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.College of Automation and Electronic Engineering, Institute of Artificial Intelligence and ControlQingdao University of Science and TechnologyQingdaoPeople’s Republic of China
  2. 2.School of Electrical and Electronic EngineeringHubei University of TechnologyWuhanPeople’s Republic of China
  3. 3.Internet of Things EngineeringJiangnan UniversityWuxiPeople’s Republic of China
  4. 4.Department of MathematicsKing Abdulaziz UniversityJeddahSaudi Arabia

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