Circuits, Systems, and Signal Processing

, Volume 37, Issue 5, pp 1846–1862 | Cite as

Decomposition-Based Gradient Estimation Algorithms for Multivariate Equation-Error Autoregressive Systems Using the Multi-innovation Theory

  • Ping Ma
  • Feng Ding
  • Ahmed Alsaedi
  • Tasawar Hayat


This paper studies the parameter estimation algorithms of multivariate equation-error autoregressive systems. By using the decomposition technique, the multivariate equation-error autoregressive system is decomposed into two subsystems, and a decomposition-based generalized stochastic gradient algorithm is deduced for estimating the parameters of these two subsystems. In order to further improve the parameter accuracy, a decomposition-based multi-innovation generalized stochastic gradient algorithm is developed by means of the multi-innovation theory. The simulation results confirm that these two algorithms are effective.


Parameter estimation Gradient search Multi-innovation Decomposition technique Multivariate system 



This work was supported by the National Natural Science Foundation of China (No. 61273194) and the 111 Project (B12018).


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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  • Ping Ma
    • 1
  • Feng Ding
    • 1
    • 2
  • Ahmed Alsaedi
    • 2
  • Tasawar Hayat
    • 2
    • 3
  1. 1.Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), School of Internet of Things EngineeringJiangnan UniversityWuxiPeople’s Republic of China
  2. 2.Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of ScienceKing Abdulaziz UniversityJeddahSaudi Arabia
  3. 3.Department of MathematicsQuaid-I-Azam UniversityIslamabadPakistan

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