Nonlinear Dynamics

, Volume 45, Issue 1–2, pp 31–43 | Cite as

Gradient-Based Identification Methods for Hammerstein Nonlinear ARMAX Models

  • Feng Ding
  • Yang Shi
  • Tongwen Chen


Two identification algorithms, an iterative gradient and a recursive stochastic gradient based, are developed for a Hammerstein nonlinear ARMAX model, a linear dynamical block following a memoryless nonlinear block. The basic idea is to use the gradient search principle, to replace unmeasurable noise terms in the information vectors by their estimates, and to compute iteratively or recursively the noise estimates based on the obtained parameter estimates. Convergence analysis of the recursive stochastic gradient algorithm indicates that the parameter estimation error consistently converges to zero under certain conditions. The simulation results show the effectiveness of the proposed algorithms.

Key words

convergence properties Hammerstein models least squares martingale convergence theorem parameter estimation recursive identification stochastic gradient Wiener models 


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Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Control Science and Engineering Research CenterSouthern Yangtze UniversityWuxiChina
  2. 2.Department of Mechanical EngineeringUniversity of SaskatchewanSaskatoonCanada
  3. 3.Department of Electrical and Computer EngineeringUniversity of AlbertaEdmontonCanada

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