Skip to main content
SpringerLink
Log in

Decomposition Based Newton Iterative Identification Method for a Hammerstein Nonlinear FIR System with ARMA Noise

  • Published:
Circuits, Systems, and Signal Processing Aims and scope Submit manuscript

Abstract

This paper derives a Newton iterative algorithm for identifying a Hammerstein nonlinear FIR system with ARMA noise (i.e., Hammerstein nonlinear controlled autoregressive moving average system). This method decomposes a Hammerstein nonlinear system into two subsystems using the hierarchical identification principle, estimating the parameters of the system directly without using the over-parameterization method. The simulation results show that the proposed algorithm is effective.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  1. C.E. Chidume, Y. Shehu, Iterative approximation of solutions of equations of Hammerstein type in certain Banach spaces. Appl. Math. Comput. 219(10), 5657–5667 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  2. M. Dehghan, M. Hajarian, Analysis of an iterative algorithm to solve the generalized coupled Sylvester matrix equations. Appl. Math. Model. 35(7), 3285–3300 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  3. K.P. Deng, F. Ding, Newton iterative identification method for an input nonlinear finite impulse response system with moving average noise using the key variables separation technique. Nonlinear Dyn. (2014). doi:10.1007/s11071-013-1202-3

    MathSciNet  Google Scholar 

  4. F. Ding, Hierarchical multi-innovation stochastic gradient algorithm for Hammerstein nonlinear system modeling. Appl. Math. Model. 37(4), 1694–1704 (2013)

    Article  MathSciNet  Google Scholar 

  5. F. Ding, Two-stage least squares based iterative estimation algorithm for CARARMA system modeling. Appl. Math. Model. 37(7), 4798–4808 (2013)

    Article  MathSciNet  Google Scholar 

  6. F. Ding, Combined state and least squares parameter estimation algorithms for dynamic systems. Appl. Math. Model. 38(1), 403–412 (2014)

    Article  MathSciNet  Google Scholar 

  7. F. Ding, Coupled-least-squares identification for multivariable systems. IET Control Theor. Appl. 7(1), 68–79 (2013)

    Article  Google Scholar 

  8. F. Ding, Decomposition based fast least squares algorithm for output error systems. Signal Process. 93(5), 1235–1242 (2013)

    Article  Google Scholar 

  9. F. Ding, Hierarchical parameter estimation algorithms for multivariable systems using measurement. Info. Sci. (2014). doi:10.1016/j.ins.2014.02.103

  10. F. Ding, X.M. Liu, H.B. Chen, G.Y. Yao, Hierarchical gradient based and hierarchical least squares based iterative parameter identification for CARARMA systems. Signal Process. 97, 31–39 (2014)

    Article  Google Scholar 

  11. F. Ding, X.G. Liu, J. Chu, Gradient-based and least-squares-based iterative algorithms for Hammerstein systems using the hierarchical identification principle. IET Control Theor. Appl. 7(2), 176–184 (2013)

    Article  MathSciNet  Google Scholar 

  12. F. Ding, X.P. Liu, G. Liu, Identification methods for Hammerstein nonlinear systems. Digit. Signal Process. 21(2), 215–238 (2011)

    Article  Google Scholar 

  13. F. Ding, J.X. Ma, Y.S. Xiao, Newton iterative identification for a class of output nonlinear systems with moving average noises. Nonlinear Dyn. 74(1–2), 21–30 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  14. F. Ding, Y. Shi, T. Chen, Auxiliary model-based least-squares identification methods for Hammerstein output-error systems. Syst. Control Lett. 56(5), 373–380 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  15. A. Hagenblad, L. Ljung, A. Wills, Maximum likelihood identification of Wiener models. Automatica 44(11), 2697–2705 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  16. Y.B. Hu, Iterative and recursive least squares estimation algorithms for moving average systems. Simul. Model. Pract. Theor. 34, 12–19 (2013)

    Article  Google Scholar 

  17. Y.B. Hu, B.L. Liu, Q. Zhou, C. Yang, Recursive extended least squares parameter estimation for Wiener nonlinear systems with moving average noises. Circ. Syst. Signal Process. 33(2), 655–664 (2014)

    Article  MathSciNet  Google Scholar 

  18. J.H. Li, Parameter estimation for Hammerstein CARARMA systems based on the Newton iteration. Appl. Math. Lett. 26(1), 91–96 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  19. J.H. Li, F. Ding, G.W. Yang, Maximum likelihood least squares identification method for input nonlinear finite impulse response moving average systems. Math. Comput. Model. 55(3–4), 442–450 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  20. Y.J. Liu, R. Ding, Consistency of the extended gradient identification algorithm for multi-input multi-output systems with moving average noises. Int. J. Comput. Math. 90(9), 1840–1852 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  21. Y.J. Liu, F. Ding, Y. Shi, An efficient hierarchical identification method for general dual-rate sampled-data systems. Automatica 50(3), 962–973 (2014)

    Google Scholar 

  22. Y.J. Liu, F. Ding, Y. Shi, Least squares estimation for a class of non-uniformly sampled systems based on the hierarchical identification principle. Circ. Syst. Signal Process. 31(6), 1985–2000 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  23. X.G. Liu, J. Lu, Least squares based iterative identification for a class of multirate systems. Automatica 46(3), 549–554 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  24. Y.J. Liu, J. Sheng, R.F. Ding, Convergence of stochastic gradient estimation algorithm for multivariable ARX-like systems. Comput. Math. Appl. 59(8), 2615–2627 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  25. Y.J. Liu, Y.S. Xiao, X.L. Zhao, Multi-innovation stochastic gradient algorithm for multiple-input single-output systems using the auxiliary model. Appl. Math. Comput. 215(4), 1477–1483 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  26. S.H. Mousavi, B. Ranjbar-Sahraei, N. Noroozi, Output feedback controller for hysteretic time-delayed MIMO nonlinear systems. Nonlinear Dyn. 68(1–2), 63–76 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  27. Q.Y. Shen, F. Ding, Iterative estimation methods for Hammerstein controlled autoregressive moving average systems based on the key-term separation principle. Nonlinear Dyn. 75(4), 709–716 (2014)

    Article  MATH  Google Scholar 

  28. Y. Shi, H. Fang, Kalman filter based identification for systems with randomly missing measurements in a network environment. Int. J. Control 83(3), 538–551 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  29. Y. Shi, B. Yu, Output feedback stabilization of networked control systems with random delays modeled by Markov chains. IEEE Trans. Autom. Control 54(7), 1668–1674 (2009)

    Article  MathSciNet  Google Scholar 

  30. Y. Shi, B. Yu, Robust mixed H-2/H-infinity control of networked control systems with random time delays in both forward and backward communication links. Automatica 47(4), 754–760 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  31. W. Sun, H. Gao, Adaptive backstepping control for active suspension systems with hard constraints. IEEE/ASME Trans. Mechatron. 18(3), 1072–1079 (2013)

    Article  MathSciNet  Google Scholar 

  32. W. Sun, Z. Zhao, H. Gao, Saturated adaptive robust control for active suspension systems. IEEE Trans. Ind. Electron. 60(9), 3889–3896 (2013)

    Article  Google Scholar 

  33. V. Tuzlukov, Signal processing by generalized receiver in DS-CDMA wireless communication systems with frequency-selective channels. Circ. Syst. Signal Process. 30(6), 1197–1230 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  34. D.N. Vizireanu, S.V. Halunga, Simple, fast and accurate eight points amplitude estimation method of sinusoidal signals for DSP based instrumentation. J. Instrum. 7(4), P04001 (2012)

    Article  Google Scholar 

  35. D.N. Vizireanu, S.V. Halunga, Analytical formula for three points sinusoidal signals amplitude estimation errors. Int. J. Electron. 99(1), 149–151 (2012)

    Article  Google Scholar 

  36. J. Vörös, Modeling and parameter identification of systems with multi-segment piecewise-linear characteristics. IEEE Trans. Autom. Control 47(1), 184–188 (2002)

    Article  Google Scholar 

  37. J. Vörös, Identification of Hammerstein systems with time-varying piecewise-linear characteristics. IEEE Trans. Circ. Syst. II 52(12), 865–869 (2005)

    Google Scholar 

  38. J. Vörös, Parameter identification of Wiener systems with multisegment piecewise-linear nonlinearities. Syst. Control Lett. 56(2), 99–105 (2007)

    Article  MATH  Google Scholar 

  39. D.Q. Wang, F. Ding, Least squares based and gradient based iterative identification for Wiener nonlinear systems. Signal Process. 91(5), 1182–1189 (2011)

    Article  MATH  Google Scholar 

  40. D.Q. Wang, F. Ding, X.M. Liu, Least squares algorithm for an input nonlinear system with a dynamic subspace state space model. Nonlinear Dyn. 75(1–2), 49–61 (2014)

    Article  MATH  MathSciNet  Google Scholar 

  41. D.Q. Wang, F. Ding, Hierarchical least squares estimation algorithm for Hammerstein–Wiener systems. IEEE Signal Process. Lett. 19(12), 825–828 (2012)

    Article  Google Scholar 

  42. D.Q. Wang, F. Ding, Y.Y. Chu, Data filtering based recursive least squares algorithm for Hammerstein systems using the key-term separation principle. Inform. Sci. 222, 203–212 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  43. D.Q. Wang, R. Ding, X.Z. Dong, Iterative parameter estimation for a class of multivariable systems based on the hierarchical identification principle and the gradient search. Circ. Syst. Signal Process. 31(6), 2167–2177 (2012)

    Article  MathSciNet  Google Scholar 

  44. D.Q. Wang, T. Shan, R. Ding, Data filtering based stochastic gradient algorithms for multivariable CARAR-like systems. Math. Model. Anal. 18(3), 374–385 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  45. A. Wills, T.B. Schön, L. Ljung, B. Ninness, Identification of Hammerstein–Wiener models. Automatica 49(1), 70–81 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  46. B. Yao, M. Tomizuka, Adaptive robust control of MIMO nonlinear systems in semi-strict feedback forms. Automatica 37(9), 1305–1321 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  47. Z.N. Zhang, F. Ding, X.G. Liu, Hierarchical gradient based iterative parameter estimation algorithm for multivariable output error moving average systems. Comput. Math. Appl. 61(3), 672–682 (2011)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Acknowledgments

This work was supported by the National Natural Science Foundation of China (No. 61304093) the Taishan Scholar Project Fund of Shandong Province of China.

Author information

Authors and Affiliations

  1. College of Automation and Electronic Engineering, Qingdao University of Science and Technology, Qingdao , 266061, People’s Republic of China

    Feng Ding & Ximei Liu

  2. School of Internet of Things Engineering, Jiangnan University, Wuxi , 214122, People’s Republic of China

    Kepo Deng

Authors
  1. Feng Ding
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kepo Deng
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ximei Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Feng Ding.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ding, F., Deng, K. & Liu, X. Decomposition Based Newton Iterative Identification Method for a Hammerstein Nonlinear FIR System with ARMA Noise . Circuits Syst Signal Process 33, 2881–2893 (2014). https://doi.org/10.1007/s00034-014-9772-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-014-9772-y

Keywords

Search

Navigation