Skip to main content
Log in

Data Filtering-Based Multi-innovation Stochastic Gradient Algorithm for Nonlinear Output Error Autoregressive Systems

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

Abstract

This paper discusses the parameter estimation problems of nonlinear output error autoregressive systems and presents a data filtering-based multi-innovation stochastic gradient algorithm for improving the parameter estimation accuracy of the stochastic gradient algorithm by combining the multi-innovation identification theory and the data filtering technique. The proposed algorithm is effective and can generate highly accurate parameter estimates compared with the multi-innovation stochastic gradient algorithm. The simulation results confirm this conclusion.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. M.S. Ahmad, O. Kukrer, A. Hocanin, Recursive inverse adaptive filtering algorithm. Digit. Signal Process 21(4), 491–496 (2011)

    Article  Google Scholar 

  2. E.W. Bai, K.S. Chan, Identification of an additive nonlinear system and its applications in generalized Hammerstein models. Automatica 44(2), 430–436 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  3. J. Chen, Y.X. Ni, Parameter identification methods for an additive nonlinear system. Circuits Syst. Signal Process 33(10), 3053–3064 (2014)

    Article  Google Scholar 

  4. H.B. Chen, W.G. Zhang et al., Data filtering based least squares iterative algorithm for parameter identification of output error autoregressive systems. Inf. Process. Lett. 114(10), 573–578 (2014)

    Article  MATH  Google Scholar 

  5. E. De Carvalho, S.M. Omar, D.T.M. Slock, Performance and complexity analysis of blind FIR channel identification algorithms based on deterministic maximum likelihood in SIMO systems. Circuits Syst. Signal Process 32(2), 683–709 (2013)

    Article  Google Scholar 

  6. F. Ding, T. Chen, Performance analysis of multi-innovation gradient type identification methods. Automatica 43(1), 1–14 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  7. F. Ding, Several multi-innovation identification methods. Digit. Signal Process 20(4), 1027–1039 (2010)

    Article  Google Scholar 

  8. F. Ding, Y. Gu, Performance analysis of the auxiliary model-based stochastic gradient parameter estimation algorithm for state-space systems with one-step state delay. Circuits Syst. Signal Process 32(2), 585–599 (2013)

    Article  MathSciNet  Google Scholar 

  9. 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 

  10. J. Ding, C.X. Fan, J.X. Lin, Auxiliary model based parameter estimation for dual-rate output error systems with colored noise. Appl. Math. Model. 37(6), 4051–4058 (2013)

    Article  MathSciNet  Google Scholar 

  11. J. Ding, J.X. Lin, Modified subspace identification for periodically non-uniformly sampled systems by using the lifting technique. Circuits Syst. Signal Process 33(5), 1439–1449 (2014)

    Article  Google Scholar 

  12. F. Ding, Y.J. Wang, J. Ding, Recursive least squares parameter identification for systems with colored noise using the filtering technique and the auxiliary model. Digit. Signal Process 37, 100–108 (2015)

    Article  Google Scholar 

  13. L. Han, F. Ding, Multi-innovation stochastic gradient algorithms for multi-input multi-output systems. Digit. Signal Process 19(4), 545–554 (2009)

    Article  MathSciNet  Google Scholar 

  14. H.Y. Hu, Y.S. Xiao, R. Ding, Multi-innovation stochastic gradient identification algorithm for Hammerstein controlled autoregressive autoregressive systems based on the key term separation principle and on the model decomposition. J. Appl. Math. Article ID 596141, pp. 1–7(2013). doi:10.1155/2013/596141

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

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  17. Y. Ji, X.M. Liu, Unified synchronization criteria for hybrid switching-impulsive dynamical networks. Circuits Syst. Signal Process (2015). doi:10.1007/s00034-014-9916-0

  18. Y. Ji, X.M. Liu et al., New criteria for the robust impulsive synchronization of uncertain chaotic delayed nonlinear systems. Nonlinear Dyn. 79(1), 1–9 (2015)

    Article  MathSciNet  Google Scholar 

  19. 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 

  20. 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 

  21. Y.J. Liu, L. Yu et al., Multi-innovation extended stochastic gradient algorithm and its performance analysis. Circuits Syst. Signal Process 29(4), 649–667 (2010)

    Article  MATH  Google Scholar 

  22. L. Ljung, System Identification: Theory for the User, 2nd edn. (Prentice Hall, Englewood Cliffs, New Jersey, 1999)

    Google Scholar 

  23. L. Ljung, Recursive identification algorithms. Circuits Syst. Signal Process 21(1), 57–68 (2002)

    Article  MathSciNet  Google Scholar 

  24. Y.W. Mao, F. Ding, Multi-innovation stochastic gradient identification for Hammerstein controlled autoregressive autoregressive systems based on the filtering technique. Nonlinear Dyn. 79(3), 1745–1755 (2015)

    Article  Google Scholar 

  25. B. Sun, D.Q. Zhu, S.X. Yang, A bio-inspired filtered backstepping cascaded tracking control of 7000 m manned submarine vehicle. IEEE Trans. Ind. Electron. 61(7), 3682–3692 (2014)

    Article  Google Scholar 

  26. J. van Wingerden, M. Verhaegen, Subspace identification of bilinear and LPV systems for open-and closed-loop data. Automatica 45(2), 372–381 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  27. 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 

  28. J. Vörös, Recursive identification of Hammerstein systems with discontinuous nonlinearities containing dead-zones. IEEE Trans. Autom. Control 48(12), 2203–2206 (2003)

    Article  Google Scholar 

  29. X.R. Wang, B. Huang, T. Chen, Multirate minimum variance control design and control performance assessment: a data-driven subspace approach. IEEE Trans. Control Syst. Technol. 15(1), 65–74 (2007)

    Article  Google Scholar 

  30. D.Q. Wang, Least squares-based recursive and iterative estimation for output error moving average systems using data filtering. IET Control Theory Appl. 5(14), 1648–1657 (2011)

    Article  MathSciNet  Google Scholar 

  31. 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. Circuits Syst. Signal Process 31(6), 2167–2177 (2012)

    Article  MathSciNet  Google Scholar 

  32. C. Wang, T. Tang, Several gradient-based iterative estimation algorithms for a class of nonlinear systems using the filtering technique. Nonlinear Dyn. 77(3), 769–780 (2014)

    Article  Google Scholar 

  33. W. Wang, T. Tang, Recursive least squares estimation algorithm applied to a class of linear-in-parameters output error moving average systems. Appl. Math. Lett. 29, 36–41 (2014)

    Article  MathSciNet  Google Scholar 

  34. G. Zheng, J.P. Barbot, D. Boutat, Identification of the delay parameter for nonlinear time-delay systems with unknown inputs. Automatica 49(6), 1755–1760 (2013)

    Article  MathSciNet  Google Scholar 

  35. D.Q. Zhu, H. Huang, S.X. Yang, Dynamic task assignment and path planning of multi-AUV system based on an improved self-organizing map and velocity synthesis method in 3D underwater workspace. IEEE Trans. Cybern. 43(2), 504–514 (2013)

    Article  Google Scholar 

  36. D.Q. Zhu, X. Hua, B. Sun, A neurodynamics control strategy for real-time tracking control of autonomous underwater vehicles. J. Navig. 67(1), 113–127 (2014)

    Article  Google Scholar 

Download references

Acknowledgments

This work was supported by the National Natural Science Foundation of China (No. 61273194) and the PAPD of Jiangsu Higher Education Institutions.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Feng Ding.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mao, Y., Ding, F. Data Filtering-Based Multi-innovation Stochastic Gradient Algorithm for Nonlinear Output Error Autoregressive Systems. Circuits Syst Signal Process 35, 651–667 (2016). https://doi.org/10.1007/s00034-015-0064-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-015-0064-y

Keywords

Navigation