Advertisement

Circuits, Systems and Signal Processing

, Volume 29, Issue 4, pp 649–667 | Cite as

Multi-innovation Extended Stochastic Gradient Algorithm and Its Performance Analysis

  • Yanjun Liu
  • Li Yu
  • Feng Ding
Article

Abstract

This paper derives the multi-innovation extended stochastic gradient algorithm for controlled autoregressive moving average models by expanding the scalar innovation to an innovation vector and analyzes its performance in detail. Four convergence theorems are given for the multi-innovation extended stochastic gradient algorithm to show that the parameter estimates converge to their true values under the weak persistent excitation condition. The simulation results show that the proposed algorithm can produce more accurate parameter estimates than the traditional extended stochastic gradient algorithm.

Keywords

Recursive identification Parameter estimation Signal processing Multi-innovation identification Stochastic gradient Performance analysis 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    F. Ding, T. Chen, Parameter estimation of dual-rate stochastic systems by using an output error method. IEEE Trans. Autom. Control 50(9), 1436–1441 (2005) CrossRefMathSciNetGoogle Scholar
  2. 2.
    F. Ding, T. Chen, Performance analysis of multi-innovation gradient type identification methods. Automatica 43(1), 1–14 (2007) MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    F. Ding, D.Y. Xiao, T. Ding, Multi-innovation stochastic gradient identification method. Control Theory Appl. 20(6), 870–874 (2003), (in Chinese) MathSciNetGoogle Scholar
  4. 4.
    F. Ding, H.B. Chen, M. Li, Multi-innovation least squares identification methods based on the auxiliary model for MISO systems. Appl. Math. Comput. 187(2), 658–668 (2007) MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    F. Ding, Y. Shi, T. Chen, Amendments to “Performance analysis of estimation algorithms of non-stationary ARMA processes”. IEEE Trans. Signal Process. 56(10-1), 4983–4984 (2008) CrossRefGoogle Scholar
  6. 6.
    F. Ding, H.Z. Yang, F. Liu, Performance analysis of stochastic gradient algorithms under weak conditions. Sci. China Ser. F Inf. Sci. 51(9), 1269–1280 (2008) MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    F. Ding, P.X. Liu, G. Liu, Auxiliary model based multi-innovation extended stochastic gradient parameter estimation with colored measurement noises. Signal Process. 89(10), 1883–1890 (2009) CrossRefGoogle Scholar
  8. 8.
    G.C. Goodwin, K.S. Sin, Adaptive Filtering Prediction and Control (Prentice-Hall, Englewood Cliffs, 1984) MATHGoogle Scholar
  9. 9.
    L.L. Han, F. Ding, Multi-innovation stochastic gradient algorithms for multi-input multi-output systems. Digit. Signal Process. 19(4), 545–554 (2009) CrossRefGoogle Scholar
  10. 10.
    L.L. Han, F. Ding, Identification for multirate multi-input systems using the multi-innovation identification theory. Comput. Math. Appl. 57(9), 1438–1449 (2009) MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    L. Ljung, System Identification: Theory for the User, 2nd edn. (Prentice-Hall, Englewood Cliffs, 1999) Google Scholar
  12. 12.
    D.Q. Wang, F. Ding, Auxiliary models based multi-innovation generalized extended stochastic gradient algorithms. Control Decis. 23(9), 999–1003 (2008), 1010 (in Chinese) MATHMathSciNetGoogle Scholar
  13. 13.
    D.Q. Wang, F. Ding, Performance analysis of the auxiliary models based multi-innovation stochastic gradient estimation algorithm for output error systems. Digit. Signal Process. 20(3), 750–762 (2010) CrossRefMathSciNetGoogle Scholar
  14. 14.
    C.Z. Wei, Adaptive prediction by least squares prediction in stochastic regression models. Ann. Stat. 15(4), 1667–1682 (1987) MATHCrossRefGoogle Scholar
  15. 15.
    L. Yu, F. Ding, Multi-innovation stochastic gradient identification methods for CARMA systems. Sci. Technol. Eng. 8(2), 473–475 (2008), (in Chinese) MathSciNetGoogle Scholar
  16. 16.
    L. Yu, F. Ding, J.B. Zhang, Convergence of multi-innovation stochastic gradient identification methods. Sci. Technol. Eng. 7(21), 5474–5478 (2007), 5484 (in Chinese) Google Scholar
  17. 17.
    L. Yu, F. Ding, P.X. Liu, On consistency of multi-innovation extended stochastic gradient algorithms with colored noises, in Proceedings of IEEE International Instrumentation and Measurement Technology Conference, Victoria, Canada, 12–16 May 2008, pp. 1695–1700 Google Scholar
  18. 18.
    L. Yu, Y.J. Liu, F. Ding, Convergence of multi-innovation extended stochastic gradient parameter estimation for CARMA models. Syst. Eng. Electron. 31(6), 1446–1449 (2009), (in Chinese) Google Scholar
  19. 19.
    J.B. Zhang, F. Ding, Y. Shi, Self-tuning control based on multi-innovation stochastic gradient parameter estimation. Syst. Control. Lett. 58(1), 69–75 (2009) MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.School of Communication and Control EngineeringJiangnan UniversityWuxiP.R. China

Personalised recommendations