Skip to main content
SpringerLink
Log in

Least Squares-Based Iterative Identification Methods for Linear-in-Parameters Systems Using the Decomposition Technique

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

Abstract

By extending the least squares-based iterative (LSI) method, this paper presents a decomposition-based LSI (D-LSI) algorithm for identifying linear-in-parameters systems and an interval-varying D-LSI algorithm for handling the identification problems of missing-data systems. The basic idea is to apply the hierarchical identification principle to decompose the original system into two fictitious sub-systems and then to derive new iterative algorithms to estimate the parameters of each sub-system. Compared with the LSI algorithm and the interval-varying LSI algorithm, the decomposition-based iterative algorithms have less computational load. The numerical simulation results demonstrate that the proposed algorithms work quite well.

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
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. M. Amairi, Recursive set-membership parameter estimation using fractional model. Circuits Syst. Signal Process. 34(12), 3757–3788 (2015)

    Article  MathSciNet  Google Scholar 

  2. H.B. Chen, F. Ding, Y.S. Xiao, Decomposition-based least squares parameter estimation algorithm for input nonlinear systems using the key term separation technique. Nonlinear Dyn. 79(3), 2027–2035 (2015)

    Article  MATH  Google Scholar 

  3. H.B. Chen, Y.S. Xiao et al., Hierarchical gradient parameter estimation algorithm for Hammerstein nonlinear systems using the key term separation principle. Appl. Math. Comput. 247, 1202–1210 (2014)

    MathSciNet  MATH  Google Scholar 

  4. M. Dehghan, M. Hajarian, Iterative algorithms for the generalized centro-symmetric and central anti-symmetric solutions of general coupled matrix equations. Eng. Comput. 29(5), 528–560 (2012)

    Article  Google Scholar 

  5. F. Ding, System Identification—New Theory and Methods (Science Press, Beijing, 2013)

    Google Scholar 

  6. F. Ding, System Identification—Performances Analysis for Identification Methods (Science Press, Beijing, 2014)

    Google Scholar 

  7. F. Ding, K.P. Deng, X.M. Liu, Decomposition based Newton iterative identification method for a Hammerstein nonlinear FIR system with ARMA noise. Circuits Syst. Signal Process. 33(9), 2881–2893 (2014)

    Article  MathSciNet  Google Scholar 

  8. F. Ding, J. Ding, Least squares parameter estimation with irregularly missing data. Int. J. Adapt. Control Signal Process. 24(7), 540–553 (2010)

    MathSciNet  MATH  Google Scholar 

  9. 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 

  10. 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 

  11. F. Ding, X.M. Liu, Y. Gu, An auxiliary model based least squares algorithm for a dual-rate state space system with time-delay using the data filtering. J. Frankl. Inst. Eng. Appl. Math. 353 (2015). doi:10.1016/j.jfranklin.2015.10.025

  12. F. Ding, G. Liu, X.P. Liu, Parameter estimation with scarce measurements. Automatica 47(8), 1646–1655 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  13. F. Ding, X.H. Wang, Q.J. Chen, Y.S. Xiao, Recursive least squares parameter estimation for a class of output nonlinear systems based on the model decomposition. Circuits Syst. Signal Process. 35 (2016). doi:10.1007/s00034-015-0190-6

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

    Article  Google Scholar 

  15. C.L. Fan, H.J. Li, X. Ren, The order recurrence quantification analysis of the characteristics of two-phase flow pattern based on multi-scale decomposition. Trans. Inst. Meas. Control 37(6), 793–804 (2015)

    Article  Google Scholar 

  16. Y.Q. Hei, W.T. Li, W.H. Fu, X.H. Li, Efficient parallel artificial bee colony algorithm for cooperative spectrum sensing optimization. Circuits Syst. Signal Process. 34(11), 3611–3629 (2015)

    Article  Google Scholar 

  17. 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 

  18. 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 

  19. J. Huang, Y. Shi, H.N. Huang, Z. Li, l-2-l-infinity filtering for multirate nonlinear sampled-data systems using T–S fuzzy models. Digit. Signal Process. 23(1), 418–426 (2013)

    Article  MathSciNet  Google Scholar 

  20. Y. Ji, X.M. Liu, Unified synchronization criteria for hybrid switching-impulsive dynamical networks. Circuits Syst. Signal Process. 34(5), 1499–1517 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  21. 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  MATH  Google Scholar 

  22. Q.B. Jin, Z. Wang, X.P. Liu, Auxiliary model-based interval-varying multi-innovation least squares identification for multivariable OE-like systems with scarce measurements. J. Process Control 35, 154–168 (2015)

    Article  Google Scholar 

  23. Q.B. Jin, Z. Wang, J. Wang, Least squares based iterative identification for multivariable integrating and unstable processes in closed loop. Appl. Math. Comput. 242, 10–19 (2014)

    MathSciNet  MATH  Google Scholar 

  24. Q.B. Jin, Z. Wang, Q. Wang, R.G. Yang, Optimal input design for identifying parameters and orders of MIMO systems with initial values. Appl. Math. Comput. 224, 735–742 (2013)

    MathSciNet  MATH  Google Scholar 

  25. Q.B. Jin, Z. Wang, R.G. Yang, J. Wang, An effective direct closed loop identification method for linear multivariable systems with colored noise. J. Process Control 24(5), 485–492 (2014)

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  27. W.L. Li, Y.M. Jia, J.P. Du, J. Zhang, Robust state estimation for jump Markov linear systems with missing measurements. J. Frankl. Inst. 350(6), 1476–1487 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  28. J. Li, J.D. Zhu, Z.H. Feng, Y.J. Zhao, D.H. Li, Passive multipath time delay estimation using MCMC methods. Circuits Syst. Signal Process. 34(12), 3897–3913 (2015)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  30. H. Raghavan, A.K. Tangirala, R.B. Gopaluni, S.L. Shah, Identification of chemical processes with irregular output sampling. Control Eng. Pract. 14(4), 467–480 (2006)

    Article  Google Scholar 

  31. C.F. So, S.H. Leung, Maximum likelihood whitening pre-filtered total least squares for resolving closely spaced signals. Circuits Syst. Signal Process. 34(8), 2739–2747 (2015)

    Article  Google Scholar 

  32. Y.J. Wang, F. Ding, Iterative estimation for a nonlinear IIR filter with moving average noise by means of the data filtering technique. IMA J. Math. Control Inf. (2016). doi:10.1093/imamci/dnv067

  33. X.H. Wang, F. Ding, Convergence of the recursive identification algorithms for multivariate pseudo-linear regressive systems. Int. J. Adapt. Control Signal Process. 30 (2015). doi:10.1002/acs.2642

  34. X.H. Wang, F. Ding, Recursive parameter and state estimation for an input nonlinear state space system using the hierarchical identification principle. Signal Process. 117, 208–218 (2015)

    Article  Google Scholar 

  35. D.Q. Wang, Y.P. Gao, Recursive maximum likelihood identification method for a multivariable controlled autoregressive moving average system. IMA J. Math. Control Inf. (2015). doi:10.1093/imamci/dnv021

  36. D.Q. Wang, H.B. Liu et al., Highly efficient identification methods for dual-rate Hammerstein systems. IEEE Trans. Control Syst. Technol. 23(5), 1952–1960 (2015)

    Article  Google Scholar 

  37. 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  MathSciNet  MATH  Google Scholar 

  38. D.Q. Wang, W. Zhang, Improved least squares identification algorithm for multivariable Hammerstein systems. J. Frankl. Inst. Eng. Appl. Math. 352(11), 5292–5370 (2015)

    Article  MathSciNet  Google Scholar 

  39. L. Xu, The damping iterative parameter identification method for dynamical systems based on the sine signal measurement. Signal Process. 120, 660–667 (2016)

    Article  Google Scholar 

  40. L. Xu, A proportional differential control method for a time-delay system using the Taylor expansion approximation. Appl. Math. Comput. 236, 391–399 (2014)

    MathSciNet  MATH  Google Scholar 

  41. L. Xu, Application of the Newton iteration algorithm to the parameter estimation for dynamical systems. J. Comput. Appl. Math. 288, 33–43 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  42. L. Xu, L. Chen, W.L. Xiong, Parameter estimation and controller design for dynamic systems from the step responses based on the Newton iteration. Nonlinear Dyn. 79(3), 2155–2163 (2015)

    Article  MathSciNet  Google Scholar 

  43. W.G. Zhang, Decomposition based least squares iterative estimation for output error moving average systems. Eng. Comput. 31(4), 709–725 (2014)

    Article  Google Scholar 

Download references

Acknowledgments

This work was supported by the National Natural Science Foundation of China (No. 61304138), the Natural Science Foundation of Jiangsu Province (China, BK20130163), the 111 Project (B12018) and the University Graduate Practice Innovation Program of Jiangsu Province (SJZZ15_0151). The first author is grateful to her supervisor—Professor Feng Ding, and the main idea of this paper is from him and his books “System Identification—Multi-Innovation Identification Theory and Methods, Beijing: Science Press, 2016” and Ding [5, 6].

Author information

Authors and Affiliations

  1. Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Jiangnan University, Wuxi, 214122, People’s Republic of China

    Feifei Wang & Yanjun Liu

  2. Department of Design, Manufacture and Engineering Management, Space Mechatronic Systems Technology Laboratory, Strathclyde Space Institute, University of Strathclyde, Glasgow, G1 1XJ, Scotland, UK

    Erfu Yang

Authors
  1. Feifei Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yanjun Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Erfu Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Feifei Wang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, F., Liu, Y. & Yang, E. Least Squares-Based Iterative Identification Methods for Linear-in-Parameters Systems Using the Decomposition Technique. Circuits Syst Signal Process 35, 3863–3881 (2016). https://doi.org/10.1007/s00034-015-0232-0

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-015-0232-0

Keywords

Search

Navigation