Skip to main content
SpringerLink
Log in

Two-Stage Generalized Projection Identification Algorithms for Stochastic Systems

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

Abstract

This paper considers the parameter estimation problem of stochastic systems (i.e., controlled autoregressive systems) by adopting the projection method and the hierarchical identification principle. To improve the performance of the projection identification algorithm, a generalized projection algorithm is proposed by introducing a data window length. By means of the hierarchical identification principle, we divide the system into two fictitious subsystems and derive a two-stage generalized projection identification algorithm. The simulation example tests the effectiveness of the proposed identification algorithms.

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.

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

Similar content being viewed by others

References

  1. Y. Cao, P. Li, Y. Zhang, Parallel processing algorithm for railway signal fault diagnosis data based on cloud computing. Future Gener. Comput. Syst. 88, 279–283 (2018)

    Article  Google Scholar 

  2. Y. Cao, L.C. Ma, S. Xiao et al., Standard analysis for transfer delay in CTCS-3. Chin. J. Electron. 26(5), 1057–1063 (2017)

    Article  Google Scholar 

  3. Y. Cao, Y. Wen, X. Meng, W. Xu, Performance evaluation with improved receiver design for asynchronous coordinated multipoint transmissions. Chin. J. Electron. 25(2), 372–378 (2016)

    Article  Google Scholar 

  4. M.Z. Chen, D.Q. Zhu, A workload balanced algorithm for task assignment and path planning of inhomogeneous autonomous underwater vehicle system. IEEE Trans. Cogn. Dev. Syst. (2018). https://doi.org/10.1109/TCDS.2018.2866984

  5. F. Ding, System Identification: Hierarchical Identification Principle and Methods (Science Press, Beijing, 2019). (To be published)

    Google Scholar 

  6. J.L. Ding, Recursive and iterative least squares parameter estimation algorithms for multiple-input-output-error systems with autoregressive noise. Circuits Syst Signal Process 37(5), 1884–1906 (2018)

    Article  MathSciNet  Google Scholar 

  7. J.L. Ding, The hierarchical iterative identification algorithm for multi-input-output-error systems with autoregressive noise. Complexity 2017, 1–11 (2017). https://doi.org/10.1155/2017/5292894

    Article  MathSciNet  Google Scholar 

  8. F. Ding, H.B. Chen et al., A hierarchical least squares identification algorithm for Hammerstein nonlinear systems using the key term separation. J. Frankl. Inst. 355(8), 3737–3752 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  9. F. Ding, L. Xu et al., Iterative parameter identification for pseudo-linear systems with ARMA noise using the filtering technique. IET Control Theory Appl. 12(7), 892–899 (2018)

    Article  MathSciNet  Google Scholar 

  10. F. Ding, L. Xu, Q.M. Zhu, Performance analysis of the generalised projection identification for time-varying systems. IET Control Theory Appl. 10(18), 2506–2514 (2016)

    Article  MathSciNet  Google Scholar 

  11. M. Gan, C.L.P. Chen, G.Y. Chen, L. Chen, On some separated algorithms for separable nonlinear squares problems. IEEE Trans. Cybern. 48(10), 2866–2874 (2018)

    Article  Google Scholar 

  12. M. Gan, H.X. Li, H. Peng, A variable projection approach for efficient estimation of RBF-ARX model. IEEE Trans. Cybern. 45(3), 462–471 (2015)

    Article  Google Scholar 

  13. H.L. Gao, C.C. Yin, The perturbed sparre Andersen model with a threshold dividend strategy. J. Comput. Appl. Math. 220(1–2), 394–408 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  14. F.Z. Geng, S.P. Qian, An optimal reproducing kernel method for linear nonlocal boundary value problems. Appl. Math. Lett. 77, 49–56 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  15. G. Golub, V. Pereyra, Separable nonlinear least squares: the variable projection method and its applications. Inverse Probl. 19(2), R1–R26 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  16. P.C. Gong, W.Q. Wang, F.C. Li, H. Cheung, Sparsity-aware transmit beamspace design for FDA-MIMO radar. Signal Process. 144, 99–103 (2018)

    Article  Google Scholar 

  17. Y. Gu, J. Liu, X. Li, Y. Chou, Y. Ji, State space model identification of multirate processes with time-delay using the expectation maximization. J. Frankl. Inst. (2019). https://doi.org/10.1016/j.jfranklin.2018.08.030

  18. Z. Hidayat, R. Babuška, A. Núez, B.D. Schutter, Identification of distributed-parameter systems from sparse measurements. Appl. Math. Modell. 51, 605–625 (2017)

    Article  MathSciNet  Google Scholar 

  19. 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 

  20. Y.B. Hu, B.L. Liu, Q. Zhou, A multi-innovation generalized extended stochastic gradient algorithm for output nonlinear autoregressive moving average systems. Appl. Math. Comput. 247, 218–224 (2014)

    MathSciNet  MATH  Google Scholar 

  21. 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 

  22. M.H. Li, X.M. Liu, The least squares based iterative algorithms for parameter estimation of a bilinear system with autoregressive noise using the data filtering technique. Signal Process. 147, 23–34 (2018)

    Article  Google Scholar 

  23. M.H. Li, X.M. Liu, Auxiliary model based least squares iterative algorithms for parameter estimation of bilinear systems using interval-varying measurements. IEEE Access 6, 21518–21529 (2018)

    Article  Google Scholar 

  24. X.Y. Li, B.Y. Wu, A new reproducing kernel collocation method for nonlocal fractional boundary value problems with non-smooth solutions. Appl. Math. Lett. 86, 194–199 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  25. X. Li, D.Q. Zhu, An improved SOM neural network method to adaptive leader–follower formation control of AUVs. IEEE Trans. Ind. Electron. 65(10), 8260–8270 (2018)

    Google Scholar 

  26. F. Liu, A note on Marcinkiewicz integrals associated to surfaces of revolution. J. Aust. Math. Soc. 104(3), 380–402 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  27. F. Liu, H.X. Wu, A note on the endpoint regularity of the discrete maximal operator. Proc. Am. Math. Soc. 147(2), 583–596 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  28. F. Liu, H.X. Wu, Singular integrals related to homogeneous mappings in Triebel–Lizorkin spaces. J. Math. Inequal. 11(4), 1075–1097 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  29. J. Pan, W. Li, H.P. Zhang, Control algorithms of magnetic suspension systems based on the improved double exponential reaching law of sliding mode control. Int. J. Control Autom. Syst. 16(6), 2878–2887 (2018)

    Article  Google Scholar 

  30. J. Pan, H. Ma, X. Jiang, et al., Adaptive gradient-based iterative algorithm for multivariate controlled autoregressive moving average systems using the data filtering technique. Complexity (2018), Article ID 9598307. https://doi.org/10.1155/2018/9598307

  31. Z.H. Rao, C.Y. Zeng, M.H. Wu et al., Research on a handwritten character recognition algorithm based on an extended nonlinear kernel residual network. KSII Trans. Internet Inf. Syst. 12(1), 413–435 (2018)

    Google Scholar 

  32. R.S. Risuleo, G. Bottegal, H. Hjalmarsson, A nonparametric kernel-based approach to Hammerstein system identification. Automatica 85, 234–247 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  33. L. Xu, The parameter estimation algorithms based on the dynamical response measurement data. Adv. Mech. Eng. 9(11), 1–12 (2017). https://doi.org/10.1177/1687814017730003

    Article  Google Scholar 

  34. L. Xu, F. Ding, Recursive least squares and multi-innovation stochastic gradient parameter estimation methods for signal modeling. Circuits Syst. Signal Process. 36(4), 1735–1753 (2017)

    Article  MATH  Google Scholar 

  35. L. Xu, F. Ding, Iterative parameter estimation for signal models based on measured data. Circuits Syst. Signal Process. 37(7), 3046–3069 (2018)

    Article  MathSciNet  Google Scholar 

  36. L. Xu, F. Ding, Parameter estimation for control systems based on impulse responses. Int. J. Control Autom. Syst. 15(6), 2471–2479 (2017)

    Article  Google Scholar 

  37. L. Xu, F. Ding, The parameter estimation algorithms for dynamical response signals based on the multi-innovation theory and the hierarchical principle. IET Signal Process. 11(2), 228–237 (2017)

    Article  Google Scholar 

  38. L. Xu, F. Ding, Y. Gu et al., A multi-innovation state and parameter estimation algorithm for a state space system with d-step state-delay. Signal Process. 140, 97–103 (2017)

    Article  Google Scholar 

  39. G.H. Xu, Y. Shekofteh, A. Akgul, C.B. Li, S. Panahi, A new chaotic system with a self-excited attractor: entropy measurement, signal encryption, and parameter estimation. Entropy 20(2), 1–23 (2018). https://doi.org/10.3390/e20020086

    Article  Google Scholar 

  40. L. Xu, W.L. Xiong et al., Hierarchical parameter estimation for the frequency response based on the dynamical window data. Int. J. Control Autom. Syst. 16(4), 1756–1764 (2018)

    Article  Google Scholar 

  41. C.C. Yin, C.W. Wang, The perturbed compound Poisson risk process with investment and debit interest. Methodol. Comput. Appl. Probab. 12(3), 391–413 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  42. C.C. Yin, Y.Z. Wen, Exit problems for jump processes with applications to dividend problems. J. Comput. Appl. Math. 245, 30–52 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  43. C.C. Yin, Y.Z. Wen, Optimal dividend problem with a terminal value for spectrally positive Levy processes. Insur. Math. Econ. 53(3), 769–773 (2013)

    Article  MATH  Google Scholar 

  44. C.C. Yin, K.C. Yuen, Optimality of the threshold dividend strategy for the compound Poisson model. Stat. Probab. Lett. 81(12), 1841–1846 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  45. C.C. Yin, J.S. Zhao, Nonexponential asymptotics for the solutions of renewal equations, with applications. J. Appl. Probab. 43(3), 815–824 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  46. Y.Z. Zhang, Y. Cao, Y.H. Wen, L. Liang, F. Zou, Optimization of information interaction protocols in cooperative vehicle-infrastructure systems. Chin. J. Electron. 27(2), 439–444 (2018)

    Article  Google Scholar 

  47. X. Zhang, F. Ding et al., Recursive parameter identification of the dynamical models for bilinear state space systems. Nonlinear Dyn. 89(4), 2415–2429 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  48. X. Zhang, F. Ding et al., State filtering-based least squares parameter estimation for bilinear systems using the hierarchical identification principle. IET Control Theory Appl. 12(12), 1704–1713 (2018)

    Article  MathSciNet  Google Scholar 

  49. X. Zhang, L. Xu et al., Combined state and parameter estimation for a bilinear state space system with moving average noise. J. Frankl. Inst. 355(6), 3079–3103 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  50. W.H. Zhang, L. Xue, X. Jiang, Global stabilization for a class of stochastic nonlinear systems with SISS-like conditions and time delay. Int. J. Robust Nonlinear Control 28(13), 3909–3926 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  51. N. Zhao, R. Liu, Y. Chen, M. Wu, Y. Jiang, W. Xiong, C. Liu, Contract design for relay incentive mechanism under dual asymmetric information in cooperative networks. Wirel. Netw. 24(8), 3029–3044 (2018)

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Key R&D Program of China (No. 2016YFE0202200) and the Research Foundation of China University of Petroleum-Beijing At Karamay (No. CYJ2017B-01-001).

Author information

Authors and Affiliations

  1. Key Laboratory of Deep GeoDrilling Technology of Ministry of Natural Resources, School of Engineering and Technology, China University of Geosciences, Beijing, 100083, People’s Republic of China

    Yuanbiao Hu, Qin Zhou, Hao Yu & Zheng Zhou

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

    Feng Ding

Authors
  1. Yuanbiao Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Qin Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hao Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Zheng Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Feng Ding
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Yuanbiao Hu or Feng Ding.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hu, Y., Zhou, Q., Yu, H. et al. Two-Stage Generalized Projection Identification Algorithms for Stochastic Systems. Circuits Syst Signal Process 38, 2846–2862 (2019). https://doi.org/10.1007/s00034-018-0996-0

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-018-0996-0

Keywords

Search

Navigation