Skip to main content
SpringerLink
Log in

Instrumental variables for parameter estimation in stochastic systems with coloured noise

  • Published:
International Journal of Dynamics and Control Aims and scope Submit manuscript

Abstract

This paper presents an estimation algorithm for continuous-time stochastic systems under coloured perturbations using an extended form of the instrumental variable method. A comparison between the extended an the simple form was done using two numerical examples to test their efficiency. The results showed that the simple version is able to estimate coloured noise without additional information and it is easier to implement than the extended version.

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. Pugachev VS, Sinitsyn IN (2001) Stochastic systems. Theory and applications. World Scientific, Singapore

    MATH  Google Scholar 

  2. Gard T (1988) Introduction to stochastic differential equations. Marcel Dekker, New York

    MATH  Google Scholar 

  3. Davis MHA (1977) Linear estimation and stochastic control. Chapman and Hall, London

    MATH  Google Scholar 

  4. Beck JV, Arnold KJ (1977) Parameter estimation in engineering and science. John Wiley & Sons, New York, Chichester, Brisbane, Toronto

    MATH  Google Scholar 

  5. Chen H, Guo L (1991) Identification and stochastic adaptive control. Birkhäuser, Boston, Basel, Berlin

    Book  MATH  Google Scholar 

  6. Ljung L (1999) System identification. Theory for the user. Prentice Hall, Upper Saddle River

  7. Poznyak A (1980) Estimating the parameters of autoregressing processes by the method of least squares. Int J Syst Sci 5(11):235254

    Google Scholar 

  8. Kumar P, Varaiya P (1986) Stochastic systems: estimation, identification,and adaptive control. Prentice Hall, Upper Saddle River

    MATH  Google Scholar 

  9. Bowden R, Darrel A (1984) Instrumental variables. Cambridge University Press, Cambridge

    Google Scholar 

  10. Söderström T, Stoica P (1981) Comparison of some instrumental variable methods consistency and accuracy aspects. Automatica 17(1):101–115

    Article  MathSciNet  MATH  Google Scholar 

  11. Söderström T (2011) A generalized instrumental variable estimation method for errors-in-variables identification problems. Automatica 47:1656–1666

    Article  MathSciNet  MATH  Google Scholar 

  12. Liu X, Wang J, Zheng WX (2011) Convergence analysis of refined instrumental variable method for continuous-time system identification. IET Control Theory Appl 5(7):868–877

    Article  MathSciNet  Google Scholar 

  13. Escobar J, Enqvist M (2016) Instrumental variables and LSM in continuous-time parameter estimation, ESAIM: Control, Optimisation and Calculus of Variations

  14. Escobar J, Poznyak A (2011) Time-varying matrix estimation in stochastic continuous-time models under coloured noise using LSM with forgetting factor. Int J Syst Sci 42(12):2009–2020

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Instituto Politécnico Nacional, ESIME Zac, UPALM, Av IPN S/N, Col. Lindavista, C.P. 07738, Mexico, DF, Mexico

    J. Escobar

  2. IMSS Research Center in Metabolic Diseases, Cuauhtemoc 330 Col. Doctores, C.P. 06720, Mexico, DF, Mexico

    A. Gallardo

Authors
  1. J. Escobar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Gallardo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to J. Escobar.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Escobar, J., Gallardo, A. Instrumental variables for parameter estimation in stochastic systems with coloured noise. Int. J. Dynam. Control 6, 1105–1110 (2018). https://doi.org/10.1007/s40435-017-0304-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40435-017-0304-z

Keywords

Search

Navigation