http://iet.metastore.ingenta.com
1887

Refined instrumental variable parameter estimation of continuous-time Box–Jenkins models from irregularly sampled data

Refined instrumental variable parameter estimation of continuous-time Box–Jenkins models from irregularly sampled data

For access to this article, please select a purchase option:

Buy article PDF
$19.95
(plus tax if applicable)
Buy Knowledge Pack
10 articles for $120.00
(plus taxes if applicable)

IET members benefit from discounts to all IET publications and free access to E&T Magazine. If you are an IET member, log in to your account and the discounts will automatically be applied.

Learn more about IET membership 

Recommend Title Publication to library

You must fill out fields marked with: *

Librarian details
Name:*
Email:*
Your details
Name:*
Email:*
Department:*
Why are you recommending this title?
Select reason:
 
 
 
 
 
IET Control Theory & Applications — Recommend this title to your library

Thank you

Your recommendation has been sent to your librarian.

This study investigates the estimation of continuous-time Box–Jenkins model parameters from irregularly sampled data. The Box–Jenkins structure has been successful in describing systems subject to coloured noise, since it contains two sub-models that feature the characteristics of both plant and noise systems. Based on plant-noise model decomposition, a two-step iterative procedure is proposed to solve the estimation problem, which consists of an instrumental variable method for the plant model and a prediction error method for the noise model. The proposed method is of low complexity and shows good estimation robustness and accuracy. Implementation issues are discussed to improve the computational efficiency. Numerical examples are presented to demonstrate the effectiveness of the proposed method.

References

    1. 1)
      • 1. Young, P.C.: ‘Recursive estimation and time-series analysis: an introduction for the student and practitioner’ (Springer-Verlag, Berlin, 2011).
    2. 2)
      • 2. Garnier, H., Wang, L. (Eds.): ‘Identification of continuous-time models from sampled data’ (Springer-Verlag, London, 2008).
    3. 3)
      • 3. Rao, G.P., Unbehauen, H.: ‘Identification of continuous-time systems’, IEE Proc. Control Theory Appl., 2006, 153, (2), pp. 185220.
    4. 4)
      • 4. Garnier, H., Mensler, M., Richard, A.: ‘Continuous-time model identification from sampled data: implementation issues and performance evaluation’, Int. J. Control, 2003, 76, (13), pp. 13371357.
    5. 5)
      • 5. Young, P.C.: ‘Parameter estimation for continuous-time models – a survey’, Automatica, 1981, 17, (1), pp. 2339.
    6. 6)
      • 6. Box, G.E.P., Jenkins, G.M., Reinsel, G.C., et al: ‘Time series analysis: forecasting and control’ (Wiley, 2015, 5th edn.).
    7. 7)
      • 7. Pintelon, R., Schoukens, J.: ‘Box–Jenkins identification revisited – Part I: theory’, Automatica, 2006, 42, (1), pp. 6375.
    8. 8)
      • 8. Young, P.C., Jakeman, A.J.: ‘Refined instrumental variable methods of recursive time-series analysis part III, Extensions’, Int. J. Control, 1980, 31, pp. 741764.
    9. 9)
      • 9. Ding, F., Wang, Y., Ding, J.: ‘Recursive least squares parameter identification algorithms for systems with colored noise using the filtering technique and the auxiliary model’, Digital Signal Process., 2015, 37, (2), pp. 100108.
    10. 10)
      • 10. Wang, Y., Ding, F.: ‘The auxiliary model based hierarchical gradient algorithms and convergence analysis using the filtering technique’, Signal Process., 2016, 128, (11), pp. 212221.
    11. 11)
      • 11. Young, P.C.: ‘Refined instrumental variable estimation: maximum likelihood optimization of a unified Box–Jenkins model’, Automatica, 2015, 51, (1), pp. 3546.
    12. 12)
      • 12. Garnier, H., Young, P.C.: ‘The advantages of directly identifying continuous-time transfer function models in practical applications’, Int. J. Control, 2014, 87, (7), pp. 13191338.
    13. 13)
      • 13. Gilson, M., Garnier, H., Van den Hof, P.: ‘Optimal instrumental variable method for closed-loop identification’, IET Control Theory Appl., 2011, 5, (10), pp. 11471154.
    14. 14)
      • 14. Chen, F., Garnier, H., Gilson, M.: ‘Robust identification of continuous-time models with arbitrary time-delay from irregularly sampled data’, J. Process Control, 2015, 25, pp. 1927.
    15. 15)
      • 15. Laurain, V., Toth, R., Gilson, M., et al: ‘Direct identification of continuous-time linear parameter-varying input/output models’, IET Control Theory Appl., 2011, 5, (7), pp. 878888.
    16. 16)
      • 16. Åström, K.J., Bernhardsson, B.: ‘Systems with Lebesgue sampling, in Rantzer, A., Byrnes, C.I. Eds.: ‘Directions in mathematical systems theory and optimization’ (Springer-Verlag, Berlin Heidelberg, 2003), pp. 113.
    17. 17)
      • 17. Tsai, H., Chan, K.S.: ‘Maximum likelihood estimation of linear continuous time long memory processes with discrete time data’, J. R. Stat. Soc. B, 2005, 67, (5), pp. 703716.
    18. 18)
      • 18. Yuz, J.I., Alfaro, J., Agüero, J.C., et al: ‘Identification of continuous-time state-space models from non-uniform fast-sampled data’, IET Control Theory Appl., 2011, 5, (7), pp. 842855.
    19. 19)
      • 19. Wang, J., Zheng, W.X., Chen, T.: ‘Identification of linear dynamic systems operating in a networked environment’, Automatica, 2009, 45, (12), pp. 27632772.
    20. 20)
      • 20. Chen, F., Garnier, H., Gilson, M., et al: ‘Identification of continuous-time transfer function models from non–uniformly sampled data in presence of colored noise’. The 19th IFAC World Congress, Cape Town, South Africa, 24–29 August 2014.
    21. 21)
      • 21. Larsson, E.K., Söderström, T.: ‘Identification of continuous-time AR processes from unevenly sampled data’, Automatica, 2002, 38, (4), pp. 709718.
    22. 22)
      • 22. Gillberg, J., Ljung, L.: ‘Frequency-domain identification of continuous-time ARMA models from sampled data’, Automatica, 2009, 45, (6), pp. 13711378.
    23. 23)
      • 23. Kirshner, H., Maggio, S., Unser, M.: ‘A sampling theory approach for continuous ARMA identification’, IEEE Trans. Signal Process., 2011, 59, (10), pp. 46204634.
    24. 24)
      • 24. Young, P.C., Garnier, H., Gilson, M.: ‘Refined instrumental variable identification of continuous-time hybrid Box–Jenkins models’, in Garnier, H., Wang, L. (Eds.): ‘Identification of continuous-time models from sampled data’ (Springer-Verlag, London, 2008), pp. 91132.
    25. 25)
      • 25. Øksendal, B.: ‘Stochastic differential equations-an Introduction with applications’ (Springer-Verlag, Berlin Heidelberg, 2003).
    26. 26)
      • 26. Söderström, T.: ‘Discrete-time stochastic systems’ (Springer Verlag, London, 2002).
    27. 27)
      • 27. Goodwin, G.C., Agüero, J.C., Cea-Garrido, M.E., et al: ‘Sampling and sampled-data models’, IEEE Control Syst. Mag., 2013, 33, (5), pp. 3453.
    28. 28)
      • 28. Shumway, R.H., Stoffer, D.S.: ‘Time series analysis and its applications’ (Springer Science+Business Media, New York, 2011, 3rd edn.).
    29. 29)
      • 29. Liu, X., Wang, J., Zheng, W.X.: ‘Convergence analysis of refined instrumental variable method for continuous-time system identification’, IET Control Theory Appl., 2011, 5, (7), pp. 868877.
    30. 30)
      • 30. Söderström, T., Stoica, P.: ‘Instrumental variable methods for system identification’ (Springer-Verlag, New York, 1983).
    31. 31)
      • 31. Söderström, T., Stoica, P.: ‘System Identification. Series in Systems and Control Engineering’ (Prentice-Hall, Englewood Cliffs, 1989).
    32. 32)
      • 32. Watson, M.W., Engle, R.F.: ‘Alternative algorithms for the estimation of dynamic factor, mimic and varying coefficient regression models’, J. Econometrics, 1983, 23, (3), pp. 385400.
    33. 33)
      • 33. Mossberg, M.: ‘Estimation of continuous-time stochastic signals from sample covariances’, IEEE Trans. Signal Process., 2008, 56, (2), pp. 821825.
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2016.0506
Loading

Related content

content/journals/10.1049/iet-cta.2016.0506
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading
This is a required field
Please enter a valid email address