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

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.

Inspec keywords: parameter estimation; continuous time systems; iterative methods; sampled data systems

Other keywords: two-step iterative procedure; computational efficiency; instrumental variable method; plant-noise model decomposition; Box–Jenkins structure; prediction error method; noise model; continuous-time Box–Jenkins model parameter estimation; irregularly sampled data; plant model

Subjects: Simulation, modelling and identification; Interpolation and function approximation (numerical analysis); Discrete control systems

References

    1. 1)
      • 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.
    2. 2)
      • 30. Söderström, T., Stoica, P.: ‘Instrumental variable methods for system identification’ (Springer-Verlag, New York, 1983).
    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)
      • 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.
    5. 5)
      • 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.
    6. 6)
      • 21. Larsson, E.K., Söderström, T.: ‘Identification of continuous-time AR processes from unevenly sampled data’, Automatica, 2002, 38, (4), pp. 709718.
    7. 7)
      • 26. Söderström, T.: ‘Discrete-time stochastic systems’ (Springer Verlag, London, 2002).
    8. 8)
      • 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.
    9. 9)
      • 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.
    10. 10)
      • 7. Pintelon, R., Schoukens, J.: ‘Box–Jenkins identification revisited – Part I: theory’, Automatica, 2006, 42, (1), pp. 6375.
    11. 11)
      • 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.
    12. 12)
      • 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.
    13. 13)
      • 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.
    14. 14)
      • 19. Wang, J., Zheng, W.X., Chen, T.: ‘Identification of linear dynamic systems operating in a networked environment’, Automatica, 2009, 45, (12), pp. 27632772.
    15. 15)
      • 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.
    16. 16)
      • 33. Mossberg, M.: ‘Estimation of continuous-time stochastic signals from sample covariances’, IEEE Trans. Signal Process., 2008, 56, (2), pp. 821825.
    17. 17)
      • 11. Young, P.C.: ‘Refined instrumental variable estimation: maximum likelihood optimization of a unified Box–Jenkins model’, Automatica, 2015, 51, (1), pp. 3546.
    18. 18)
      • 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.
    19. 19)
      • 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.
    20. 20)
      • 23. Kirshner, H., Maggio, S., Unser, M.: ‘A sampling theory approach for continuous ARMA identification’, IEEE Trans. Signal Process., 2011, 59, (10), pp. 46204634.
    21. 21)
      • 28. Shumway, R.H., Stoffer, D.S.: ‘Time series analysis and its applications’ (Springer Science+Business Media, New York, 2011, 3rd edn.).
    22. 22)
      • 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.
    23. 23)
      • 6. Box, G.E.P., Jenkins, G.M., Reinsel, G.C., et al: ‘Time series analysis: forecasting and control’ (Wiley, 2015, 5th edn.).
    24. 24)
      • 25. Øksendal, B.: ‘Stochastic differential equations-an Introduction with applications’ (Springer-Verlag, Berlin Heidelberg, 2003).
    25. 25)
      • 22. Gillberg, J., Ljung, L.: ‘Frequency-domain identification of continuous-time ARMA models from sampled data’, Automatica, 2009, 45, (6), pp. 13711378.
    26. 26)
      • 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.
    27. 27)
      • 5. Young, P.C.: ‘Parameter estimation for continuous-time models – a survey’, Automatica, 1981, 17, (1), pp. 2339.
    28. 28)
      • 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.
    29. 29)
      • 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.
    30. 30)
      • 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.
    31. 31)
      • 1. Young, P.C.: ‘Recursive estimation and time-series analysis: an introduction for the student and practitioner’ (Springer-Verlag, Berlin, 2011).
    32. 32)
      • 2. Garnier, H., Wang, L. (Eds.): ‘Identification of continuous-time models from sampled data’ (Springer-Verlag, London, 2008).
    33. 33)
      • 31. Söderström, T., Stoica, P.: ‘System Identification. Series in Systems and Control Engineering’ (Prentice-Hall, Englewood Cliffs, 1989).
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