Frequency domain identification of MIMO state space models using the em algorithm

2007 European Control Conference, ECC 2007

Volumn , Issue , 2007, Pages 5686-5693

  Aguero, Juan C ^a   Yuz, Juan I ^b   Goodwin, Graham C ^a  

^a UNIVERSITY OF NEWCASTLE   (Australia)

^b DEPARTAMENTO DE FÍSICA   (Chile)

Author keywords

[No Author keywords available]

Indexed keywords

MAXIMUM LIKELIHOOD ESTIMATION; MIMO SYSTEMS; STATE SPACE METHODS;

EXPECTATION-MAXIMISATION; FREQUENCY-DOMAIN IDENTIFICATION; INPUT/OUTPUT DATUM; MAXIMUM LIKELIHOOD ESTIMATE; MIMO STATE-SPACE MODELS; MULTIPLE INPUT MULTIPLE OUTPUT SYSTEM; SPECIFIC FREQUENCIES; STATE - SPACE MODELS;

FREQUENCY DOMAIN ANALYSIS;

EID: 84927720966     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.23919/ecc.2007.7068691     Document Type: Conference Paper

References (48)

1. G. C. Goodwin, S. F. Graebe, and M. E. Salgado, Control system design. Upper Saddle River, NJ: Prentice Hall, 2001.
2. E. J. Hannan, "The identification and parameterization of Armax and state space forms," Econometrica, vol. 44, no. 4, pp. 713-723, 1976.
3. J. Durbin and S. J. Koopman, Time series analysis by state space methods. Oxford University Press, 2005.
4. B. Wahlberg, L. Ljung, and T. Söderström, "On sampling of continuous time stochastic processes," Control Theory and Advanced Technology, vol. 9, pp. 99-112, 1993.
5. J. I. Yuz and G. C. Goodwin, "Sampled-data models for stochastic nonlinear systems," in 14th IFAC symposium on system identification, Newcastle, Australia, 2006.
6. G. C. Goodwin and R. Payne, Dynamic system identification: Experiment design and data analysis. Academic Press, 1977.
7. L. Ljung, System identification: Theory for the user, 2nd ed. Prentice Hall, 1999.
8. P. Van Overschee and B. De Moor, Subspace identification for linear systems: Theory-implementation-applications. Kluwer Academic Publishers, 1996.
9. R. Pintelon and J. Schoukens, System identification: A frequency domain approach. IEEE press, 2001.
10. M. Deistler, "System identification-general aspects and structure," Model Identification and Adaptive Control: From windsurfing to telecommunications. Edited by G. C. Goodwin., pp. 3-26, 2000.
11. T. McKelvey and A. Helmersson, "State space parameterization of multivariable linear systems using tridiagonal matrix form," Proceedings of the 35th IEEE Conference on Decision and Control, CDC, pp. 3654-3659, 1996.
12. R. Shumway and D. Stoffer, "An approach to time series smoothing and forecasting using the EM algorithm," Division of Statistics, University of California, Davis, Tech. Rep., 1981.
13. G. C. Goodwin and A. Feuer, "Estimation with missing data," Mathematical and Computer Modelling of Dynamical Systems, vol. 5, no. 3, pp. 220-244, 1999.
14. V. Solo, "An EM algorithm for singular state space models," Proceedings of the 42th IEEE Conference on Decision and Control, pp. 3457-3460, 2003.
15. -, "An EM algorithm for singular state space models: II," Proceedings of the 43rd IEEE Conference on Decision and Control, pp. 3611-3612, 2004.
16. S. Gibson and B. M. Ninness, "Robust maximum-likelihood estimation of multivariable dynamic systems," Automatica, vol. 41, no. 10, pp. 1667-1682, 2005.
17. L. Ljung, "Some results on identifying linear systems using frequency domain data," in Proceedings of the 32nd IEEE Conference on Decision and Control, 1993, pp. 3534-3538.
18. T. McKelvey, "Frequency domain identification methods," Circuits systems signal processing, vol. 21, no. 1, pp. 39-55, 2002.
19. T. McKelvey, H. Akcay, and L. Ljung, "Subspace-based multivariable system identification from frequency response data," IEEE Transactions on Automatic Control, vol. 41, no. 7, pp. 960-979, 1996.
20. B. Cauberghe, P. Guillaume, R. Pintelon, and P. Verboven, "Frequencydomain subsapce identification using FRF data from arbitrary signals," Journal of sound and vibration, no. 290, pp. 555-571, 2006.
21. A. P. Dempster, N. M. Laird, and D. B. Rubin, "Maximum likelihood from imcomplete data via the EM algorithm," Journal of the Royal Statistical Society, Series B, vol. 39, no. 1, pp. 1-38, 1977.
22. G. J. McLachlan and T. Krishnan, The EM Algorithm and Extensions. Wiley, 1997.
23. S. Gibson, "Maximum likelihood estimation of multivariable dynamic systems via the EM algorithm," Ph. D. Dissertation, School of Electrical Engineering and Computer Science, The University of Newcastle, Australia, 2003.
24. K. Lange, "A gradient algorithm locally equivalent to the EM algorithm," Journal of the Royal Statistical Society, Series B, vol. 57, no. 2, pp. 425-437, 1995.
25. M. A. Tanner, Tools for Statistical Inference. Springer, 1993.
26. G. C. Goodwin and J. C. Agüero, "Approximate EM algortihms for parameter and state estimation in nonlinear stochastic models," in Proceedings of the 44th IEEE Conference on Decision and Control (CDC) and European Control Conference (ECC), Seville, Spain, 2005.
27. D. Ghosh, "Maximum likelihood estimation of the dynamic shockerror model," Journal of econometrics, vol. 41, pp. 121-143, 1989.
28. A. Isaksson, "Identification of ARX models subject to missing data," IEEE Transactions on Automatic Control, vol. 38, no. 5, pp. 813-819, 1993.
29. R. Elliott and V. Krishnamurthy, "New finite-dimensional filters for paramter estimation of discrete-time linear Gaussian models," IEEE Transactions on Automatic Control, vol. 44, no. 5, pp. 938-951, 1999.
30. S. Gibson, A. Wills, and B. M. Ninness, "Maximum-likelihood parameter estimation of bilinear systems," IEEE Transactions on Automatic Control, vol. 50, no. 10, pp. 1581-1596, 2005.
31. E. J. Hannan, Multiple time series. John Wiley and Sons, Inc., 1970.
32. M. B. Priestley, Spectral analysis and time series. Elsevier Academic Press, 1981.
33. W. Hirt and J. L. Massey, "Capacity of the discrete-time Gaussian channel with intersymbol interference," IEEE Transactions on Information Theory, vol. 34, no. 3, pp. 380-388, 1988.
34. F. D. Neeser and J. L. Massey, "Proper complex random processes with applications to information theory," IEEE Transactions on Information Theory, vol. 39, no. 4, pp. 1293-1302, 1993.
35. D. R. Brillinger, Time series: Data analysis and theory. SIAM, 2001.
36. R. Pintelon and J. Schoukens, "Box-jenkins identification revisited-part i: Theory;," Automatica, vol. 42, no. 1, pp. 63-75, 2006.
37. B. Picinbono, "On circularity," IEEE Transactions on Signal Processing, vol. 42, no. 12, pp. 3473-3482, 1994.
38. -, "Second-order complex random vectors and normal distributions," IEEE Transactions on Signal Processing, vol. 44, no. 10, pp. 2637-2640, 1996.
39. A. Van den Bos, "The real-complex normal distribution," IEEE Transactions on Information Theory, vol. 44, no. 4, pp. 1670-1672, 1998.
40. C. R. Rao, Linear Statistical Inference and its Applications. New York: Wiley, 1965.
41. C. F. J. Wu, "On the convergence properties of the EM algorithm," The Annals of Statistics, vol. 11, no. 1, pp. 95-103, 1983.
42. R. A. Boyles, "On the convergence of the EM algorithm," Journal of the Royal Statistical Society, vol. 45, no. 1, pp. 47-50, 1983.
43. G. Goodwin, J. Yuz, and H. Garnier, "Robustness issues in continuoustime system identification from sampled data," in Proc. of 16th IFAC World Congress, Prague, Czech Republic, July 2005.
44. J. Yuz and G. Goodwin, Continuous-Time System Identification. Springer, To appear 2007, ch. Robust Identification of Continuous-Time Systems from Sampled Data. Edited by H. Garnier and L. Wang.
45. D. J. Higham and N. J. Higham, Matlab guide, 2nd ed. SIAM, 2005.
46. L. Wu, J. Pai, and J. Hosking, "An algorithm for estimating parameters of state-space models," Statistics and Probability Letters, vol. 28, pp. 99-106, 1996.
47. J. C. Agüero, "System identification methodologies incorporating constraints," Ph. D. Dissertation, School of Electrical Engineering and Computer Science, The University of Newcastle, Australia, 2005.
48. K. S. Miller, Complex stochastic processes: An introduction to theory and applications. Addison-Wesley Publishing Company, INC., 1974.