Accuracy of linear multiple-input multiple-output (MIMO) models obtained by maximum likelihood estimation

Automatica

Volumn 48, Issue 4, 2012, Pages 632-637

  Agüero, Juan C ^a   Rojas, Cristian R ^b   Hjalmarsson, Håkan ^b   Goodwin, Graham C ^a  

^a UNIVERSITY OF NEWCASTLE   (Australia)

^b ROYAL INSTITUTE OF TECHNOLOGY   (Sweden)

Author keywords

Accuracy; Maximum likelihood estimation; System identification

Indexed keywords

ACCURACY; FREQUENCY DOMAINS; INFORMATION MATRIX; LINEAR MIMO SYSTEMS; MULTI VARIABLES; PARAMETRIC MODELS; SPECTRAL ESTIMATION;

COMMERCE; IDENTIFICATION (CONTROL SYSTEMS); MIMO SYSTEMS; SPECTRUM ANALYSIS;

MAXIMUM LIKELIHOOD ESTIMATION;

EID: 84858149529     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.automatica.2012.01.015     Document Type: Article

References (43)

1. J.C. Agero, and G.C. Goodwin Choosing between open and closed loop experiments in linear system identification IEEE Transactions on Automatic Control 52 8 2007 1475 1480 (Pubitemid 47316696)
2. J.C. Agero, and G.C. Goodwin Identifiability of errors in variables dynamic systems Automatica 44 2 2008 371 382
3. Agero, J. C.; Rojas, C. R.; & Goodwin, G. C. (2009). Fundamental limitations on the accuracy of MIMO models obtained by PEM. In Proceedings of the 48th IEEE conference on decision and control, CDC.
4. J.C. Agero, J.I. Yuz, G.C. Goodwin, and R.A. Delgado On the equivalence of time and frequency domain maximum likelihood estimation Automatica 46 2 2010 260 270
5. strm, K.J. (1967). On the achievable accuracy in identification problems. In Proceedings of the IFAC congress on identification in automatic control systems. Prague, Czechoslovakia.
6. M.C. Campi, and E. Weyer Finite sample properties of system identification methods IEEE Transactions on Automatic Control 47 8 2002 1329 1334 (Pubitemid 34959768)
7. M.C. Campi, and E. Weyer Guaranteed non-asymptotic confidence regions in system identification Automatica 41 2005 1751 1764 (Pubitemid 41119032)
8. G. Casella, and R.L. Berger Statistical inference 2nd edition 2002 Duxbury
9. A. Esparza, J.C. Agero, C.R. Rojas, and B.I. Godoy Asymptotic statistical analysis for model-based control design strategies Automatica 47 5 2011 1041 1046
10. B. Friedlander, and B. Porat A general lower bound for parametric spectrum estimation IEEE Transactions on Acoustics, Speech, and Signal Processing 32 4 1984 728 733 (Pubitemid 15463737)
11. M. Gevers, and L. Ljung Optimal experiment designs with respect to the intended model application Automatica 22 5 1986 543 554 (Pubitemid 17465673)
12. G.C. Goodwin, S.F. Graebe, and M.E. Salgado Control system design 2001 Prentice Hall Upper Saddle River, NJ
13. G.C. Goodwin, and R.L. Payne Dynamic system identification: experiment design and data analysis 1977 Academic Press
14. E.J. Hannan, and M. Deistler The statistical theory of linear systems 1988 John Wiley and Sons, Inc.
15. H. Hjalmarsson, and J. Mrtensson A geometric approach to variance analysis in system identification IEEE Transactions on Automatic Control 56 5 2011 983 997
16. H. Hjalmarsson, and B. Ninness Least-squares estimation of a class of frequency functions: a finite sample variance expression Automatica 42 4 2006 589 600 (Pubitemid 43267652)
17. H. Jansson, and H. Hjalmarsson Input design via LMIs admitting frequency-wise model specifications in confidence regions IEEE Transactions on Automatic Control 50 10 2005 1534 1549 (Pubitemid 41555603)
18. E. Karlsson, T. Sderstrm, and P. Stoica The CramrRao lower bound for noisy inputoutput systems Signal Processing 80 11 2000 2421 2447
19. A.A.B. Klein A generalization of Whittle's formula for the information matrix of vector-mixed time series Linear Algebra and its Applications 321 13 2000 197 208
20. A.A.B. Klein, and G. Mlard The information matrix of multiple-input single-output time series models Journal of Computational and Applied Mathematics 51 1994 349 356
21. A.A.B. Klein, and P. Spreij Matrix differential calculus applied to multiple stationary time series and an extended Whittle formula for information matrices Linear Algebra and its Applications 430 23 2009 674 691
22. Larimore, W.E. (1982). A survey of some recent developments in system parameter estimation. In Proceedings of the 6th IFAC symposium on identification and parameter estimation (pp. 979984). Arlington, VA.
23. L. Ljung System identification: theory for the user 2nd edition 1999 Prentice Hall
24. L. Ljung Asymptotic variance expressions for identified black-box transfer function models IEEE Transactions on Automatic Control 30 9 1985 834 844 (Pubitemid 16494285)
25. L. Ljung, and P.E. Caines Asymptotic normality of prediction error estimators for approximative system models Stochastics 3 1979 29 46 (Pubitemid 10428005)
26. B. Ninness, and H. Hjalmarsson Variance error quantifications that are exact for finite model order IEEE Transactions on Automatic Control 49 8 2004 1275 1291
27. B. Ninness, and H. Hjalmarsson On the frequency domain accuracy of closed loop estimates Automatica 41 7 2005 1109 1122 (Pubitemid 40644851)
28. B. Ninness, H. Hjalmarsson, and F. Gustafsson The fundamental role of general orthonormal bases in system identification IEEE Transactions on Automatic Control 44 7 1999 1384 1406
29. Rojas, C.R.; Agero, J.C.; Welsh, J.S.; Goodwin, G.C.; & Feuer, A. (2012). Robustness in experiment design. IEEE Transactions on Automatic Control, in press (doi:10.1109/TAC.2011.2166294).
30. C.R. Rojas, J.S. Welsh, and J.C. Agero Fundamental limitations on the variance of estimated parametric models IEEE Transactions on Automatic Control 54 5 2009 1077 1081
31. G.A.F. Seber A matrix handbook for statisticians 2008 Wiley
32. Sderstrm, T. (2005). Computing the covariance matrix for PEM estimates and the CramrRao lower bound for linear state space models. Technical Report 2005-019. Department of Information Technology, Uppsala University.
33. T. Sderstrm Errors-in-variables methods in system identification Automatica 43 6 2007 939 958
34. T. Sderstrm, M. Hong, J. Schoukens, and R. Pintelon Accuracy analysis of time domain maximum likelihood method and sample maximum likelihood method for errors-in-variables and output error identification Automatica 46 4 2010 721 727
35. T. Sderstrm, and P. Stoica System identification 1989 Prentice-Hall International
36. P. Stoica, J. Li, and B. Ninness The waterbed effect in spectral estimation Signal Processing Magazine, IEEE 21 3 2004 88 100
37. P. Stoica, and R. Moses Spectral analysis of signals 2005 Prentice Hall
38. P. Whittle The analysis of multiple stationary time series Journal of the Royal Statistical Society 15 1953 125 139
39. Z.D. Yuan, and L. Ljung Black-box identification of multivariable transfer functionsasymptotic properties and optimal input design International Journal of Control 40 2 1984 233 256 (Pubitemid 14629261)
40. Z.D. Yuan, and L. Ljung Unprejudiced optimal open loop input-design for identification of transfer-functions Automatica 21 6 1985 697 708 (Pubitemid 16488085)
41. M.B. Zarrop, R.L. Payne, and G.C. Goodwin Experiment design for time series analysis: the multivariate case SIAM Journal on Applied Mathematics 37 2 1979 370 381 (Pubitemid 10420604)
42. Y. Zhu Black-box identification of MIMO transfer functions: asymptotic properties of prediction error models International Journal of Adaptive Control and Signal Processing 3 1989 357 373 (Pubitemid 20644563)
43. Zhu, Y. (2006). System identification for process control: recent experience and outlook. In 14th IFAC symposium on system identification.