Periodic signal analysis by maximum likelihood modeling of orbits of nonlinear ODEs

Automatica

Volumn 41, Issue 5, 2005, Pages 793-805

  Söderström, Torsten ^a   Wigren, Torbjörn ^a   Abd Elrady, Emad ^a  

^a UPPSALA UNIVERSITY   (Sweden)

Author keywords

Nonlinear systems; Ordinary differential equations; Periodic orbits; Spectrum estimation; System identification

Indexed keywords

ALGORITHMS; FAST FOURIER TRANSFORMS; IDENTIFICATION (CONTROL SYSTEMS); KALMAN FILTERING; LEAST SQUARES APPROXIMATIONS; MATHEMATICAL MODELS; NONLINEAR SYSTEMS; ORDINARY DIFFERENTIAL EQUATIONS; TIME VARYING SYSTEMS;

AUTOREGRESSIVE MOVING AVERAGE (ARMA) MODELS; PERIODIC ORBITS; PERIODIC SIGNALS; SPECTRUM ESTIMATION;

MAXIMUM LIKELIHOOD ESTIMATION;

EID: 14844364382     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.automatica.2004.11.033     Document Type: Article

References (28)

1. Abd-Elrady, E. (2002). An adaptive grid point RPEM algorithm for harmonic signal modeling. Proceedings of the 15th IFAC World Congress, Barcelona, Spain.
2. E. Abd-Elrady A nonlinear approach to harmonic signal modeling Signal Processing 84 2004 163 195
3. Abd-Elrady, E., & Schoukens, J. (2004). Least squares periodic signal modeling using orbits of nonlinear ODE's and fully automated spectral analysis. In Proceedings of the 6th IFAC Symposium on Nonlinear Control Systems (NOLCOS 04). Stuttgart, Germany.
4. Abd-Elrady, E., & Söderström, T. (2004). Bias analysis in least-squares estimation of periodic signals using nonlinear ODE's. Submitted for publication.
5. E. Abd-Elrady, T. Söderström, and T. Wigren Periodic signal modeling based on Lienard's equation IEEE Transactions on Automatic Control 49 2004 1773 1778
6. Abd-Elrady, E., Söderström, T., Wigren, T. (2004b). Periodic signal analysis using periodic orbits of ODE's based on the Markov estimate. In Proceedings of the second IFAC workshop on periodic control systems, Yokohama, Japan.
7. E. Benhadj-Braiek, and F. Rotella Identification of non-stationary continuous systems using modulating functions Journal of Franklin Institute 327 1990 831 840
8. T.B. Co, and S. Ungarala Batch scheme recursive parameter estimation of continuous-time systems using the modulating functions method Automatica 33 1997 1185 1191
9. T.B. Co, and B.E. Ydstie System identification using modulating functions method and fast Fourier transforms Computer and Chemical Engineering 14 1990 1051 1066
10. S. Daniel-Berhe, and H. Unbehauen Bilinear continuous-time systems identification via Hartley based modulating function Automatica 34 1998 301 318
11. M.P. Fitz Further results in the fast estimation of a single frequency IEEE Transactions on Communications 42 1994 862 864
12. P. Händel, and P. Tichavsky Adaptive estimation for periodic signal enhancement and tracking International Journal of Adaptive Control and Signal Processing 8 1994 447 456
13. H.K. Khalil Nonlinear systems (2nd ed) 1996 Prentice-Hall Upper Saddle River, NJ
14. R. Kumaresan, and D.W. Tufts Estimating the parameters of exponentially damped sinusoids and pole-zero modeling in noise IEEE Transactions on Acoustics, Speech, and Signal Processing 30 1982 833 840
15. J. Li, and P. Stoica An adaptive filtering approach to spectral estimation and SAR imaging IEEE Transactions on Signal Processing 44 1996 1469 1484
16. D.G. Luenberger Introduction to linear and nonlinear programming 1973 Addison-Wesley Reading, MA
17. A. Nehorai, and B. Porat Adaptive comb filtering for harmonic signal enhancement IEEE Transactions on Acoustics, Speech, and Signal Processing 34 1986 1124 1138
18. B. Porat, and B. Friedlander On the accuracy of the Kumaresan-Tufts method for estimating complex damped exponentials IEEE Transactions on Acoustics, Speech, and Signal Processing 35 1987 231 235
19. D.C. Rife, and R.R. Boorstyn Multiple tone parameter estimation from discrete-time observations Bell System Technical Journal 55 1976 1389 1410
20. T. Söderström, and P. Stoica System identification 1989 Prentice-Hall Int. Hemel Hempstead, UK
21. P. Stoica, and R. Moses Introduction to spectral analysis 1997 Prentice-Hall Upper Saddle River, NJ
22. P. Stoica, and A. Nehorai Statistical analysis of two nonlinear estimators of sine wave parameters in the colored noise case Circular Systems and Signal Processing 8 1989 3 15
23. P. Tichavsky, and P. Händel Recursive estimation of frequencies and frequency rates of multiple cisoids in noise Signal Processing 58 1997 117 129
24. M. Vidyasagar Nonlinear system analysis 1978 Prentice-Hall Englewood Cliffs, NJ
25. Wigren, T., Abd-Elrady, E., & Söderström, T. (2003a). Harmonic signal analysis with Kalman filters using periodic orbits of nonlinear ODEs. ICASSP 2003, Hongkong, P.R. China, 669-672.
26. Wigren, T., Abd-Elrady, E., & Söderström, T. (2003b). Least squares harmonic signal analysis using periodic orbits of ODEs. Proceedings of the IFAC SYSID 2003, Rotterdam, The Netherlands, 1584-1589.
27. Wigren, T., & Händel, P. (1996). Harmonic signal modeling using adaptive nonlinear function estimation. IEEE international conference on acoustics, speech and signal processing, Atlanta, GA, USA.
28. Wigren, T., & Söderström, T. (2003). Second order ODEs are sufficient for modeling of many periodic signals. Tech. Rep. 2003-025, Department of Information Technology, Uppsala University, Uppsala, Sweden, April, 2003.