Nonlinear system identification using autoregressive quadratic models

Signal Processing

Volumn 81, Issue 2, 2001, Pages 357-379

  Le Caillec, Jean Marc ^a   Garello, René ^a  

^a ECOLE DES MINES DE NANTES   (France)

Author keywords

[No Author keywords available]

Indexed keywords

CORRELATION METHODS; DATA STRUCTURES; MATHEMATICAL MODELS; REGRESSION ANALYSIS;

HIGHER-ORDER MOMENTS; QUADRATIC AUTOREGRESSIVE MOVING AVERAGE (QARMA); VOLTERRA MODELS;

NONLINEAR FILTERING;

EID: 0035250776     PISSN: 01651684     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0165-1684(00)00213-9     Document Type: Article

References (36)

1. Aase K.K. Recursive estimation in nonlinear time series models of autoregressive type. JRSS Ser. B. 1983;228-233.
2. Aguirre L.A., Billings S.A. Nonlinear chaotic systems: approaches and implications for science and engineering-a survey. Appl. Signal Process. 1995;224-248.
3. Alpers W.R. Theory of radar imaging of internal waves. Nature. 314:1985;245-247.
4. Bendat J.S. Nonlinear System Analysis and Identification. 1990;Wiley, New York.
5. Chen S., Billings S.A. Representation of non-linear systems: the narmax model. Int. J. Control. 3:1989;1013-1032.
6. Chiang H-H., Nikias C.L. Adaptative deconvolution and identification of nonminimum phase FIR systems based on cumulants. IEEE Trans. Automat. Control. 35:1990;36-47.
7. Engle R.F. Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom Inflation. Econometrika. 1982;987-1007.
8. Fonollosa J.R., Nikias C.L. Wigner higher order moment spectra: definition, properties, computation and application to transient signal analysis. IEEE Trans. Signal Process. 41:1993;245-265.
9. Giannakis G.B. Cumulants: a powerful tool in signal processing. Proc. IEEE. 75:1987;1333-1334.
10. Giannakis G.B., Swami A. On estimating noncausal nonminimum phase ARMA models of non-gaussian processes. IEEE Trans. Acoust. Speech Signal Process. 38:1990;478-495.
11. Haggan V., Ozaki T. A study of application of modeling nonlinear random vibrations using an amplitude time dependent autoregressive time series models. Biometrika. 1981;189-196.
12. Hasselmann K., Hasselmann S. On the nonlinear mapping of an ocean wave spectrum into a synthetic aperture radar image spectrum and its inversion. J. Geophys. Res. 96:1991;10,713-10,729.
13. Hatzanikos D., Nikias C.L. Blind equalization using a tricepstrum-based algorithm. IEEE Trans. Commun. 39:1991;669-681.
14. Haykin S. Adaptative Filter Theory. 1986;PTR Prentice-Hall, Englewood Cliffs, NJ.
15. Kay S.M. Modern Spectral Estimation, Theory and Application. 1988;PTR Prentice-Hall, Englewood Cliffs, NJ.
16. Kim K.I., Powers E.J. A digital method of modeling quadratically nonlinear systems with a general random input. IEEE Trans. Acoust. Speech Signal Process. 36:1988;1758-1769.
17. Koh T., Powers E.J. Second-order volterra filtering and its application to nonlinear system identification. IEEE Trans. Acoust. Speech Signal Process. 33:1985;1445-1455.
18. Korenberg M.J., Hunter I.W. The identification of biological systems: Wiener kernel approach. Ann. Biomed. Eng. 18:1990;628-654.
19. Korenberg M.J., Hunter I.W. The identification of biological systems: Volterra kernel approach. Ann. Biomed. Eng. 24:1996;250-268.
20. Krogstad H.E. A simple derivation of Hasselmann's nonlinear ocean-synthetic aperture radar transform. J. Geophys. Res. 97:1992;2421-2425.
21. Le Caillec J-M., Garello R., Chapron B. Two dimensional bispectral estimates from ocean SAR images. Nonlinear Process. Geophys. 3:1996;196-215.
22. Lee J., Mathews V.J. A stability condition for certain bilinear systems. IEEE Trans. Signal Process. 42:1994;1871-1873.
23. Leontaritis I.J., Billings S.A. Input-output parametric models for nonlinear systems part i: deterministic nonlinear model. Int. J. Control. 1985;303-328.
24. Leontaritis I.J., Billings S.A. Input-output parametric models for nonlinear systems part ii: stochastic nonlinear model. Int. J. Control. 1985;329-344.
25. Liu Y.P., Korenberg M., Billings S.A., McIlroy P.J. Orthogonal parameter estimation algorithm for non-linear stochastic systems. Int. J. Control. 48:1988;193-210.
26. Marple S.L. Digital Spectral Analysis with Application. 1988;PTR Prentice-Hall, Englewood Cliffs, NJ.
27. Mohler R.R. Bilinear Control Processes. 1973;Academic, New York.
28. Narenda K.S., Mukhopadhyay S. Adaptative control using neural networks and approximate models. IEEE Trans. Signal Process. 8:1997;475-485.
29. Raghuveer M.R., Nikias C.L. Bispectrum estimation: a digital signal processing framework. Proc. IEEE. 75:1987;869-891.
30. Rao T.S., Gabr M.M. An Introduction to Bispectral Analysis and Bilinear Time Series Models. 1984;Springer, Berlin.
31. Rosenblatt M., Van Ness J.W. Estimation of the bispectrum. Ann. Math. Stat. 1965;1120-1136.
32. Schetzen J.S. The Volterra and Wiener Theories of Nonlinear Systems. 1980;Wiley, New York.
33. Swain A.K., Billings S.A. Weighted complex orthogonal estimator for identifying linear and non-linear continuous time models from generalized frequency response functions. Mech. Systems Signal Process. 12:1998;269-292.
34. Urick R.J. Principal of Underwater Sound. 1983;McGraw-Hill, New York.
35. Van Ness J.W. Asymptotic normality of bispectral estimate. Ann. Math. Stat. 1966;1257-1272.
36. Zheng F.C., McLaughlin S., Mulgrew B. Blind equalization of nonminimum phase channels: higher order cumulant based algorithm. IEEE Trans. Signal Process. 41:1993;681-691.