Second-Order Volterra Filtering and Its Application to Nonlinear System Identification

IEEE Transactions on Acoustics, Speech, and Signal Processing

Volumn 33, Issue 6, 1985, Pages 1445-1455

  Koh, Taiho ^a   Powers, Edward J ^b  

^a LUCENT TECHNOLOGIES   (United States)

^b UNIVERSITY OF TEXAS AT AUSTIN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CONTROL SYSTEMS, NONLINEAR - IDENTIFICATION;

NONLINEAR FILTERING; NONLINEAR SYSTEMS IDENTIFICATION; VOLTERRA SERIES;

ELECTRIC FILTERS, DIGITAL;

EID: 0022231252     PISSN: 00963518     EISSN: None     Source Type: Journal    
DOI: 10.1109/TASSP.1985.1164730     Document Type: Article

References (25)

1. N. Wiener, Nonlinear Problems in Random Theory. New York: Wiley, 1958.
2. J. Katzenelson and L. A. Gould, “The design of nonlinear filters and control systems,” Inform. Contr., vol. 5, pp. 108–143, 1962.
3. J. F. Barret, “The use of functionals in the analysis of nonlinear system,” J. Electron. Contr., vol. 15, no. 6, pp. 567–615, 1963.
4. P. Eykhoff, “Some fundamental aspects of process-parameter estimation,” IEEE Trans. Automat. Contr., vol. AC-8, pp. 347–357, Oct. 1963.
5. A. V. Barakrishnan, “A general theory of nonlinear estimation problems in control systems,” J. Math. Anal. Appl., vol. 8, pp. 4–30, Feb. 1964.
6. M. Schetzen, “Nonlinear system modelling based on the Wiener theory,” Proc. IEEE, vol. 69, pp. 1557–1573, Dec. 1981.
7. A. S. French and E. G. Butz, “Measuring the Wiener kernels of a non-linear system using the fast Fourier transform algorithm,” Int. J. Contr., vol. 17, no. 3, pp. 529–539, 1973.
8. Y. W. Lee and M. Schetzen, “Measurement of the Wiener kernels of a non-linear system by cross-correlation,” Int. J. Contr., vol. 2, no. 3, pp. 237–254, 1965.
9. A. V. Barakrishnan, “On a class of nonlinear estimation problems,” IEEE Trans. Inform. Theory, vol. IT-10, pp. 314–320, Oct. 1964.
10. D. R. Brillinger, “The identification of polynomial systems by means of higher order spectra,” J. Sound Vib., vol. 12, no. 3, pp. 301–313, 1970.
11. M. J. Coker and D. N. Simkins, “A nonlinear adaptive noise canceller,” in Proc. 1980 IEEE Int. Conf. Acoust., Speech, Signal Processing, 1980, pp. 470–473.
12. D. M. Mansour and A. H. Gray, Jr., “Frequency domain non-linear filter,” in Proc. 1981 IEEE Int. Conf. Acoust., Speech, Signal Processing, 1981, pp. 550–553.
13. S. R. Parker and F. A. Perry, “A discrete ARMA model for nonlinear system identification,” IEEE Trans. Circuits Syst., vol. CAS-28, pp. 224–233, Mar. 1981.
14. T. Koh and E. J. Powers, “An adaptive nonlinear digital filter with lattice orthogonalization,” in Proc. 1983 IEEE Int. Conf. Acoust., Speech, Signal Processing, 1983, pp. 37–40.
15. T. Koh, E. J. Powers, R. W. Miksad, and F. J. Fischer, “Application of nonlinear digital filters to modelling low-frequency drift oscillations of moored vessels in random seas, in Proc. 1984 Offshore Technol. Conf., 1984, pp. 309–314.
16. B. Picinbono, “Quadratic filters,” in Proc. 1982 IEEE Int. Conf. Acoust., Speech, Signal Processing, 1982, pp. 298–301.
17. E. Biglieri, “Theory of Volterra processors and some applications,” in Proc. 1982 IEEE Int. Conf. Acoust., Speech, Signal Processing, 1982, pp. 294–297.
18. S. R. Parker, “An autoregressive moving average (ARMA) discrete nonlinear model,” in Proc. IEEE Int. Symp. Circuits Syst., 1980, pp. 918–920.
19. S. Y. Fakhouri, “Identification of the Volterra kernels of nonlinear systems,” Proc. IEE, vol. 127, pt. D, pp. 296–304, Nov. 1980.
20. P. Alper, “A consideration of the discrete Volterra series,” IEEE Trans. Automat. Contr., vol. AC-10, pp. 322–327, July 1965.
21. J. Y. Hong, Y. C. Kim, and E. J. Powers, “On modeling the nonlinear relationship between fluctuations with nonlinear transfer functions,” Proc. IEEE, vol. 68, pp. 1026–1027, Aug. 1982.
22. P. S. Maybeck, Stochastic Models, Estimation and Control, Vol. 1. New York: Academic, 1979, p. 213.
23. B. Widrow, J. M. McCool, M. G. Larimore, and C. R. Johnson, “Stationary and nonstationary characteristics of the LMS adaptive filter,” Proc. IEEE, vol. 64, pp. 1151–1162, Aug. 1976.
24. J. A. Pinkster, “Mean and low frequency wave drifting forces on floating structures,” Ocean Eng., vol. 6, pp. 593–612, 1979.
25. G. F. M. Remery and A. J. Hermans, “The slow drift oscillations of a moored object in random seas,” Soc. Petroleum Eng. J., pp. 191–198, June 1972.