Advanced Methods of Physiological System Modeling pp 163-178 | Cite as
Identification of Multiple-Input Nonlinear Systems Using Non-White Test Signals
Chapter
Abstract
The parallel cascade method (Korenberg, 1982, 1991; Palm 1979) provides an elegant means of estimating the Volterra kernels of a nonlinear system. Korenberg (1991) demonstrated methods for producing the individual paths in this parallel array that require relatively few calculations, and are hence practical for use under a variety of conditions. In this paper, we propose alternative methods for determining the paths in a parallel cascade array. Our methods prove to be more robust in the presence of output noise, at the expense of slightly slower convergence under low noise conditions.
Keywords
Minimum Mean Square Error Volterra Series Volterra Kernel Wiener Kernel Eigenvector Method
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Preview
Unable to display preview. Download preview PDF.
References
- 1.Billings, S.A. and Fakhouri, S.Y. (1982) Identification of systems containing linear dynamic and static nonlinear elements. Automatica., 18:15–26.MathSciNetMATHCrossRefGoogle Scholar
- 2.French, A.S. (1976) Practical nonlinear system analysis by Wiener kernel estimation in the frequency domain. Biol. Cybern., 24:111–119.MATHCrossRefGoogle Scholar
- 3.Golub, G.H. and van Loan, C.F. (1983) Matrix Computations, Johns Hopkins University Press, Baltimore, Maryland.MATHGoogle Scholar
- 4.Hunter, I.W. and Kearney, R.E. (1983) Two-sided linear filter identification. Med. Biol. Eng. Comput., 21:203–209.CrossRefGoogle Scholar
- 5.Hunter, I.W. and Korenberg, M.J. (1986) The identification of nonlinear biological systems: Wiener and Hammerstein cascade models. Biol. Cybern., 55:135–144.MathSciNetMATHGoogle Scholar
- 6.Korenberg, M.J. (1973) Crosscorrelation analysis of neural cascades. Proc. 10th Ann. Rocky Mountain Bioeng. Symp., pp. 47–52.Google Scholar
- 7.Korenberg, M.J. and Hunter, I.W. (1986) The identification of nonlinear biological systems: LNL cascade models. Biol. Cybern., 55:125–134.MathSciNetMATHGoogle Scholar
- 8.Korenberg, M.J. and Hunter, I.W. (1990) The identification of nonlinear biological systems: Wiener kernel approaches. Ann. Biomed. Eng., 18:629–654.CrossRefGoogle Scholar
- 9.Korenberg, M.J. (1982) Statistical identification of parallel cascades of linear and nonlinear systems. IFAC Symp. Ident. & Syst. Param. Est, Rosslyn, Virginia, pp. 669–674.Google Scholar
- 10.Korenberg, M.J. (1984) Statistical identification of Volterra kernels of high order systems. ICAS’84, pp. 570–575.Google Scholar
- 11.Korenberg, M.J. (1985) Identifying noisy cascades of linear and static nonlinear systems. IFAC Symp. Ident. & Syst. Param. Est., York, United Kingdom, pp. 421–426.Google Scholar
- 12.Korenberg, M.J. (1991) Parallel cascade identification and kernel estimation for nonlinear systems. Ann. Biomed. Eng., 19:429–455.CrossRefGoogle Scholar
- 13.Lee, Y.W. and Schetzen, M. (1965) Measurement of the Wiener kernels of a non-linear system by cross-correlation. Int. J. Control, 2:237–254.CrossRefGoogle Scholar
- 14.Marmarelis, R.Z. and Naka, K.I. (1974) Identification of multi-input biological systems. IEEE Trans. Biomed. Eng., 21:88–101.CrossRefGoogle Scholar
- 15.Marmarelis, V.Z. (1991) Wiener analysis of nonlinear feedback in sensory systems. Ann. Biomed. Eng., 19:345–382.CrossRefGoogle Scholar
- 16.Marmarelis, R.Z. and Marmarelis, V.Z. (1978) Analysis of Physiological Systems, Plenum Press, New York, New York.CrossRefGoogle Scholar
- 17.Palm, G. (1978) On representation and approximation of nonlinear systems. Part II: discrete time. Biol Cybern., 34:49–52.MathSciNetCrossRefGoogle Scholar
- 18.Rugh, W.J. (1981) Nonlinear System Theory: The Volterra/Wiener Approach, Johns Hopkins University Press, Baltimore, Maryland.MATHGoogle Scholar
- 19.Volterra, V. (1959) Theory of Functionals and of Integral and Integro-differential Equations, Dover, New York, New York.MATHGoogle Scholar
- 20.Westwick, D.T. and Kearney, R.E. (1992) A new algorithm for the identification of multiple input Wiener systems. Biol. Cybern., 68:75–85.MATHCrossRefGoogle Scholar
- 21.Wiener, N. (1958) Nonlinear Problems in Random Theory, Wiley, New York, New York.MATHGoogle Scholar
Copyright information
© Springer Science+Business Media New York 1994