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.
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References
Billings, S.A. and Fakhouri, S.Y. (1982) Identification of systems containing linear dynamic and static nonlinear elements. Automatica., 18:15–26.
French, A.S. (1976) Practical nonlinear system analysis by Wiener kernel estimation in the frequency domain. Biol. Cybern., 24:111–119.
Golub, G.H. and van Loan, C.F. (1983) Matrix Computations, Johns Hopkins University Press, Baltimore, Maryland.
Hunter, I.W. and Kearney, R.E. (1983) Two-sided linear filter identification. Med. Biol. Eng. Comput., 21:203–209.
Hunter, I.W. and Korenberg, M.J. (1986) The identification of nonlinear biological systems: Wiener and Hammerstein cascade models. Biol. Cybern., 55:135–144.
Korenberg, M.J. (1973) Crosscorrelation analysis of neural cascades. Proc. 10th Ann. Rocky Mountain Bioeng. Symp., pp. 47–52.
Korenberg, M.J. and Hunter, I.W. (1986) The identification of nonlinear biological systems: LNL cascade models. Biol. Cybern., 55:125–134.
Korenberg, M.J. and Hunter, I.W. (1990) The identification of nonlinear biological systems: Wiener kernel approaches. Ann. Biomed. Eng., 18:629–654.
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.
Korenberg, M.J. (1984) Statistical identification of Volterra kernels of high order systems. ICAS’84, pp. 570–575.
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.
Korenberg, M.J. (1991) Parallel cascade identification and kernel estimation for nonlinear systems. Ann. Biomed. Eng., 19:429–455.
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.
Marmarelis, R.Z. and Naka, K.I. (1974) Identification of multi-input biological systems. IEEE Trans. Biomed. Eng., 21:88–101.
Marmarelis, V.Z. (1991) Wiener analysis of nonlinear feedback in sensory systems. Ann. Biomed. Eng., 19:345–382.
Marmarelis, R.Z. and Marmarelis, V.Z. (1978) Analysis of Physiological Systems, Plenum Press, New York, New York.
Palm, G. (1978) On representation and approximation of nonlinear systems. Part II: discrete time. Biol Cybern., 34:49–52.
Rugh, W.J. (1981) Nonlinear System Theory: The Volterra/Wiener Approach, Johns Hopkins University Press, Baltimore, Maryland.
Volterra, V. (1959) Theory of Functionals and of Integral and Integro-differential Equations, Dover, New York, New York.
Westwick, D.T. and Kearney, R.E. (1992) A new algorithm for the identification of multiple input Wiener systems. Biol. Cybern., 68:75–85.
Wiener, N. (1958) Nonlinear Problems in Random Theory, Wiley, New York, New York.
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© 1994 Springer Science+Business Media New York
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Westwick, D.T., Kearney, R.E. (1994). Identification of Multiple-Input Nonlinear Systems Using Non-White Test Signals. In: Marmarelis, V.Z. (eds) Advanced Methods of Physiological System Modeling. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-9024-5_8
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DOI: https://doi.org/10.1007/978-1-4757-9024-5_8
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