The identification of nonlinear biological systems: Wiener and Hammerstein cascade models
Biological Cybernetics
System identification: theory for the user
System identification: theory for the user
Practical methods of optimization; (2nd ed.)
Practical methods of optimization; (2nd ed.)
Nonlinearity estimation in Hammerstein systems based on orderedobservations
IEEE Transactions on Signal Processing
Blind identification of LTI-ZMNL-LTI nonlinear channel models
IEEE Transactions on Signal Processing
Blind identification of linear subsystems of LTI-ZMNL-LTI modelswith cyclostationary inputs
IEEE Transactions on Signal Processing
Blind identification of Volterra-Hammerstein systems
IEEE Transactions on Signal Processing - Part I
Quasi-nonparametric blind inversion of Wiener systems
IEEE Transactions on Signal Processing
Identification of systems containing linear dynamic and static nonlinear elements
Automatica (Journal of IFAC)
A blind approach to the Hammerstein-Wiener model identification
Automatica (Journal of IFAC)
Brief Fast approximate identification of nonlinear systems
Automatica (Journal of IFAC)
Box-Jenkins identification revisited-Part I: Theory
Automatica (Journal of IFAC)
Identification methods for Hammerstein nonlinear systems
Digital Signal Processing
Computers & Mathematics with Applications
Finite model order accuracy in Hammerstein model estimation
Automatica (Journal of IFAC)
| Hi-index | 22.16 |
This paper is about the identification of discrete-time Hammerstein systems from output measurements only (blind identification). Assuming that the unobserved input is white Gaussian noise, that the static nonlinearity is invertible, and that the output is observed without errors, a Gaussian maximum likelihood estimator is constructed. Its asymptotic properties are analyzed and the Cramer-Rao lower bound is calculated. In practice, the latter can be computed accurately without using the strong law of large numbers. A two-step procedure is described that allows to find high quality initial estimates to start up the iterative Gauss-Newton based optimization scheme. The paper includes the illustration of the method on a simulation example. A theoretical analysis demonstrates that additive output measurement noise introduces a bias that is proportional to the variance of that additive, unmodeled noise source. The simulations support this result, and show that this bias is insignificant beyond a certain Signal-to-Noise Ratio (40 dB in the example).