The identification of nonlinear biological systems: Wiener and Hammerstein cascade models
Biological Cybernetics
An optimal two-stage identification algorithm for Hammerstein-Wiener nonlinear systems
Automatica (Journal of IFAC)
Blind maximum likelihood identification of Hammerstein systems
Automatica (Journal of IFAC)
Brief paper: Making parametric Hammerstein system identification a linear problem
Automatica (Journal of IFAC)
Automatica (Journal of IFAC)
Quantifying the accuracy of Hammerstein model estimation
Automatica (Journal of IFAC)
Identification of Hammerstein nonlinear ARMAX systems
Automatica (Journal of IFAC)
Identification of MIMO Hammerstein models using least squares support vector machines
Automatica (Journal of IFAC)
| Hi-index | 22.14 |
Hammerstein models is one of the most commonly used model classes used for identifying nonlinear systems. A static input nonlinearity followed by a linear dynamical part is an adequate way to model many real-life systems. This paper investigates the asymptotic (in terms of sample size) variance of Hammerstein model estimates. The work extends earlier results by Ninness and Gibson (2002) in the following ways. Not only frequency function estimation but estimation of general quantities is considered. The expressions are not restricted to be valid asymptotically in the model order. In addition, the results cover model structures having noise models and allow for data generated under feedback. The increase in variance due to the estimation of the input nonlinearity is characterized. In particular, under open loop operation, white additive noise and the assumption of a separable process, it is shown that the variance increase is exactly a term that was observed in Ninness and Gibson (2002) to result in good agreement with simulations. This term vanishes in the formal asymptotic in model order analysis in Ninness and Gibson (2002).