Hammerstein system identification by non-parametric instrumental variables
- 23 February 2009
- journal article
- research article
- Published by Taylor & Francis Ltd in International Journal of Control
- Vol. 82 (3), 440-455
- https://doi.org/10.1080/00207170802225930
Abstract
A mixed, parametric–non-parametric routine for Hammerstein system identification is presented. Parameters of a non-linear characteristic and of ARMA linear dynamical part of Hammerstein system are estimated by least squares and instrumental variables assuming poor a priori knowledge about the random input and random noise. Both subsystems are identified separately, thanks to the fact that the unmeasurable interaction inputs and suitable instrumental variables are estimated in a preliminary step by the use of a non-parametric regression function estimation method. A wide class of non-linear characteristics including functions which are not linear in the parameters is admitted. It is shown that the resulting estimates of system parameters are consistent for both white and coloured noise. The problem of generating optimal instruments is discussed and proper non-parametric method of computing the best instrumental variables is proposed. The analytical findings are validated using numerical simulation results.Keywords
This publication has 26 references indexed in Scilit:
- Convergence of the Iterative Hammerstein System Identification AlgorithmIEEE Transactions on Automatic Control, 2004
- Combined Parametric–Nonparametric Identification of Hammerstein SystemsIEEE Transactions on Automatic Control, 2004
- Instrumental variable methods for system identificationCircuits, Systems, and Signal Processing, 2002
- Nonlinear system identification by the Haar multiresolution analysisIEEE Transactions on Circuits and Systems I: Regular Papers, 1998
- Non-parametric orthogonal series identification of Hammerstein systemsInternational Journal of Systems Science, 1989
- Identification of discrete Hammerstein systems using kernel regression estimatesIEEE Transactions on Automatic Control, 1986
- The Levenberg-Marquardt algorithm: Implementation and theoryPublished by Springer Science and Business Media LLC ,1978
- Notes on the instrumental variable methodIEEE Transactions on Automatic Control, 1977
- A noniterative method for identification using Hammerstein modelIEEE Transactions on Automatic Control, 1971
- An iterative method for the identification of nonlinear systems using a Hammerstein modelIEEE Transactions on Automatic Control, 1966