System identification: theory for the user
System identification: theory for the user
An optimal two-stage identification algorithm for Hammerstein-Wiener nonlinear systems
Automatica (Journal of IFAC)
Identification of MIMO Hammerstein models using least squares support vector machines
Automatica (Journal of IFAC)
Brief paper: Making parametric Hammerstein system identification a linear problem
Automatica (Journal of IFAC)
Finite model order accuracy in Hammerstein model estimation
Automatica (Journal of IFAC)
Hi-index | 22.15 |
The Two-Stage Algorithm (TSA) has been extensively used and adapted for the identification of Hammerstein systems. It is essentially based on a particular formulation of Hammerstein systems in the form of bilinearly parameterized linear regressions. This paper has been motivated by a somewhat contradictory fact: though the optimality of the TSA has been established by Bai in 1998 only in the case of some special weighting matrices, the unweighted TSA is usually used in practice. It is shown in this paper that the unweighted TSA indeed gives the optimal solution of the weighted nonlinear least squares problem formulated with a particular weighting matrix. This provides a theoretical justification of the unweighted TSA, and also leads to a generalization of the obtained result to the case of colored noise with noise whitening. Numerical examples of identification of Hammerstein systems are presented to validate the theoretical analysis.