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Revisiting Hammerstein system identification through the Two-Stage Algorithm for bilinear parameter estimation
- Source :
- Automatica, Automatica, Elsevier, 2009, 45 (11), pp.2627--2633. ⟨10.1016/j.automatica.2009.07.033⟩, Automatica, 2009, 45 (11), pp.2627--2633. ⟨10.1016/j.automatica.2009.07.033⟩
- Publication Year :
- 2009
- Publisher :
- Elsevier BV, 2009.
-
Abstract
- International audience; 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.
- Subjects :
- 0209 industrial biotechnology
Nonlinear system identification
Estimation theory
Generalization
020208 electrical & electronic engineering
System identification
02 engineering and technology
16. Peace & justice
Weighting
Noise
020901 industrial engineering & automation
Control and Systems Engineering
Colors of noise
Control theory
[INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering
Non-linear least squares
0202 electrical engineering, electronic engineering, information engineering
Applied mathematics
Electrical and Electronic Engineering
Mathematics
Subjects
Details
- ISSN :
- 00051098
- Volume :
- 45
- Database :
- OpenAIRE
- Journal :
- Automatica
- Accession number :
- edsair.doi.dedup.....f06cd42ec33f18282d61f04b1abc63e9