Abstract
The fundamental relation between the Hammerstein system nonlinearity and the regression function of the system output on the system input is presented. It allows recovery of the system nonlinearity with the help of the nonparametric regression function estimates. Several implications of this approach are discussed. In particular, the fact that the nonlinearity is estimated independently of the dynamics is emphasized. Some limitations, i.e., an ability of identification of the genuine nonlinear characteristic up to some system-dependent constants only and a small system-to-noise ratio of the measurement data, are also pointed out.
Keywords
- Nonparametric Regression Function Estimation
- Hammerstein System
- System-dependent Constant
- Nonparametric Assumptions
- Greblicki
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Notes
- 1.
The symmetric triangular pdffunction is further used in algorithms tests (see Sect. 5.1).
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Śliwiński, P. (2013). Identification Goal. In: Nonlinear System Identification by Haar Wavelets. Lecture Notes in Statistics, vol 210. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29396-2_3
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