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Hammerstein system identification by the Haar multiresolution approximation
Author(s) -
Hasiewicz Zygmunt
Publication year - 1999
Publication title -
international journal of adaptive control and signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.73
H-Index - 66
eISSN - 1099-1115
pISSN - 0890-6327
DOI - 10.1002/(sici)1099-1115(199912)13:8<691::aid-acs591>3.0.co;2-7
Subject(s) - pointwise convergence , pointwise , white noise , rate of convergence , convergence (economics) , parametric statistics , mathematics , a priori and a posteriori , wavelet , noise (video) , algorithm , system identification , haar wavelet , multiresolution analysis , mathematical optimization , computer science , wavelet transform , mathematical analysis , statistics , artificial intelligence , discrete wavelet transform , network topology , measure (data warehouse) , telecommunications , channel (broadcasting) , operating system , epistemology , economics , philosophy , database , image (mathematics) , economic growth
The paper deals with recovering non‐linearities in the Hammerstein systems using the multiresolution approximation—a basic concept of wavelet theory. The systems are driven by random signals and are disturbed by additive, white or coloured, random noise. The a priori information about system components is non‐parametric and a delay in the dynamical part of systems is admitted. A non‐parametric identification algorithm for estimating non‐linear characteristics of static parts is proposed and investigated. The algorithm is based on the Haar multiresolution approximation. The pointwise convergence and the pointwise asymptotic rate of convergence of the algorithm are established. It is shown that neither the form nor the convergence conditions of the algorithm need any modification if the noise is not white but correlated. Also the asymptotic rate of convergence is the same for white and coloured noise. The theoretical results are confirmed by computer simulations. Copyright © 1999 John Wiley & Sons, Ltd.