Hammerstein system identification by the Haar multiresolution approximation

✍ Scribed by Zygmunt Hasiewicz

• Publisher: John Wiley and Sons
• Year: 1999
• Tongue: English
• Weight: 203 KB
• Volume: 13
• Category: Article
• ISSN: 0890-6327
• DOI: 10.1002/(sici)1099-1115(199912)13:8<691::aid-acs591>3.0.co;2-7

✦ Synopsis

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 identi"cation 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 modi"cation 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 con"rmed by computer simulations.