Information matrix and D-optimal design with Gaussian inputs for Wiener model identification

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• 作者：Kaushik Mahata^a ; ^{Kaushik.Mahata@newcastle.edu.au" class="auth_mail" title="E-mail the corresponding author}Author Vitae ; Johan Schoukens^b ; ^{Johan.Schoukens@vub.ac.be" class="auth_mail" title="E-mail the corresponding author}Author Vitae ; Alexander De Cock^b ; ^{Alexander.De.Cock@vub.ac.be" class="auth_mail" title="E-mail the corresponding author}Author Vitae
• 关键词：Wiener model identification ; Fischer&rsquo ; s information matrix ; Cramé ; r&ndash ; Rao bound ; D-optimal design ; Nevanlinna&ndash ; Pick interpolation
• 刊名：Automatica
• 出版年：2016
• 出版时间：July 2016
• 年：2016
• 卷：69
• 期：Complete
• 页码：65-77
• 全文大小：693 K

文摘

We present a closed form expression for the Fischer’s information matrix associated with the identification of Wiener models. In the derivation we assume that the input signal is Gaussian. The analysis allows the linear sub-system in the Wiener model to have a generic rational transfer function of arbitrary order. It also allows the static nonlinearity of the Wiener model to be a polynomial of arbitrary degree. In addition, we show how this analysis can be used to design tractable algorithms for D-optimal input design. The idea is further extended to design optimal inputs consisting of a sequence of Gaussian signals with different mean values and variances. By combining Gaussian inputs with different means we can tune the amplitude distribution of the input to achieve the best identification accuracy in D-optimal sense. The analytical results are also illustrated with some numerical simulations.