Information matrix and D-optimal design with Gaussian inputs for Wiener model identification. (July 2016)

• Record Type: Journal Article
• Authors: Mahata, Kaushik; Schoukens, Johan; De Cock, Alexander
• Is Part Of: Automatica. Volume 69(2016)
• Page Start: 65
• Page End: 77
• Publication Date: 2016-07
• Subjects: Wiener model identification -- Fischer's information matrix -- Cramér–Rao bound -- D-optimal design -- Nevanlinna–Pick interpolation; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2016.02.026
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: 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.