Maximum likelihood identification of Wiener models

Authors:
Anna Hagenblad;Lennart Ljung;Adrian Wills
Affiliations:
Division of Automatic Control, Linköpings universitet, SE-581 80 Linköping, Sweden;Division of Automatic Control, Linköpings universitet, SE-581 80 Linköping, Sweden;School of Electrical Engineering and Computer Science, University of Newcastle, Callaghan, NSW, 2308, Australia
Venue:
Automatica (Journal of IFAC)
Year:
2008

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Abstract

The Wiener model is a block oriented model, having a linear dynamic system followed by a static nonlinearity. The dominating approach to estimate the components of this model has been to minimize the error between the simulated and the measured outputs. We show that this will, in general, lead to biased estimates if there are other disturbances present than measurement noise. The implications of Bussgang's theorem in this context are also discussed. For the case with general disturbances, we derive the Maximum Likelihood method and show how it can be efficiently implemented. Comparisons between this new algorithm and the traditional approach, confirm that the new method is unbiased and also has superior accuracy.