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Entropy 2019, 21(4), 351; https://doi.org/10.3390/e21040351

Bayesian Input Design for Linear Dynamical Model Discrimination

Department of Automatic Control and Robotics, AGH University of Science and Technology, Al. A. Mickiewicza 30, 30-059 Krakow, Poland
Received: 16 January 2019 / Revised: 12 March 2019 / Accepted: 27 March 2019 / Published: 30 March 2019
(This article belongs to the Section Signal and Data Analysis)
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Abstract

A Bayesian design of the input signal for linear dynamical model discrimination has been proposed. The discrimination task is formulated as an estimation problem, where the estimated parameter indexes particular models. As the mutual information between the parameter and model output is difficult to calculate, its lower bound has been used as a utility function. The lower bound is then maximized under the signal energy constraint. Selection between two models and the small energy limit are analyzed first. The solution of these tasks is given by the eigenvector of a certain Hermitian matrix. Next, the large energy limit is discussed. It is proved that almost all (in the sense of the Lebesgue measure) high energy signals generate the maximum available information, provided that the impulse responses of the models are different. The first illustrative example shows that the optimal signal can significantly reduce error probability, compared to the commonly-used step or square signals. In the second example, Bayesian design is compared with classical average D-optimal design. It is shown that the Bayesian design is superior to D-optimal design, at least in this example. Some extensions of the method beyond linear and Gaussian models are briefly discussed. View Full-Text
Keywords: bayesian experimental design; model discrimination; information; entropy bayesian experimental design; model discrimination; information; entropy
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Bania, P. Bayesian Input Design for Linear Dynamical Model Discrimination. Entropy 2019, 21, 351.

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