Information Entropy with Globally Identifiable Case

1 Information Entropy with Globally Identifiable Case 

The updated PDF p 0 S jf, A, C) in Equation (3.67) is given by Equation (3.60) with Equation (3.61) for the general case of uncertain excitation. The formulation presented here is based on the spectral density estimators obtained from the measured data V and it depends on the class of structural, excitation and prediction-error models chosen to describe the system. The updated parameter vector is obtained by minimizing the objective function J 0) = — In p 0 C)p S jf 0, A, C) with the likelihood function p S 0, A, C) given by Equation (3.61). Eurthermore, the updated PDF of the model parameter vector 0 can be 

The first term on the right hand side vanishes for a non-informative prior distribution that is absorbed into the normalizing constant. In this case, the information entropy can be simplified as follows  

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