Model approximations via prediction error identification

Identification is considered of a dynamic system by a model in a model set of which the system is not a member. This is achieved by defining a performance index related to prediction error performance indices, and taking that model minimizing the performance index as that which is closest to the system. The index has an intuitively pleasing spectral interpretation in the stationary case for large measurement intervals. The length of measurement interval needed for identification is discussed by studying the limiting behaviour of the performance indices, as is also the relation of the index to the Kullback information measure. The communication theoretic issue of convergence of a posteriori densities when Bayesian estimation is being undertaken with a finite model set is examined.