Statistical optimality and canonical variate analysis system identification

The Kullback information is developed as the natural measure of the error in model approximation for general model selection methods including the selection of model state order in large as well as small samples. It also plays a central role in developing statistical decision procedures for the optimal selection of model order as well as structure based on the observed data. The optimality of the canonical variate analysis (CVA) method is demonstrated for both an open- and closed-loop multivariable system with stochastic disturbances. The optimality is shown to hold in quite small samples of 100 time points when estimating the 43 parameters of a six-state, two-input, two-output system assuming that the state order is known. When the state order is estimated using the Akaike information criterion (AIC) corrected for small samples, the optimality is achieved if there is sufficient input excitation for reliable order selection, and otherwise there is a modest increase in the error of model approximation when the order is underestimated.