Weighting sequences, optimal truncation and optimal frequency-response uncertainty bounds

The use of finite weighting sequence models to describe the behaviour of dynamic systems is particularly helpful when attempting to characterise the frequency-response uncertainty introduced by the model identification process. However, existing model selection criteria are not well suited for the identification of an appropriate level of truncation, nor do they attempt to identify the errors introduced by the specified truncation. The paper develops a new model-order selection criterion that will establish a statistically optimal truncation level and, simultaneously, quantify the frequency-response bias introduced by this truncation. In addition, modifications of the criterion are proposed to refine the frequency-response bias information at selected frequencies. The resulting bias information is then combined with earlier results, to establish a complete and quantitative description of frequency-response uncertainty.