Identification of linear systems in the presence of model errors

In this paper a method is presented to qualify and to quantify the remaining model errors at the end of a frequency domain identification of linear dynamic systems. The method is based on an analysis of the auto correlation of the frequency domain residues. In the qualification step the user is provided with information to decide if the model errors are due to unmodelled dynamics (a too low model order), or if they are caused by a nonlinear distortion of the linear system. In the quantification step an idea of the influence of the model errors on the estimated model is given. An improved covariance matrix describing the global uncertainty of the model parameters is given, accounting not only for the disturbing noise influences but also for the systematic model errors