Robustness of wave-fitting with respect to uncertain parameter values

A simple criterion for model order selection has been derived. This criterion holds when the model is linear in the unknown parameters. The correction term in the MSSE holds exactly for linear models. A generalization of the result to include nonlinear parameters have been studied in the special case with one nonlinear parameter. Numerical illustrations of the theoretical results have shown good agreement with the theoretical analysis. From the two examples above we can conclude that estimation of the DC-level is superfluous if |C| <radic sigma²/N in sinewave-fitting, as well as in linear models with a CRB associated to the DC-level given by sigma²/N. The assumption under which the results have been derived includes a Gaussian requirement on the white noise additive model imperfections, and that the model Mscr₂ describes the signal correctly. Thus, the result may not be applicable for example in ADC-testing where the considered noise model is questionable (Kollar and Blair, 2004)