How to Estimate Model Uncertainty in the Case of Under-Modelling

Abstract

In System Identification, traditionally, the uncertainty estimate provided with the model is based on the assumption that the model structure used is capable of achieving a correct system description. This estimate is however not correct unless the parameter estimate is close to a "true" model parameter, that yields white noise residuals. The correct expression is known but more complex. The main difficulty, though, is that it is not easily estimated. We suggest a simple and explicit method for estimating the model uncertainty, applicable also to severe under-modelling. The method is illustrated by an example.