Model selection through a statistical analysis of the global minimum of a weighted nonlinear least squares cost function

This paper presents a model selection algorithm for the identification of parametric models that are linear in the measurements. It is based on the mean and variance expressions of the global minimum of a weighted nonlinear least squares cost function. The method requires the knowledge of the noise covariance matrix but does not assume that the true model belongs to the model set. Unlike the traditional order estimation methods available in literature, the presented technique allows to detect undermodeling. The theory is illustrated by simulations on signal modeling and system identification problems and by one real measurement example.