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 weigh ted nonlinear least squares cost function. The method requires the kno wledge of the noise covariance matrix but does not assume that the tru e model belongs to the model set. Unlike the traditional order estimat ion methods available in literature, the presented technique allows to detect undermodeling. The theory is illustrated by simulations on sig nal modeling and system identification problems and by one real measur ement example.