A Geometric Approach to Variance Analysis in System Identification

This paper addresses the problem of quantifying the model error (“variance-error”) in estimates of dynamic systems. It is shown that, under very general conditions, the asymptotic (in data length) covariance of an estimated system property (represented by a smooth function of estimated system parameters) can be interpreted in terms of an orthogonal projection of a certain function, associated with the property of interest, onto a subspace determined by the model structure and experimental conditions. The presented geometric approach simplifies structural analysis of the model variance and this is illustrated by analyzing the influence of inputs and sensors on the model accuracy.