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A geometric approach to variance analysis in system identification: Theory and nonlinear systems

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 gamma, associated with the property of interest, onto a subspace determined by the model structure and experimental conditions. An explicit method to construct a suitable gamma, in such a way that the individual impacts of model structure, model order and experimental conditions become visible, is presented. The technique is used to derive asymptotic variance expressions for a Hammerstein model and a nonlinear regression problem.