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.

Ämnesord

TEKNIK OCH TEKNOLOGIER  -- Elektroteknik och elektronik -- Reglerteknik (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Electrical Engineering, Electronic Engineering, Information Engineering -- Control Engineering (hsv//eng)

Nyckelord

covariance analysis

covariance matrices

geometry

identification

nonlinear systems

regression analysis

Hammerstein model

asymptotic covariance matrix

dynamic system

geometric approach

nonlinear regression problem

nonlinear system

system identification

variance analysis

Accuracy of identification

Asymptotic variance expressions

Automatic control

Reglerteknik

SRA - ICT

SRA - Informations- och kommunikationsteknik

Publikations- och innehållstyp

ref (ämneskategori)

kon (ämneskategori)