Variance analysis for identification of cascade systems

The contribution of this paper is a variance analysis of estimated models of cascade dynamical systems. Models of such systems are important in for example cascade control applications. The model quality is analyzed by means of the asymptotic covariance matrix of the prediction error method parameters estimates. Recent work has shown that identification of two cascaded linear systems, where the transfer functions of the sub-systems are identical, has some fundamental limitations in terms of asymptotic statistical performance. Under this condition, the output from the second sub-system does not influence the quality of the estimated model of the first subsystem. The objective of this paper is to extend this result to the case where the transfer functions of the sub-systems are not completely identical, but do have some common dynamics. We will also study cascaded systems with three sub-systems, and show that a similar variance result also holds for this case. The results are illustrated by some simple FIR examples.