Accuracy Aspects of Parameter Estimation in Linear Dynamical Systems

Abstract The paper considers the influence of feedback on the accuracy of parameter estimates in discrete-time stochastic dynamical systems. It was shown by Goodwin and Payne (1977), and others, that the accuracy of noise parameters is independent of the input signal used for a certain classes of systems. This result has been considered in the design of optimal input signal by some authors, e.g. Zarrop (1979). However, it will be shown that for a commonly used model, Astrom model, in system identification and adaptive control, the accuracy of noise parameters are dependent of experimental conditions. The relation between the accuracies of system and noise parameter estimates will be derived. Results concerning the role of feedback in identification experiment will be presented and illustrated by examples.