Robust identification of stochastic linear systems with correlated noise

The normal least-squares (LS) approach is one of the most simple and powerful identification methods widely used. Unfortunately, direct implementation of the LS method can give rise to biased or nonconsistent estimates of system parameters in the presence of correlated disturbances. In this paper, an up-to-date LS based identification approach is introduced to obtain consistent parameter estimates for stochastic systems subject to correlated noise. A designed filter is inserted into the identified system so that the resulting system has some known zeros which can, based on asymptotic analysis, be used for eliminating the coloured-noise-induced bias in the LS estimators. It is shown that the proposed identification method can not only produce consistent estimates, but be a very feasible, robust identification technique in practical applications as well. The theoretical analysis is verified through Monte-Carlo stochastic simulation studies