Parameter estimation of stochastic linear systems subject to colored noise

In this paper a generalized version of bias-eliminated least-squares (BELS) method is developed for the purpose of unbiased estimation of the system transfer function, without parametric modelling of the process disturbance acting on the system. Three weighting matrices are introduced to construct a new composite signal in terms of the delayed system inputs and the delayed system outputs. Identification of the corresponding new model provides an estimate of the colored-noise-induced bias, which is then removed from the LS parameter estimate. It is shown that several existing BELS based methods are a special case of the developed method if the three weighting matrices are properly selected. The interplay between the developed method and the instrumental variables methods is also studied.