On a least-squares-based algorithm for identification of stochastic linear systems

A new form of bias-eliminated least-squares (BELS) algorithm is developed to identify transfer function parameters of a linear time-invariant system, irrespective of noise dynamics. Unlike the BELS estimator previously presented, the main feature with the developed algorithm is that the transfer function parameters are consistently estimated in such a direct way that there is no need to prefilter observed data or to deal with a high-order augmented system. This greatly simplifies implementation of the BELS-based algorithms and reduces numerical efforts, whereas a desirable estimation accuracy can still be achieved. Two simulation examples are presented that clearly illustrate the good performances of the developed algorithm, including its superiority over one type of simple instrumental variable method.