A unified form for BELS method in colored noise case

The bias eliminated least squares (BELS) method is one of consistent estimation methods for unknown parameters of transfer function in the presence of colored noise. In this paper, a unified form for BELS (UBELS) method is proposed by means of introducing an auxiliary vector and a nonsingular matrix. The introduced nonsingular matrix and auxiliary vector uncorrelated with noise are used to construct a new signal regression vector and new parameter vector. The new model described by the new signal regression vector and new parameter vector is an equivalent expression of the true system model. Consequently the estimate of colored-noise-induced bias can be obtained so that the bias of LS parameter estimate is removed to get consistent parameter estimate. It is shown that the UBELS method turns out to be a more general type of bias-correction based algorithms than the GBELS method that is recently presented. Moreover comparison between UBELS and GBELS methods and relationship between UBELS and instrumental variables (IV) methods are studied.