Unbiased identification of stochastic linear systems subject to coloured noise

Parameter estimation of transfer function models in the case of coloured pr ocess noise is studied. A new bias correction based method is proposed with a view to attaining estimation consistency irrespective of noise dynamics. A new vector of transfer function parameters is introduced, accompanied by a new data regression vector. The special structure of the new parameter v ector enables calculation of the coloured-noise-induced bias, which can eve ntually result in unbiased parameter estimates via the bias correction sche me. It is demonstrated that the proposed method belongs to the family of th e weighted instrumental variable methods while it also presents a simple ye t efficient technique to compose a special type of instruments. The theoret ical analysis is supported by numerical results.