Unbiased identification of stochastic linear systems subject to coloured noise

Parameter estimation of transfer function models in the case of coloured process 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 vector enables calculation of the coloured-noise-induced bias, which can eventually result in unbiased parameter estimates via the bias correction scheme. It is demonstrated that the proposed method belongs to the family of the weighted instrumental variable methods while it also presents a simple yet efficient technique to compose a special type of instruments. The theoretical analysis is supported by numerical results