A new bias-compensating least-squares method for identification of stochastic linear systems in presence of coloured noise

In this paper, a new bias-compensating least-squares method is presented for the identification of linear, single-input single-output, discrete-time systems in which the output is corrupted by an additive coloured noise. It is well known that the ordinary least-squares method may lead to biased or nonconsistent estimates of system parameters in the presence of disturbances. The bias problem may be solved, for example, by using the generalised least-squares method. In the generalised least-squares method, a digital filter is used to filter the observed input-output data. The principle of the proposed method is to introduce the filter of the conventional generalised least-squares method on the input of the identified system. By using this filter with known zeros, the bias of the ordinary least-squares estimator may then be estimated and removed, which consists of the bias-compensating method principle. The proposed and the generalised least-squares methods are applied to two simulated systems via Monte Carlo simulations