A new bias-compensating LS method for continuous system identification in the presence of coloured noise

A new bias-compensating least squares (LS) method is presented for the parameter estimation of linear single-input single-output (SISO) continuous-time systems. A discrete-time model obtained by using the linear integral filter is augmented by introducing a pre-filter on the input and then the parameters of the augmented model are estimated by the conventional LS method. The distinct characteristic roots of the pre-filter are used to estimate the bias in the LS estimate. The pre-filter should be chosen so that its frequency bandwidth is wider than those of the system and the input signals. Since the new method requires minimal information on the noise characteristics, it is easily applicable to the case of coloured noise.