Time-subspace projection for bias-correction in system identification

We present results concerning the parameter estimates obtained by prediction error methods in the case of input signals that are insufficiently rich when considered locally in time. As is intuitively obvious, the data located in time intervals where the system excitation is poor carry only an incomplete information about the system input-to-output (I/O) dynamics. In noise undermodeling situations, this leads to "local" model parameters presenting large bias outside the related excitation subspace. We here propose to decrease this bias error in taking into account the parameter estimates only in the system excitation subspaces associated to the different-time intervals.