Discarding data may help in system identification

We present results concerning the parameter estimates obtained by prediction error methods in the case of input that are insufficiently rich. Such input signals are typical of industrial measurements where occasional stepwise reference changes occur. As is intuitively obvious, the data located around the input signal discontinuities carry most of the useful information. Using singular value decomposition (SVD) techniques, we show that in noise undermodeling situations, the remaining data may introduce large bias on the model parameters with a possible increase of their total mean square error. A data selection criterion is then proposed to discard such poorly informative data to increase the accuracy of the transfer function estimate. The system discussed in particular is a SISO ARMAX system