A weighted principal component regression approach for system identification

In this paper, we present a parametric LTI system identification approach, which is based on weighted principal component regression (PCR). It can be shown that this method asymptotically implements model selection in the frequency domain and allows the data to play a significant role in determining the candidate models. Moreover, the estimates of the optimal model parameters reflect a trade-off between bias and variance to reach a relatively small mean squared prediction error. Compared with the conventional autoregressive exogenous input (ARX) identification, our approach is shown to identify the system´s impulse response function more accurately when the input signal is colored.