Utilizing periodic excitation in prediction error based system identification

The standard prediction error method (PEM) in system identification for estimating output error models is studied. The PEM has recently been proposed to be formulated in the frequency domain, and in this context it has been pointed out that a periodic excitation signal give many advantages. The most immediate is data reduction when using data averaged over the periods, We will here project the main results onto the time domain, and show how to utilize a nonparametric noise model as a pre-filter to increase accuracy and numerical convergence speed in output error modeling. A possible drawback with using only the averaged data is decreased estimation accuracy when the system and noise model have common parameters. A new result is presented that shows how the nonparametric noise model can be used to recover the original accuracy for ARX models