System identification in the presence of unmodeled dynamics-a principal components extraction approach

In this paper a two-step method for identification is presented. The first step is to identify FIR sequences using any existing efficient algorithm. The second step is principal components extraction. It tries to recover the complete system performance from the FIR sequences estimated. It is shown that the denominator parameter of the obtained ARMAX model is the eigenvector corresponding to the eigenvalue of a certain matrix composed of the estimated FIR sequence. The eigenvalue itself can be an index of model order selection. A criterion for selecting the FIR sequence length is presented. Simulation result demonstrates the effectiveness of the approach.