THE USE OF A BILINEAR TRANSFORMATION OF THE SHIFT OPERATOR IN SUBSPACE MODEL IDENTIFICATION

We propose a mechanism which can improve the numerical robustness of a subspace based system identification method, the PI scheme [14, Part III], when the unknown system has poles situated close to z = 1, a con dition that often arises in applications where the sampling rate is to o high. The PI method is capable of solving a deterministic MIMO ident ification problem in which the output can be corrupted by a very gener al perturbation including arbitrarily colored noise, transients due to nonzero initial conditions, and a deterministic zero bias, By perform ing a bilinear transformation on the shift operator we are able to mov e the poles away from the point z = 1 and a more robust identification results. The implementation of this transformation gives rise to a se ries of anticausal filters applied to the input/output data. Estimatio n accuracy is further improved by taking the unknown end conditions of the anticausal filters into account, particularly when only short dat a records are available, A numerical simulation highlights the improve ments realized by our new algorithms.