The use of a bilinear transformation of the shift operator in subspace model identification

Proposes a mechanism which can improve the numerical robustness of a subspace based system identification method, the PI scheme, when the unknown system has poles situated close to z=1, a condition that often arises in applications where the sampling rate is too high. The PI method is capable of solving a deterministic MIMO identification problem in which the output can be corrupted by a very general perturbation including arbitrarily colored noise, transients due to nonzero initial conditions, and a deterministic zero bias. By performing a bilinear transformation on the shift operator the authors are able to move the poles away from the point z=1 and a more robust identification results. The implementation of this transformation gives rise to a series of anticausal filters applied to the input/output data. Estimation accuracy is further improved by taking the unknown end conditions of the anticausal filters into account, particularly when only short data records are available. A numerical simulation highlights the improvements realized by the authors´ new algorithms