Approximate realization based upon an alternative to the Hankel matrix

The Ho-Kalman algorithm creates a minimum realization of a system, when given a series of deterministic Markov parameters. However, when such a ‘truncated’ series of Markov parameters has been disturbed with noise, an approximating Hankel matrix has to be constructed for applying the realization algorithm. This approximating Hankel matrix has either the improper rank, or it lacks the Hankel structure. Furthermore the Markov parameters are not processed with a constant weighting factor, which implies that the noise filtering is inadequate. In this paper we propose to use an alternative matrix: the Page matrix. It is shown that this method is better suited for handling the noisy Markov parameters. This holds with respect to three aspects: order testing, noise filtering and realization. Even in the deterministic case, the Page matrix offers the advantage of a considerable reduction in computation.