Abstract

This chapter deals with the problem of constructing a state-space model for a stochastic process from a finite number of estimated covariance lags. The approach is to first obtain a high-order model which exactly matches the estimated covariance sequence, and then use balanced model reduction techniques to obtain a lower order model which approximates the given sequence. It is shown that balanced models can be obtained from a realization algorithm which uses an infinite covariance sequence. Scaling ideas are then introduced so that balanced realizations can be obtained from finite covariance sequences.

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