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An extension to the stochastic realization problem where we have knowledge only of the Auto-correlation (covariance) function of the output of an LTI system driven by white noise, was derived by researchers like Akaike<ref>H. Akaike, "A new look at the statistical model identification", IEEE Transactions on Automatic Control, vol. 19, pp. 716-723, 1974.</ref>.
A second generation of SID methods attempted to make SID methods directly operate on input-output measurements of the LTI system in the decade 1985-1995. One such generalization was presented under the name of the [[Eigensystem realization algorithm|Eigensystem Realization Algorithm]] (ERA) made use of specific input-output measurements considering the impulse inputs<ref>J.-N. Juang and R. S. Pappa, R. S., "An Eigensystem Realization Algorithm for modal parameter identification and model reduction", Journal of Guidance, Control, and Dynamics. vol. 8, 1985.</ref>. It has been used for modal analysis of flexible structures, like bridges, space structures, etc. These methods have demonstrated to work in practice for resonant structures they did not work well for other type of systems and an input different from an impulse. A new impulse to the development of SID methods was made for operating directly on generic input-output data and avoiding to first explicitly compute the Markov parameters or estimating the samples of covariance functions prior to realizing the system matrices. Pioneers that contributed to these breakthroughs were Van Overschee and De Moor - introducing the N4SID approach<ref>P. Van Overschee and B. De Moor, "N4SID: Subspace algorithms for the identification of combined deterministic-stochastic systems", Automatica, vol. 30 pp. 75 - 93, 1994.</ref>, Verhaegen - introducing the MOESP approach<ref>M. Verhaegen, "Identification of the deterministic part of MIMO state space models given in innovations form from input-output data", Automatica, vol. 30, pp. 61 - 74, 1994.</ref> and Larimore - presenting ST in the framework of Canonical Variate Analysis (CVA)<ref>W. Larimore, "Canonical variate analysis in identification, filtering, and adaptive control", in Proceedings of the 29th IEEE Conference on Decision and Control, 1990.</ref>
== References ==
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