In mathematics, specifically in control theory, subspace identification (SID) aims at identifying linear time invariant (LTI) state space models from input-output data.
SID does not require that the user parametrizes the system matrices before solving a parametric optimization problem and, as a consequence, SID methods do not suffer from problems related to local minima that often lead to unsatisfactory identification results.
[2] 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.
One such generalization was presented under the name of the Eigensystem Realization Algorithm (ERA) made use of specific input-output measurements considering the impulse inputs.
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.