We consider the following generic problem: minimize the l2 norm of the difference between a given time series and an estimated one under the constraint that the estimated time series is a trajectory of a linear time invariant system with a fixed order. The generic problem can be viewed as maximum likelihood system identification in the errors-in-variables setup under suitable assumptions for the measurement noises. Multiple time series and latent variables can be considered in the identification problem as well as measurement errors. Special cases of the generic problem are output only identification, noisy realization, and finite time optimal $\ell_2$ model reduction. We relate the generic problem to the structured total least squares problem. In contrast to previous results using the structured total least squares approach, we do not restrict to single input single output systems. An efficient software package that implements the theory in practice is used. The performance of the proposed method and software is tested on examples from the database for the identification of systems DAISY.
Co-ordinator(s): Bart
De Moor, Jan
Willems, Sabine
Van Huffel
Researcher(s): Ivan
Markovsky