Application of structured total least squares for system identification and model reduction

The following identification problem is considered: Minimize the ℓ₂ norm of the difference between a given time series and an approximating one under the constraint that the approximating time series is a trajectory of a linear time invariant system of a fixed complexity. The complexity is measured by the input dimension and the maximum lag. The question leads to a problem that is known as the global total least squares problem and alternatively can be viewed as maximum likelihood identification in the errors-in-variables setup. Multiple time series and latent variables can be considered in the same setting. Special cases of the problem are autonomous system identification, approximate realization, and finite time optimal ℓ₂ model reduction. The identification problem is related to the structured total least squares problem. This paper presents an efficient software package that implements the theory. The proposed method and software are tested on data sets from the database for the identification of systems DAISY.