Application of Structured Total Least Squares for System Identification

The following identification problem is considered: 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 of a fixed complexity. The complexity is measured by the input dimension and the state dimension. The problem is known as the global total least squares 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. The identificatio