Naive approximate realization of noisy data

This paper presents suboptimal solutions to the problem of Approximate Partial Realization: given a multivariable formal power series of finite length, a state space description has to be constructed with limited dimension, in such a way that it approximates the available matrix sequence with respect to some specific criterion. The methods based on the Ho-Kalman algorithm and employing a Hankel matrix or an alternative to it, a Page matrix, fail theoretically but appear to be practically quite useful. Results of the simulations allow us to determine in which cases the Hankel or Page matrix approach would be more appropriate.