Handling Certain Structure Information in Subspace Identification

The prediction-error approach to parameter estimation of linear models often involves solving a non-convex optimization problem. In some cases, it is therefore difficult to guarantee that the global optimum will be found. A common way to handle this problem is to find an initial estimate, hopefully lying in the region of attraction of the global optimum, using some other method. The prediction-error estimate can then be obtained by a local search starting at the initial estimate. In this paper, a new approach for finding an initial estimate of certain linear models utilizing structure and the subspace method is presented. The polynomial models are first written on the observer canonical state-space form, where the specific structure is later utilized, rendering least-squares estimation problems with linear equality constraints.