On the Generalization of the Koopmans-Levin Estimation Method

The paper discusses parameter estimation methods originated from the direct or indirect minimization of a performance index related to the generalized version of the Koopmans-Levin algorithm (GKL). Unlike algorithms directly minimizing an appropriate loss function, indirect estimation algorithms perform data compression into a subspace first then derive the parameter estimation from the eigenvectors spanning this subspace. The application of scaleable Hankel and Toeplitz type matrices offers a compact and uniform treatment of the various algorithms. Optimal setting of the weighting matrices applicable in the performance index to reduce the variance of the parameter estimation is also shown. A simulation study has been added to compare the performance of the presented identification algorithms.