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On Weighting in State-space Subspace System Identification

The aim of this contribution is to analyze a class of state-space subspace system identiication (4SID) methods. In particular, the eeect of diierent weighting matrices is studied. By a linear regression formulation, diierent cost-functions, which are rather implicit in the ordinary framework of 4SID, are compared. Expressions for asymptotic variances of pole estimation error are analyzed and from these expressions, some dii-culties in choosing user speciied parameters are pointed out. Another interesting result obtained is that a row weighting in the subspace estimation step does not aaect the pole estimation error, asymptotically. This result holds for two diierent pole estimation methods, namely the shift invariance method and an optimally weighted least-squares method. In a numerical example, relative eeciency of the optimally weighted pole estimation method is indicated.