Performance analysis of subspace methods in state-space system identification

This dissertation presents a new method for the statistical performance analysis of subspace system identification algorithms. A perturbation expansion of the singular value decomposition is used to approximate the effects of process and measurement noise on the identified system poles. Eigenvalue variance results are obtained that do not depend on asymptotic statistics and are therefore applicable for short data records. These performance measures are conditional upon the specific input and the parameters of the actual system being identified. This method is demonstrated on two variations of the Numerical Subspace State-Space System Identification (N4SID) algorithm. The accuracy of these theoretical performance measures is validated using simulation. Finally, this new method is applied to the first step of three well known subspace identification algorithms to determine the effects of row and column weighting on the variance of identified poles