Estimation error analysis of system matrices in some subspace identification methods

Explicit formulation of dominant parts of the estimation errors of system matrices in PO-MOESP method and a robust N4SID like method are derived based on a proposing lemma on a gap between two singular subspaces. By considering the gap instead of the perturbations of the singular vectors, it is shown that the estimate in PO-MOESP method is unbiased while the estimate in the robust N4SID like method has an asymptotic bias when the past horizon p is finite.