Order estimation for subspace methods

In this paper the question of estimating the order in the context of subspa ce methods is addressed. Three different approaches are presented and the a symptotic properties thereof derived. Two of these methods are based on the information contained in the estimated singular values, while the third me thod is based on the estimated innovation variance. The case with observed inputs is treated as well as the case without exogenous inputs. The two met hods based on the singular values are shown to be consistent under fairly m ild assumptions, while the same result for the third approach is only obtai ned on a generic set. The former can be applied to Larimore type of procedu res as well as to MOESP type of procedures, whereas the third is only appli ed to Larimore type of algorithms. This has implications for the estimation of the order of systems, which are close to the exceptional set, as is sho wn in a numerical example. All the estimation methods involve the choice of a penalty term. Sufficient conditions on the penalty term to guarantee con sistency are derived. The effects of different choices of the penalty term are investigated in a simulation study. (C) 2001 Elsevier Science Ltd. All rights reserved.