Order Estimation for Subspace Methods
2000 (English)Report (Other academic)
In this paper the question of estimating the order in the context of subspace methods is addressed. Three different approaches are presented and the asymptotic properties there of derived. Two of these methods are based on the information contained in the estimated singular values, while the third method is based on the estimated innovation variance. The case with observed inputs is treated as well as the case without exogenous inputs. The two methods based on the singular values are shown to be consistent under fairly mild assumptions, while the same result for the thirf approach is only obtained on a subset. The former can be applied to Larimore type of procedures as well as to MOESP type of procedures, where as the latter is only applied 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 shown in a numerical example. All the estimation methods involve the choice of a penalty term. Sufficient copnditions on the penalty term to guarantee consistency are derived. The effects of different choices of the penalty term are investigated in a simulation study.
Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2000. , 16 p.
LiTH-ISY-R, ISSN 1400-3902 ; 2263
Subspace methods, Order estimation, Asymptotic properties
IdentifiersURN: urn:nbn:se:liu:diva-55674ISRN: LiTH-ISY-R-2263OAI: oai:DiVA.org:liu-55674DiVA: diva2:316396