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D. Bauer:
"Order estimation for subspace methods";
Automatica, 37 (2001), 1561 - 1573.

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 thereof 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 exogeneous inputs. The two methods based on the singular values are shown
to be consistent under fairly mild assumptions, while the same result for the
third approach is only obtained on a generic set.
The former can be applied to Larimore type of procedures as well as to MOESP type of
procedures, whereas 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 conditions on the penalty term to guarantee consistency
are derived. The effects of different choices of the penalty term are investigated in a simulation study.