The statistical theory of linear systems
The statistical theory of linear systems
Subspace algorithms for the stochastic identification problem
Automatica (Journal of IFAC)
Consistency and relative efficiency of subspace methods
Automatica (Journal of IFAC) - Special issue on trends in system identification
Automatica (Journal of IFAC)
Statistical analysis of novel subspace identification methods
Signal Processing - Special issue: subspace methods, part II: system identification
IEEE Transactions on Pattern Analysis and Machine Intelligence
Analysis of the asymptotic properties of the MOESP type of subspace algorithms
Automatica (Journal of IFAC)
Asymptotic properties of subspace estimators
Automatica (Journal of IFAC)
On the ill-conditioning of subspace identification with inputs
Automatica (Journal of IFAC)
Hi-index | 22.14 |
It is sometimes claimed in the literature that subspace methods provide consistent estimates, also when the underlying observed signal has purely oscillatory modes (or the generating system has uncontrollable eigenvalues on the unit circle) but a formal proof of this assertion does not seem to exist. In this paper, we prove consistency of subspace methods with purely oscillatory modes. A well-known subspace identification procedure based on canonical correlation analysis and approximate partial realization is shown to be consistent under certain conditions on the purely deterministic part of the generating system. The algorithm uses a fixed finite regression horizon and the proof of consistency does not require that the regression horizon goes to infinity at a certain rate with the sample size N.