The statistical theory of linear systems
The statistical theory of linear systems
Automatica (Journal of IFAC) - Special issue on statistical signal processing and control
N4SID: subspace algorithms for the identification of combined deterministic-stochastic systems
Automatica (Journal of IFAC) - Special issue on statistical signal processing and control
Consistency and relative efficiency of subspace methods
Automatica (Journal of IFAC) - Special issue on trends in system identification
Statistical analysis of novel subspace identification methods
Signal Processing - Special issue: subspace methods, part II: system identification
System identification (2nd ed.): theory for the user
System identification (2nd ed.): theory for the user
Some facts about the choice of the weighting matrices in Larimore type of subspace algorithms
Automatica (Journal of IFAC)
Consistency and asymptotic normality of some subspace algorithms for systems without observed inputs
Automatica (Journal of IFAC)
Order estimation for subspace methods
Automatica (Journal of IFAC)
An analysis of the parametrization by data driven local coordinates for multivariable linear systems
Automatica (Journal of IFAC)
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This paper discusses the asymptotic properties of estimators of ARMAX systems under weak low-level assumptions on the joint input/output process. The prime representative of this class of algorithms is CVA [W.E. Larimore, System identification, reduced order filters and modeling via canonical variate analysis, in: H.S. Rao, P. Dorato (Eds.), Proc. 1983 Amer. Control Conference 2, Piscataway, NJ, 1983, pp. 445-451]. Sufficient assumptions for strong consistency of the transfer function estimators under the assumption of correct specification are derived and explicit bounds on the orders of convergence are given. The assumptions used on the exogenous inputs are considerably weaker than the ones used in the results available in the literature typically requiring the inputs to be ARMA processes themselves, such as is assumed e.g. in [K. Peternell, W. Scherrer, M. Deistler, Statistical analysis of novel subspace identification methods, Signal Processing 52 (1996) 161-177]. Further sufficient conditions for the asymptotic normality of the estimated parameters are given, again under the assumption of correct specification. Finally two order estimation methods are analyzed and conditions for their consistency are derived.