System identification: theory for the user
System identification: theory for the user
From time series to linear system—Part III. Approximate modelling
Automatica (Journal of IFAC)
Linear stochastic systems
The statistical theory of linear systems
The statistical theory of linear systems
The Frisch scheme in dynamic system identification
Automatica (Journal of IFAC) - Identification and system parameter estimation
Symmetric modeling in system identification
Three decades of mathematical system theory
Algorithms for global total least squares modelling of finite multivariable time series
Automatica (Journal of IFAC)
System Identification by Dynamic Factor Models
SIAM Journal on Control and Optimization
Parameter estimation from noisy measurements
International Journal of Systems Science
Brief Identification of nonlinear errors-in-variables models
Automatica (Journal of IFAC)
Identification methods in a unified framework
Automatica (Journal of IFAC)
| Hi-index | 22.15 |
Global total least squares (GTLS) is a method for the identification of linear systems where no distinction between input and output variables is required. This method has been developed within the deterministic behavioural approach to systems. In this paper we analyse statistical properties of this method when the observations are generated by a multivariable stationary stochastic process. In particular, sufficient conditions for the consistency of GTLS are derived. This means that, when the number of observations tends to infinity, the identified deterministic system converges to the system that provides an optimal appoximation of the data generating process. The two main results are the following. GTLS is consistent if a guaranteed stability bound can be given a priori. If this information is not available, then consistency is obtained if GTLS is applied to the observed data extended with zero values in past and future.