Uniquely identifiable state-space and ARMA parametrizations for multivariable linear systems. (English) Zbl 0537.93067
This paper considers the problem of determining the structure of the state space of ARMA model for multivariate stationary finite dimensional stochastic processes such that the model parameters become uniquely identifiable. It is shown that there are basically two ways to obtain uniquely identifiable models for multivariable systems: the canonical form approach and the overlapping form approach. The paper presents the construction of uniquely identifiable overlapping state space and ARMA models. It is shown that uniquely identifiable parametrizations in either state space or ARMA form are all related to a set of ’intrinsic invariants’ which are determined directly from the Hankel matrix of Markov parameters of the system. Different forms of overlapping ARMA parametrizations are derived and their properties discussed. The advantage that no preliminary estimation of structural invariants is required with overlapping forms is emphasized in the paper.
Reviewer: H.Hictikko
MSC:
| 93E12 | Identification in stochastic control theory |
| 62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |
| 93C35 | Multivariable systems, multidimensional control systems |
| 93C05 | Linear systems in control theory |
| 93B10 | Canonical structure |
| 70G10 | Generalized coordinates; event, impulse-energy, configuration, state, or phase space for problems in mechanics |
Keywords:
identifiability; parametrizations; autoregressive moving average model; multivariate stationary finite dimensional stochastic processes; canonical form approach; overlapping form approach; structural invariantsReferences:
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