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Identifiability in dynamic errors-in-variables models. (English) Zbl 0536.93064

The paper considers the identifiability of scalar linear discrete-time errors-in-variable systems. The noise-free (unobserved) input as well as the noise processes correcting the input and output signals are assumed to be linearly regular stationary processes. If the transfer functions in the Wold-decomposition of these processes are allowed to be non-rational (and some of them non-causal too) then an ”essential nonuniqueness” for the identification problem under consideration is shown.
A class of parameterized errors-in-variable (or noisy input-noisy output) systems is called identifiable if it does not contain two different systems with the same second-order moments of the noisy input and output processes. For rational transfer functions sufficient conditions for identifiability are given. These conditions either exploit a particular structure of measurement errors or they are in the form of some generic constraints on system parameters.
Reviewer: P.Stoica

MSC:

93E12 Identification in stochastic control theory
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
93C05 Linear systems in control theory
93C55 Discrete-time control/observation systems
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References:

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