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On the uniqueness of prediction error models for systems with noisy input-output data. (English) Zbl 0616.93074
This paper addresses the uniqueness problem of the prediction error (PE) identification for a class of linear systems with noisy input and output data. Necessary and sufficient conditions are derived for the corresponding PE loss function to have (asymptotically) a unique global minimum. The results indicate that a PE algorithm may give very bad parameter estimates for systems not satisfying these conditions. Such a possibility is illustrated by a numerical example. While the PE method is used as a vehicle for illustration, the derived conditions for global uniqueness (or identifiability) apply to any consistent estimation method based on second-order data.

MSC:
93E12 Identification in stochastic control theory
93C05 Linear systems in control theory
93C55 Discrete-time control/observation systems
62M20 Inference from stochastic processes and prediction
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