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Certain models from uncertain data: The algebraic case. (English) Zbl 0749.93018
Summary: The problem of deriving possible linear relations from data affected by additive noise has received remarkable attention in recent years particularly regarding the assumptions (‘prejudices’) behind the procedures leading to unique models. Unlike traditional approaches leading to unique solutions (least squares, maximum likelihood, etc.) the Frisch scheme, belonging to the family of Errors-in-Variables (EV) schemes, leads to a whole family of models compatible with a set of noisy data and is considered as mildly affected by prejudices. This paper shows how also under the assumptions of the Frisch scheme it is possible to obtain a unique model from uncertain data and also to derive the actual amount of noise when the noiseless data are linked by a single linear relation. The more general EV case of non-independent additive noises is then considered and it is shown how also under these assumptions it is possible to obtain the unique set of parameters linking the noiseless data and how the family of compatible noise covariance matrices is defined, in this case, by the infinite elements of a linear variety.

MSC:
93B25 Algebraic methods
93C05 Linear systems in control theory
93E11 Filtering in stochastic control theory
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