Abstract
In this paper linear dynamic errors-in-variables models with mutually uncorrelated noise components are considered. A main complication in identification here is that the systems are not uniquely determined from the (ensemble) second moments of the observations. In this paper we analyze certain properties of the set of all observationally equivalent systems. In addition we derive continuity results for the relation between the spectral densities of the observations and the sets of observationally equivalent systems. Finally we describe the sets of spectral densities corresponding to a given Frisch-corank. The results obtained are of importance for developing and analyzing identification algorithms.
Support by the Austrian “Fonds zur Förderung der wissenschaftlichen Forschung” Projekt P7580 — TEC is gratefully acknowledged.
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Deistler, M., Scherrer, W. (1993). Identification of Linear Systems from Noisy Data. In: Brillinger, D., Caines, P., Geweke, J., Parzen, E., Rosenblatt, M., Taqqu, M.S. (eds) New Directions in Time Series Analysis. The IMA Volumes in Mathematics and its Applications, vol 46. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9296-5_3
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DOI: https://doi.org/10.1007/978-1-4613-9296-5_3
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