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State estimation for linear systems with observations partially corrupted by noise. (English) Zbl 0744.93093
Summary: This paper exploits the fact that any row vector of the observability matrix applied for transforming the state converts the latter to the new state component. Using the same but appropriately chosen vectors for transforming the system with the observation not fully corrupted by white noise we can accurately determine some state components. These vectors create the basis for the \(\ell\)-dimensional subspace of transformation vectors to the new accurately determinable state components. Using this basis the state transformation is constructed which is one step converts the singular linear filtering problem to a nonsingular one with state dimension decreased by \(\ell\).

MSC:
93E11 Filtering in stochastic control theory
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