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Unbiased minimum-variance input and state estimation for linear discrete-time systems. (English) Zbl 1140.93480
Summary: This paper addresses the problem of simultaneously estimating the state and the input of a linear discrete-time system. A recursive filter, optimal in the minimum-variance unbiased sense, is developed where the estimation of the state and the input are interconnected. The input estimate is obtained from the innovation by least-squares estimation and the state estimation problem is transformed into a standard Kalman filtering problem. Necessary and sufficient conditions for the existence of the filter are given and relations to earlier results are discussed.

93E10 Estimation and detection in stochastic control theory
93C55 Discrete-time control/observation systems
93E03 Stochastic systems in control theory (general)
Full Text: DOI
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