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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.

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