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) |
Keywords:
Kalman filtering; recursive state estimation; unknown input estimation; minimum-variance estimationReferences:
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