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Unbiased minimum-variance state estimation for linear systems with unknown input. (English) Zbl 1158.93415
Summary: The problem of state estimation for a linear system with unknown input, which affects both the system and the output, is discussed in this paper. A recursive optimal filter with global optimality in the sense of unbiased minimum variance over all linear unbiased estimators, is provided. A necessary and sufficient condition for the convergence and stability is also given, which is milder than existing approaches.

MSC:
93E20 Optimal stochastic control
93E11 Filtering in stochastic control theory
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