The authors apply a theory of set-valued estimation to derive a set-valued filter and a set-valued smoother for a linear discrete-time system. The resulting estimators provide the set of all state sequences that are consistent with the available data, allowing application to weakly or partially observable systems. Simulation results demonstrating the essential features of the filter and smoother are presented. It is noted that the estimators provide a robust method of state estimation in which the observability of the system does not affect correct estimator performance. The estimator provides exactly the estimate that is supported by the data sequence.
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