Set membership state estimation for discrete-time linear systems with binary sensor measurements

This paper addresses the problem of state estimation for discrete-time linear systems, based on measurements provided by an output binary sensor. The problem is formulated and solved in a set theoretic framework. Two algorithms are devised for recursively computing outer approximations of the set of state vectors compatible with the information provided by the binary sensor. This allows one to obtain a nominal state estimate and to characterize the associated uncertainty. The procedures can be tuned to suitably trade off the quality of set approximations and the required computational load. An input design technique based on the computed feasible state sets, which is aimed at promoting uncertainty reduction, is provided. The case of time-varying sensor threshold is also considered and a strategy for selecting online the value of the threshold is formulated. All the proposed methods are validated in simulations on two numerical examples.