Exact recursive estimation of linear systems subject to bounded disturbances

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This paper addresses the classical problem of determining the sets of possible states of a linear discrete-time system subject to bounded disturbances from measurements corrupted by bounded noise. These so-called uncertainty sets evolve with time as new measurements become available. We present an exact, computationally simple procedure that propagates a point on the boundary of the uncertainty set at some time instant to a set of points on the boundary of the uncertainty set at the next time instant.