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Error evaluation for projection algorithms in conditional set membership estimation

This paper studies the role of projection algorithms in conditional set membership estimation. These algorithms are known to be suboptimal in terms of the worst-case estimation error. A tight upper bound on the error of central projection and interpolatory projection estimators is computed as a function of the conditional radius of information. Since the radius of information represents the minimum achievable error, the derived bound provides a measure of the reliability level of the suboptimal algorithms. The results are derived in a general setting, which allows to consider linearly parameterized approximations of a compact set of feasible estimates.