Reliability of projection algorithms in conditional estimation

This paper studies the role of projection algorithms in conditional set mem bership estimation. These algorithms are known to be suboptimal in terms of the worst-case estimation error. A tight upper bound on the error of centr al projection estimators and interpolatory projection estimators is compute d as a function of the conditional radius of information. Since the radius of information represents the minimum achievable error, the derived bound p rovides a measure of the reliability level of the suboptimal algorithms. Th e results are derived in a general deterministic setting, which allows the consideration of linearly parametrized approximations of a compact set of f easible problem elements.