Abstract
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 estimators 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 deterministic setting, which allows the consideration of linearly parametrized approximations of a compact set of feasible problem elements.
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Garulli, A., Kacewicz, B.Z., Vicino, A. et al. Reliability of Projection Algorithms in Conditional Estimation. Journal of Optimization Theory and Applications 101, 1–14 (1999). https://doi.org/10.1023/A:1021710825323
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DOI: https://doi.org/10.1023/A:1021710825323