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Reliability of Projection Algorithms in Conditional Estimation

Author

Listed:
  • A. Garulli

    (Università di Siena)

  • B. Z. Kacewicz

    (Università di Siena)

  • A. Vicino

    (Università di Siena)

  • G. Zappa

    (Università di Firenze)

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.

Suggested Citation

  • A. Garulli & B. Z. Kacewicz & A. Vicino & G. Zappa, 1999. "Reliability of Projection Algorithms in Conditional Estimation," Journal of Optimization Theory and Applications, Springer, vol. 101(1), pages 1-14, April.
    • Handle: RePEc:spr:joptap:v:101:y:1999:i:1:d:10.1023_a:1021710825323
    DOI: 10.1023/A:1021710825323
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    Cited by:

    1. B. Kacewicz, 2001. "Optimal Conditional Estimation: Average Case Setting," Journal of Optimization Theory and Applications, Springer, vol. 109(3), pages 649-666, June.
    2. Bolesław Kacewicz, 2005. "Optimal and suboptimal algorithms in set membership identification," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 11(2), pages 159-169, June.

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