Elsevier

Automatica

Volume 26, Issue 5, September 1990, Pages 887-898
Automatica

Paper
Parameter estimation algorithms for a set-membership description of uncertainty

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Abstract

The problem of parameter estimation when the data are corrupted by unknown but bounded errors mainly consists in characterizing the minimal parameter set consistent with the measurements, the model and the error description. Two different approaches are reviewed and compared in this paper; the first one based on a recursive parameter ellipsoidal-bounding algorithm, the other on an orthotopic-bounding set, obtained by solving linear programming problems. The original ellipsoidal algorithm, modified for higher efficiency, has been compared with the linear programming method. Although the orthotopic description may result in a more accurately defined parameter region, it is time-consuming when a large number of measurements is present. Conversely, the ellipsodal-bounding algorithm often provides a loose approximation to the parameter region, but allows a fast data preprocessing, producing a smaller number of constraints that can be subsequently fed to the linear programming algorithm. A combined use of the two procedures is outlined and tested on simulated and real data, the latter being relative to the tuning of an AD converter, resulting in a remarkable reduction in the computing time.

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The original version of this paper was presented at the 7th IFAC/IFORS Symposium on Identification and System Parameter Estimation which was held in York, U.K. during July, 1985. The Published Proceedings of this IFAC Meeting may be ordered from: Pergamon Press plc, Headington Hill Hall, Oxford OX3 0BW, U.K. This paper was recommended for publication in revised form by Associate Editor Y. Sunahara under the direction of Editor P. C. Parks.

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