Properties of Least Squares Estimates in Set Membership Identification

Abstract In this paper we investigate the properties of the least square algorithm in the identification of linear, time invariant, discrete time systems, in presence of unknown but bounded errors. It is known that the least squares algorithm enjoys strong optimality properties in the case of power bounded ( l 2 ) errors, while it may be far from optimality in the case of pointwise ( l ∞ ) bounded errors. In the paper we derive exact expressions of the local and global worst case errors of the least squares estimates and we show that the global error may diverge as the number of measurements grows. Then, we give general conditions assuring convergence of the global worst-case error.

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