Abstract
The properties of the least square algorithm in the identification of linear, time-invariant, discrete-time systems, in the presence of unknown but bounded errors are investigated. It is known that the least squares algorithm enjoys strong optimality properties in the case of power bounded (l2) errors, while it may be far from optimal in the case of pointwise (l∞) bounded errors. Exact expressions of the local and global worst case errors of the least squares estimates are derived. Using these results, general conditions assuring convergence to zero of the global worst-case error are given. It is also shown that the least squares algorithm may be optimal in l1 and l∞ identification of FIR systems with pointwise bounded errors.
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