Error bounds for FIR models in conditional set-membership identification

The present paper deals with the problem of reduced complexity model estimation in the framework of conditional set-membership identification. The measurement noise is assumed to be unknown but bounded, while the estimated model quality is evaluated according to a worst-case criterion. Since optimal conditional estimators are generally hard to compute, projection estimators are often used in view of their better tractability from a complexity viewpoint. Tight bounds on the suboptimality level of central projection estimators as compared to optimal ones are derived for the case when FIR models are employed for approximation. These bounds improve over known bounds holding for the general class of linearly parameterized models.