Optimal Approximation of Feasible Parameter Set in Estimation with Unknown but Bounded Noise

Abstract

In this paper we study problems arising in linear parameter estimation theory with unknown but bounded measurement errors. In this theory a key role is played by the feasible parameter set, i.e. the set of all parameter values consistent with the system model and the error bounds. This set is a polytope, whose exact description may be unnecessarly complex for practical use. Approximate descriptions in terms oí simple shaped sets, like boxes or ellipsoids containing (outer bounding) or contained in (inner bounding) the feasible parameter set, have been investigated and found to be useful in several applications. The minimal volume outer bounding and the maximal volume inner bounding sets are usually considered optimal choices. In this paper we report new results on optimal outer bounding ellipsoids or boxes which, together with some extension of previous work on optimal inner bounds, represent a complete set of results on the problem. The practical computability of the derived algorithms is also discussed.