Optimal inner bounds of feasible parameter set in linear estimation with bounded noise

This note considers some problems arising in 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. If a linear relationship between parameters and measurements is assumed, this set is a polytope. An exact representation of this polytope may be too complex for practical use, and approximate descriptions in terms of simple shaped sets contained in the feasible parameter set (inner bounds) have shown to be useful in several applications. In this note, we use as bounding sets balls in l(m) norms (boxes), l2 norms (ellipsoids), and l1 norms (diamonds). We give new results on the computation of maximal balls when their shape is either known or partially free.