AbstractWhen the error between the data and the corresponding model output is affine in the parameters to be estimated, the set § of all values of the parameter vector that are feasible (in the sense that the error between the model and the data falls within known prior bounds) is a convex polyhedron, or even a convex polytope if the regressors span the parameter space. Although most of the literature on parameter bounding has been concerned with finding simple‐shaped sets (ellipsoids or boxes) guaranteed to contain §, methods have also been developed that make it possible to characterize this polytope exactly and recursively as the convex combination of its vertices. the basic principles of this approach are explained and the results obtained are illustrated. For time‐varying systems a new simple policy is suggested to expand the previous polytope before intersecting it with the feasible region corresponding to the new datum. This policy allows algorithms developed for time‐invariant systems to be used without any modification. When no reliable bounds are available for the error, an extension of the exact description approach is suggested. This makes it possible to obtain the minimax estimate of the parameters exactly and recursively. As a byproduct, the polyhedral cone obtained contains all values of § that would be obtained if a bound larger than the minimax bound were assumed for the absolute value of t