Mathematical equivalence of two ellipsoid algorithms for bounded-error estimation

Bounded-error estimation aims at characterizing the set of all parameter vectors consistent with prior bounds on the errors between the measurements and model outputs. E. Fogel and Y.F. Huang (Autom., vol.18, no.2, p.229-39, 1982) have proposed a simple recursive construction of a minimal volume ellipsoidal outer bound for this set. The basic Fogel-Huang algorithm is not optimal, and a slight heuristic modification suggested by G. Belforte and B. Bona (Preprints 7th IFAC/IFORS Symp. on Identification and System Parameter Estimation, p.1507-12, 1985) has been shown to yield ellipsoids with smaller volumes. This modified algorithm is proved to be equivalent to an optimal ellipsoid algorithm developed in the context of linear programming