  Set-valued state estimation when in the presence of uncertainties in the
model have been addressed in the literature essentially following three main
approaches: i) interval arithmetic of the uncertain dynamics with the
estimates; ii) factorizing the uncertainty into matrices with unity rank; and,
iii) performing the convex hull for the vertices of the uncertainty space.
Approach i) and ii) introduce a lot of conservatism because both disregard the
relationship of the parameters with the entries of the dynamics matrix. On the
other hand, approach iii) has a large growth on the number of variables
required to represent the set or is approximated losing its main advantage in
comparison with i) and ii). In this paper, with the application of autonomous
vehicles in GPS-denied areas that resort to beacon signals for localization, we
develop an exact (meaning no added conservatism) and optimal (smallest growth
in the number of variables) closed-form definition for the convex hull of
Convex Constrained Generators (CCGs). This results in a more efficient method
to represent the minimum volume convex set corresponding to the state
estimation. Given that reductions methods are still lacking in the literature
for CCGs, we employ an approximation using ray-shooting that is comparable in
terms of accuracy with methods for Constrained Zonotopes as the ones
implemented in CORA. Simulations illustrate the greater accuracy of CCGs with
the proposed convex hull operation in comparison to Constrained Zonotopes.
