  This paper proposes novel set-theoretic approaches for state estimation in
bounded-error discrete-time nonlinear systems, subject to nonlinear
observations/constraints. By transforming the polytopic sets that are
characterized as zonotope bundles (ZB) and/or constrained zonotopes (CZ), from
the state space to the space of the generators of ZB/CZ, we leverage a recent
result on the remainder-form mixed-monotone decomposition functions to compute
the propagated set, i.e., a ZB/CZ that is guaranteed to enclose the set of the
state trajectories of the considered system. Further, by applying the
remainder-form decomposition functions to the nonlinear observation function,
we derive the updated set, i.e., an enclosing ZB/CZ of the intersection of the
propagated set and the set of states that are compatible/consistent with the
observations/constraints. Finally, we show that the mean value extension result
in [1] for computing propagated sets can also be extended to compute the
updated set when the observation function is nonlinear.
