  This paper presents new methods for set-valued state estimation of nonlinear
discrete-time systems with unknown-but-bounded uncertainties. A single time
step involves propagating an enclosure of the system states through the
nonlinear dynamics (prediction), and then enclosing the intersection of this
set with a bounded-error measurement (update). When these enclosures are
represented by simple sets such as intervals, ellipsoids, parallelotopes, and
zonotopes, certain set operations can be very conservative. Yet, using general
convex polytopes is much more computationally demanding. To address this, this
paper presents two new methods, a mean value extension and a first-order Taylor
extension, for efficiently propagating constrained zonotopes through nonlinear
mappings. These extend existing methods for zonotopes in a consistent way.
Examples show that these extensions yield tighter prediction enclosures than
zonotopic estimation methods, while largely retaining the computational
benefits of zonotopes. Moreover, they enable tighter update enclosures because
constrained zonotopes can represent intersections much more accurately than
zonotopes.
