  We propose a method to perform set-based state estimation of an unknown
dynamical system using a data-driven set propagation function. Our method comes
with set-containment guarantees, making it applicable to the estimation of
safety-critical systems. The method consists of two phases: (1) an offline
learning phase where we collect noisy state-input data to determine a function
to propagate the state-set ahead in time; and (2) an online estimation phase
consisting of a time update and a measurement update. It is assumed that sets
bound measurement noise and disturbances, but we assume no knowledge of their
statistical properties. These sets are described using zonotopes, allowing
efficient propagation and intersection operations. We propose two approaches to
perform the measurement update. The method is extended to constrained
zonotopes. Simulations show that the proposed estimator yields state sets
comparable in volume to the confidence bounds obtained by a Kalman filter
approach, but with the addition of state set-containment guarantees. We observe
that using constrained zonotopes yields smaller sets, but with higher
computational cost compared to unconstrained zonotopes.
