  We propose a method to perform set-based state estimation of an unknown
dynamical linear system using a data-driven set propagation function. Our
method comes with set-containment guarantees, making it applicable to
safety-critical systems. The method consists of two phases: (1) an offline
learning phase where we collect noisy input-output 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 known
finite 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 a new approach to compute a set of models consistent with the data and
noise-bound, given input-output data in the offline phase. The set of models is
utilized in replacing the unknown dynamics in the data-driven set propagation
function in the online phase. Then, we propose two approaches to perform the
measurement update. Simulations show that the proposed estimator yields state
sets comparable in volume to the 3{\sigma} 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 costs than unconstrained ones.
