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We propose a method to perform set-based state estimation of an unknowndynamical linear system using a data-driven set propagation function. Ourmethod comes with set-containment guarantees, making it applicable tosafety-critical systems. The method consists of two phases: (1) an offlinelearning phase where we collect noisy input-output data to determine a functionto propagate the state-set ahead in time; and (2) an online estimation phaseconsisting of a time update and a measurement update. It is assumed that knownfinite sets bound measurement noise and disturbances, but we assume noknowledge of their statistical properties. These sets are described usingzonotopes, allowing efficient propagation and intersection operations. Wepropose a new approach to compute a set of models consistent with the data andnoise-bound, given input-output data in the offline phase. The set of models isutilized in replacing the unknown dynamics in the data-driven set propagationfunction in the online phase. Then, we propose two approaches to perform themeasurement update. Simulations show that the proposed estimator yields statesets comparable in volume to the 3{\sigma} confidence bounds obtained by aKalman filter approach, but with the addition of state set-containmentguarantees. We observe that using constrained zonotopes yields smaller sets butwith higher computational costs than unconstrained ones.

Data-Driven Set-Based Estimation using Matrix Zonotopes with Set Containment Guarantees