  This paper addresses a data-driven input reconstruction problem based on
Willems' Fundamental Lemma in which unknown input estimators (UIEs) are
constructed directly from historical I/O data. Given only output measurements,
the inputs are estimated by the UIE, which is shown to asymptotically converge
to the true input without knowing the initial conditions. Both open-loop and
closed-loop UIEs are developed based on Lyapunov conditions and the
Luenberger-observer-type feedback, whose convergence properties are studied. An
experimental study is presented demonstrating the efficacy of the closed-loop
UIE for estimating the occupancy of a building on the EPFL campus via measured
carbon dioxide levels.
