  Deploying autonomous systems in safety critical settings necessitates methods
to verify their safety properties. This is challenging because real-world
systems may be subject to disturbances that affect their performance, but are
unknown a priori. This work develops a safety-verification strategy wherein
data is collected online and incorporated into a reachability analysis approach
to check in real-time that the system avoids dangerous regions of the state
space. Specifically, we employ an optimization-based moving horizon estimator
(MHE) to characterize the disturbance affecting the system, which is
incorporated into an online reachability calculation. Reachable sets are
calculated using a computational graph analysis tool to predict the possible
future states of the system and verify that they satisfy safety constraints. We
include theoretical arguments proving our approach generates reachable sets
that bound the future states of the system, as well as numerical results
demonstrating how it can be used for safety verification. Finally, we present
results from hardware experiments demonstrating our approach's ability to
perform online reachability calculations for an unmanned surface vehicle
subject to currents and actuator failures.
