Automated robotic systems operating in real-world environments require thorough test campaigns before deployment, in which engineers assess whether the system is actually exposed to critical scenarios. A well-established way to judge the efficacy of test campaigns in controlled environments is scenario coverage: It quantifies the quality of recorded data from test campaigns w.r.t. a set of (critical) scenario classes of interest. Challenges arise when transferring coverage from controlled to open environments, as it may no longer be exactly determined to which scenario class the recorded test data belongs to: sensors offer limited observability, e.g., by occlusions or hardware failures, and specifications might be inherently vague, e.g., via imprecise traffic regulations. We leverage the Open World Assumption to formally extend scenario coverage to such ambiguous test data and present algorithms for computing guaranteed lower and upper bounds on coverage. Whereas deciding the lower bound problem is \(D^p\) -complete, the upper bound can be computed in polynomial time. We extend an existing coverage software tool with two approaches for incorporating the Open World Assumption, grounded in LTLf. Our evaluation shows that meaningful statements on scenario coverage are feasible, even under intricacies of the real world.