As communications-enabled devices are becoming more ubiquitous, it becomes easier to track the movements of individuals through the radio signals broadcasted by their devices. Thus, while there is a strong interest for physical analytics platforms to leverage this information for many purposes, this tracking also threatens the privacy of individuals. To solve this issue, we propose a privacy-preserving solution for collecting aggregate mobility patterns while satisfying the strong guarantee of ε-differential privacy. More precisely, we introduce a sanitization mechanism for efficient, privacy-preserving and non-interactive approximate distinct counting for physical analytics based on perturbed Bloom filters called Pan-Private BLIP. We also extend and generalize previous approaches for estimating distinct count of events and joint events (i.e., intersection and more generally t-out-of-n cardinalities). Finally, we evaluate expirementally our approach and compare it to previous ones on real datasets.