In this paper, we propose a novel localization service to monitor the position of residents in assisted living facilities. The service supports a configurable balancing between precision and privacy, in such a way that the right of the residents to move freely in the environment in which they live without being tracked is preserved. However, in case of need, they can always be quickly localized. To do this, we implement, on top of an RFID-based architecture, a probabilistic model guaranteeing that the probability of identifying a person in a given (sensitive) place is at most k −1 , where k represents the required privacy level. This is obtained by ensuring that the EPC sent by RFID tags is not an identifier, but is equal to that of at least other k − 1 people, each afferent to a different reader. We show that our method reaches the goal, resisting also attacks aimed at breaking privacy on the basis of humans' movement models. Importantly, privacy is guaranteed against both misuse of the administrator and client-side eavesdropping attacks.