A major concern for large-scale deployment of location-based services (LBSs) is the potential abuse of their client location data, which may imply sensitive personal information. Even if a user requests a service anonymously, a location itself may still reveal the user's true identity. A promising solution to this problem is the concept of location anonymity. Instead of reporting a user's accurate location, this approach computes a cloaking area that contains the user and some others and report this area as the user's location to a service provider. Existing use of location anonymity has been limited to the LBSs where users report their location only sporadically. In this paper, we apply this concept for anonymity protection in continuous LBSs, which require frequent location updates from service users. Since a time-series sequence of cloaking areas may be correlated to find a user's actual position, simply ensuring each cloaking area contains at least K users does...