In typical location-based services (LBS), moving objects (e.g., GPS-enabled mobile phones) report their locations through a wireless network. An LBS server can use the location information to answer various types of continuous queries. Due to hardware limitations, location data reported by the moving objects are often uncertain. In this paper, we study efficient methods for the execution of Continuous Possible Nearest Neighbor Query (CPoNNQ) that accesses imprecise location data. A CPoNNQ is a standing query (which is active during a period of time) such that, at any time point, all moving objects that have non-zero probabilities of being the nearest neighbor of a given query point are reported. To handle the continuous nature of a CPoNNQ, a simple solution is to require moving objects to continuously report their locations to the LBS server, which evaluates the query at every time step. To save communication bandwidth and mobile devices' batteries, we develop two filter-based protocols for CPoNNQ evaluation. Our protocols install "filter bounds" on moving objects, which suppress unnecessary location reporting and communication between the server and the moving objects. Through extensive experiments, we show that our protocols can effectively reduce communication costs while maintaining a high query quality.