A new approach for indoor positioning is presented, aimed at designing a WiFi positioning system that is feasible and convenient for both service providers and end users. In the proposed approach, only access points (APs) need to collect the received signal strengthes (RSS) of mobile devices, and use these RSS samples to jointly estimate the devices' locations. To enhance the accuracy of positioning, the relationship between the RSS samples and their geometrical locations is explored, leading to a sparse Bayesian model for the radio power map of the RSS observations of each AP. With more than 20 training anchors, the accuracy of the proposed model-based positioning method can be lower than 3.4 meters in an indoor space with only 4 randomly deployed APs, which outperforms the fingerprinting method by 0.4 meter. Extensive experimental results also verify that the proposed positioning service can offer considerable accuracy with only limited efforts in training, suggesting that the prototype is realistic for randomly deployed dense WiFi networks.