Position information of moving as well as stationary objects is generally subject to uncertainties due to inherent measuring errors of positioning technologies, explicit tolerances of position update protocols, and approximations by interpolation algorithms. There exist a variety of approaches for specifying these uncertainties by mathematical uncertainty models such as tolerance regions or the Dilution of Precision (DOP) values of GPS. In this paper we propose a principled generic uncertainty model that integrates the different approaches and derive a comprehensive query interface for processing spatial queries on uncertain position information of different sources based on this model. Finally, we show how to implement our approach with prevalent existing uncertainty models.