This paper addresses two aspects of high accuracy GPS positioning: sin
gle point positioning and real-time kinematic positioning. In both cas
es, it is shown that use of the correct models significantly improves
the quality of the resulting positions. In the first case, emphasis is
placed on physical models, especially the satellite orbit, and in the
second case, emphasis is placed on the stochastic model, i.e. underst
anding the statistics of the GPS observables.