Although GPS kinematic relative positioning can provide high accuracy, GPS observables, like any other kind of measurement, are not free of errors. Indeed, they have several kinds of errors. In this paper, we show how to construct a functional mathematical model within the context of a Kalman Filter in order to eliminate most of these errors. Furthermore, we discuss how the multipath effect, a kind of error not modeled in the functional model, can be corrected using the proposed wavelet method. The behavior of the double difference functional model in the kinematic mode is also demonstrated and analyzed aiming to provide better insight into the problem. The results obtained from the multipath experiments were very promising and are presented here.