The objective of GPS control surveying is ultimately to determine coordinate sets of control points within targeted accuracy through a series of observations and network adjustments. To this end, it is of equivalent importance for the accuracy of these coordinates to be realistically represented by using an appropriate method. The accuracy representation can be quantitively made by the variance-covariance matrices of the estimates, of which features are sensitive to the mathematical models used in the adjustment. This paper deals with impact of functional and stochastic modeling techniques into the accuracy representation of the GPS control surveying with a view of gaining background for its standardization. In order to achieve this goal, mathematical theory and procedure of the single-baseline based multi-session adjustment has been rigorously reviewed together with numerical analysis through processing real world data. Based on this study, it was possible to draw a conclusion that weighted-constrained adjustment with the empirical stochastic model was among the best scheme to more realistically describe both of the absolute and relative accuracies of the GPS surveying results.