For high-precision GPS satellite positioning, Carrier phase observables must be processed. There are two algorithms to follows. One is to determine the correct phase ambiguity parameters, the other uses the trigonometric functions to eliminate the integer ambiguity parameters. The purpose of this paper is to establish a set of model, namely cosine function models of carrier phases. This paper begins with cosine function models of carrier phases, and compares the differences between the method and phase ambiguity resolution. A detailed discussion concerning the characteristics of cosine function models of phases is offered, it can be applied to satellite leveling with proof of fulfilling the accuracy requirement of second-order class II leveling. Besides, this model helps us to estimate the path delays of tropospheric as well as ionospheric altogether. Kinematic positioning can be applied with this model with such an achievement equivalent to that of ambiguity resolution. The last part of this paper contributes to designing the cosine function models of phases with muti-refference station.