In this paper, the applications of the Gaussian sum filtering method to the carrier phase based relative GNSS positioning are considered. The distribution of the observation noise in the double differenced carrier phases is modeled by the weighted sum of Gaussian distributions, and the Gaussian sum filter derived by extending and modifying the Gaussian sum filter proposed by Alspach and Sorenson [1] is applied to the positioning. The experiments are done by using real receiver data, and the performance of positioning as well as integer ambiguity estimation are investigated.