A new method of adaptive filtering by selecting the parameter weight factor is introduced in this paper. Based on the theoretical analysis and research, this method is firstly used for precise kinematic GPS positioning with single frequency double-differenced (DD) carrier phase observations. Two numerical examples are given to illustrate the feasibility and validity of the method. The preliminary results show that precise positioning results can be obtained by using only the GPS single frequency DD carrier phase measurements for short baselines with the new method.