Compared with pseudorange measurement, carrier phase tracking is much less noisy, which can provide accurate positioning solutions. The existing carrier phase-based positioning methods rely on precise ephemeris or base station, which may cause poor real-time and increase complexity in the system. To simplify the calculation model and achieve accurate navigation solutions with a stand-alone receiver, a new GPS/BDS based real-time non-differential positioning method is proposed. Due to the need to estimate the ambiguity terms of carrier phase measurements, the dimension of the state is larger than that of the measurement, the system observability is evaluated via the observability degrees. Both the train test on Beijing- Shenyang high speed railway and simulation were carried out, and the results confirm that the multi-constellation method can improve the positioning accuracy compared with stand-alone cases. The position and velocity Root Mean Square of the proposed method are (0.9022 m, 0.9140 m, 1.1621 m) and (0.0818 m/s, 0.0958m/s, 0.0289m/s) in the north, east, down directions. The proposed method has improved positioning performance in terms of accuracy and observability compared with different combinations of measurement methods.