In order to apply the satellite positioning to train control, a positioning algorithm with the one-dimensional constraint along the series of three-dimensional track coordinates has been developed. In the positioning algorithm, positioning solutions can be obtained even with only two satellites theoretically. We defined the factor GDOP_1D for the algorithm and showed its characteristic. By searching the minimum value of GDOP_1D, it was shown that desirable satellite constellations are the low elevation in the longitudinal direction of the track. Further, the distribution of the actual GDOP_1D obtained during train running was confirmed using the navigation satellite observation data obtained on the operating lines. It was shown that such positioning solutions as would include large errors were efficiently rejectable by selecting the threshold of maximum allowable value of GDOP_1D appropriately.