Self-driving driving support systems and autonomous vehicles require highly accurate and reliable vehicle positions. Conventionally, the FIX solution of Kinematic positioning is often used as an element indicating the reliability of the GNSS positioning result. However, there is a problem that FIX solutions with large errors occur in urban areas. Therefore, in this paper, two points of interest were prepared. One is that errors in GNSS are more likely to occur in the height direction than in the plane direction. Another is that the height fluctuation of the vehicle is small. Based on these, we proposed a method to detect highly reliable FIX solutions using height fluctuations during driving. According to the evaluation test, the proposed method achieved a decision accuracy of 99.9% on Route A, which is an urban area. On route B in a dense urban area where the environment is more severe, the accuracy of the judgment was 99.7%. Since these results were judged with higher accuracy than the ratio test, the proposed method is considered to be effective.