Enhancing the positioning precision is the primary pursuit of global positioning system (GPS) users. To achieve this goal, most studies have focused on the relationship between GPS receiver clock errors and GPS positioning precision. This study utilizes undifferentiated phase data to calculate GPS clock errors and to compare with the frequency of cesium clock directly, to verify estimated clock errors by the method used in this paper. The frequency stability calculated from this paper (the indirect method) and measured from the National Standard Time and Frequency Laboratory (NSTFL) of Taiwan (the direct method) match to 1.5 × 10-12 (the value from this study was smaller than that from NSTFL), suggesting that the proposed technique has reached a certain level of quality. The built-in quartz clocks in the GPS receivers yield relative frequency offsets that are 3-4 orders higher than those of rubidium clocks. The frequency stability of the quartz clocks is on average two orders worse than that of the rubidium clock. Using the rubidium clock instead of the quartz clock, the horizontal and vertical positioning accuracies were improved by 26-78% (0.6-3.6 mm) and 20-34% (1.3-3.0 mm), respectively, for a short baseline. These improvements are 7-25% (0.3-1.7 mm) and 11% (1.7 mm) for a long baseline. Our experiments show that the frequency stability of the clock, rather than relative frequency offset, is the governing factor of positioning accuracy.