Abstract: Detection and correction of cycle slips have always been important issues for measurement of carrier phases in the Global Positioning System (GPS). Although there are many methods to detect and correct cycle slips, methods applicable to positioning with single-frequency coarse codes are scarce. For tackling the problem of detection and correction of cycle slips in positioning as such, we propose a new method by using phase differences between successive epochs and adopting data extrapolation based on the method of Generalized Extended Interpolation (GEI). Our simulations and experimental data show that our method not only is capable of fast detection and correction of short cycle slips of about one week, but also has stabilities on levels about 50% higher than those of the conventional method of polynomial fitting. With its high execution efficiencies, practical applicabilities, and high-level stabilities, our new method is suitable for engineering applications.