Kalman-filter-based undifferenced cycle slip estimation in real-time precise point positioning

Global navigation satellite system (GNSS) precise point positioning (PPP) requires continuous carrier-phase observations to achieve a solution of high precision. Precisely correcting cycle slips caused by signal interruptions is crucial for recovering the data continuity. Most of the existing approaches usually employ only data of one epoch after the interruption for real-time cycle slip processing. In this study, we propose to introduce and estimate cycle slip parameters together with standard PPP parameters, such as position, ionospheric delay, and ambiguities in the case that possible cycle slips are detected, using a Kalman-filter-based procedure with the undifferenced and uncombined PPP model. The integer search strategy is used to fix cycle slips. To reduce the probability of wrong integer fixing, a strict integer validation threshold is suggested. As a result, it is not easy to fix all cycle slips with only one epoch of data. Our approach can be easily extended to use multi-epoch observations to enhance the cycle slip estimation. Once the cycle slips are correctly determined, continuous PPP can be achieved instantaneously. This new approach is tested and validated with three groups of experiments using GPS and GLONASS stations operated by the International GNSS Service from DOY 1–10, 2017, and a real vehicle kinematic data. Numerous experimental results showed that the proposed method can correctly fix the cycle slips for more than 99.5% of epochs suffering from re-convergence. On average, this method takes observation information from about 1.5–2.5 epochs to fix cycle slips and realize rapid re-convergence. Consequently, positioning performance is significantly improved.