An integration scheme of simultaneous cycle slips determination combining improved geometry-free combination and TDCP model for undifferenced GNSS data

Abstract Fast and reliable cycle slip determination can ensure successive ambiguity resolution and precise positioning. Generally, it is not difficult to determine big cycle slips using the linear combination of observations, for instance, the geometry-free (GF) combination and the Hatch–Melbourne–Wübbena (HMW) combination. However, the participation of pseudorange observations may fail to identify small cycle slips. This contribution proposes an integration scheme combining the improved geometry-free (IGF) combination and time-difference carrier phase (TDCP) model to determine simultaneous cycle slips for undifferenced kinematic data. The IGF combination, which is improved from the modified geometry-free (MGF) combination and utilizes the Gauss floor function to take the decimal part of GF, can directly determine small cycle slips on a specific frequency. The TDCP model is used to estimate the differences of position and clock error between adjacent epochs by least-square adjustment using clean phase observations, and repair the remaining cycle slips by the predicted TDCP measurements obtained from the predetermined parameters. The proposed method is tested against 1 Hz kinematic dataset with simulation and highway dataset with real cycle slips. In the simulation test, all cycle slips can be correctly repaired by IGF for L1/L5, E1/E5 and E1/E5a. These combinations are unavailable for MGF. Compared to the HMW-GF method, the repair success rate of IGF improves from 96.80% to 99.16%, and the number of incorrect cases reduces from 9650 to 2535. The IGF-TDCP integration scheme can further improve the performance of IGF, whose repair success rate is more than 99.97% and incorrect cases are 38. The highway test shows that the proposed method effectively processes simultaneous cycle slips on more than half of the tracking satellites caused by the overpasses, even in the case of simultaneous 3 second data gaps on 5 satellites of 6 tracking satellites.