Phase cycle slip detection of LEO satellites based on the second-order time-difference model with dynamic orbital constraints

Abstract The cycle-slip detection is the prerequisite for achieving the utmost precise carrier-phase measurements for the low earth orbit (LEO) spaceborne Global Navigation Satellite System (GNSS) receivers. However, the issue has not yet been solved entirely due to the limitations of traditional cycle-slip detection methods. In the paper, we proposed a novel cycle-slip detection method based on the second-order time-difference phase ionosphere-free (IF) or wide-lane (WL) observations with dynamic orbital constraints. Nominal orbits at the dm-level accuracy and the earth gravity field of at least 30 degrees and orders (d/o) within 30 s or higher sampling rate data could guarantee the proposed method reliable for the flying altitude of near 500 km of LEO satellites. To validate the proposed method effectiveness, numeric experiments with comparisons to the traditional cycle-slip detector based on the Melbourne–Wübbena (MW) combination are carried out with well-chosen measurements for the LEO satellite under ionospheric activities of different levels. The results, in terms of the correctness and misjudgment of the cycle slips detected and the precision of estimated orbit, indicate that, on the one hand, the detector based on the proposed phase IF test parameters are superior to one based on the proposed phase WL test parameters or the MW combinations under any level of ionospheric activities; on the other hand, under highly active ionospheric activities, the proposed phase WL cycle-slip detector discovers a fewer number of real cycle slips, which are flagged by the reference method introduced in the paper, but more misjudgments than the MW cycle-slip detector does, which leads to the inferior of the WL cycle-slip detector. However, the phase WL cycle-slip detector performs slightly better than the MW cycle-slip detector under moderately active and very quiet ionospheric activities. In view of the developing multi-frequency multi-GNSS uncombined observation data scanning, the proposed phase IF test parameter accompanied with the MW combinations is recommended to be applied to the cycle-slip detection if the predictable ionospheric refraction lies at the strongly intensive level of the ionospheric activity. Otherwise, the proposed phase WL test parameter would be involved.