An improved real-time cycle slip correction algorithm based on Doppler-aided signals for BDS triple-frequency measurements

Doppler, which is an instantaneous GNSS observable signal, has been proven effective in determining velocity and acceleration due to its high availability and accuracy. We propose a real-time triple-frequency cycle slip correction (CSC) method based on Doppler-aided signals because Doppler shift is time-independent and immune to cycle slips. When the sampling interval is less than 1 s, cycle slips on triple-frequency can be detected and repaired using pure Doppler data with high reliability; however, this method cannot be used when the sampling interval exceeds 1 s because the integral cumulative error of Doppler increases significantly. For such cases, a modified triple-frequency CSC approach has been developed based on the raw phase and smoothed code data that was refined using the Doppler signal. To suppress the effect of the integral Doppler error, a balance factor is introduced to adjust the contributions of the raw code and Doppler observables. After the refinement of the GNSS data, three independent combinations need be selected to detect and repair cycle slips with triple-frequency observations. Four constrained criteria have been proposed to select optimal combinations that can reduce the residual ionospheric delay (RID) and measurement noise to a low level. Finally, experiments were carried out to test the performance of the new method using real triple-frequency BDS observations (GPST: 3:15:00–5:55:00, March 23, 2018). The results show that pure Doppler can detect and repair cycle slips effectively with small intervals, and modified Hatch-Melbourne-Wübbena (HMW) method based on Doppler-aided signals can achieve 99.7% success rate in cycle slip correction with large intervals (up to 30 s).