A modified cycle slip detection and repair method for Galileo quad/pent-frequency observations

Abstract The detection and repair of Galileo multi-frequency (quad/pent-frequency) cycle slips are susceptible to the effects of multipath, pseudo-range noise, and high ionospheric disturbances. Taking into account the combination noise and ionospheric amplification factors, the optimal multi-frequency combination coefficients are selected for cycle slip detection. The approach addresses the issue from both the observational and computational levels, ensuring the accuracy and efficiency of cycle slip repair. On the observational level, the noise in pseudo-range observations is typically much higher than that in carrier phase observations. To mitigate the impact of pseudo-range observation noise and its associated multipath effects, the carrier smoothing pseudo-range method is considered, aiming to improve the accuracy of cycle slip repair. On the computational level, to avoid the extensive computational load caused by the LAMBDA algorithm’s space search, a dual constraint is applied to the Least Squares (LS) method using the L2-norm criterion and the non-negative solution criterion. The integer rounding of the parameter solution is then adopted as the fixed cycle slip solution. The experimental results are as follows: For quad-frequency cycle slip detection and repair (QCDR), one Geometry-Free and Ionosphere-Free (GFIF) combination [0, 1, −3, 2] and three phase Geometry-Free (GF) combinations [−1, 1, 0, 0], [0, −1, 1, 0], [0, −1, 0, 1] are selected. For pent-frequency cycle slip detection and repair (PCDR), one GFIF combination [0, −1, 2, 0, −1] and four GF combinations [0, 0, −1, −1, 2], [−1, 1, 0, 0, 0], [−1, 0, 0, 0, 1], [0, 1, −3, 0, 2] are chosen. Using the proposed algorithm, under regular conditions, the success rate for detecting quad/pent-frequency cycle slips is 100%, with repair success rates of 99.60% and 99.48%, respectively. In ionospheric environments with varying levels of disturbance, three monitoring stations are selected. The success rates for quad-frequency cycle slip repair are 99.96%, 99.05%, and 99.96%, while the success rates for pent-frequency cycle slip repair are 99.96%, 99.15%, and 99.94%.