An enhanced cycle slip repair algorithm for real-time multi-GNSS, multi-frequency data processing

Cycle slip detection and repair are crucial quality control steps in high-precision global navigation satellite system (GNSS) positioning using carrier phase measurements. Correct detection and repair of cycle slips can avoid repeated integer ambiguity resolution in real-time kinematic (RTK) or long convergence time in precise point positioning (PPP), especially in the context of multi-GNSS and multi-frequency cases. We introduce a generalized procedure for cycle slip detection and repair. The cycle slip detection is carried out using quality control theory on a single satellite–receiver pair. Upon successful detection, integer least-squares estimation is applied to repair the cycle slip vectors. Then if the cycle slips are detected but not repaired, and no cycle slip exists in the coming epochs, an enhanced repair algorithm, which uses measurements over multiple epochs, is developed. The mathematical model for cycle slip repair is strengthened to allow for higher success rate and its implementation is efficiently accomplished using Kalman filter to suit real-time applications. The generalized procedure and the enhanced algorithm for repair are theoretically analyzed for the dual- and triple-frequency cases under different elevations and ionospheric disturbances. Both high- and low-sampling rate MGEX data with artificial cycle slips are processed, and results indicate that the generalized procedure performs well in benign situations and a higher repair success rate is obtained by implementing the enhanced algorithm in extreme conditions.