Real-time triple-frequency cycle slip detection and repair method under ionospheric disturbance validated with BDS data

In order to resolve the real-time cycle slip detection and repair problem with the data under ionospheric disturbance and low sample rate, a new method is proposed by using triple-frequency combinations. First, the geometry-free and ionospheric-free (GFIF) carrier phase combination and then the GFIF pseudorange minus phase linear combination are derived for cycle slip detection. The special slip groups which cannot be discovered by the two GFIF combinations are divided into two types, and each of them is designed to be detected by using three additional geometry-free (GF) linear combinations. In the estimation step, the two GFIF combinations and the pseudorange minus phase linear combination with B3 carrier phase observations are used together to determinate the cycle slip on the original three carriers. The strategy is first to search B3 for cycle slips and then find the B1 and B2 cycles using the two GFIF combinations by integer bootstrapping method. The ionospheric delay variations between two consecutive epochs are estimated using the carrier phase data of the previous epochs and used for compensating time-differenced linear combinations that contain residual ionospheric variations. Then, in the validation step, both the criterions of threshold judgment and minimum one norm are used to validate the cycle slip candidates and finally get the correct one. The real-data tests with simulated and real cycle slips reveal that the new method can repair all cycle slips with high reliability even under ionospheric disturbance. Several failed repairs may occur with the most insensitive slip combinations ± (1, 1, 1) under bad observation conditions, but these cycle slips can be detected.