Real-time cycle-slip detection and repair for BeiDou triple-frequency undifferenced observations

A new method of real-time cycle-slip detection and repair for BeiDou navigation satellite system (BDS) triple-frequency undifferenced observations is proposed. The method, which is based on code-phase and geometry-free phase combinations, composes linearly independent combination observations to uniquely determine the cycle-slip of original frequency phase observations in two independent steps. First, two extra-wide lane (EWL) code-phase combinations are utilised to determine the EWL combination cycle-slips. The sum of the carrier phase combination coefficients is zero. Second, the geometry-free phase combination with a non-zero sum of combination coefficients composes linearly independent combination observations with two code-phase combinations. Ionospheric delay variance systematic deviation is corrected with several previous carrier-phase observations without cycle-slip, which seriously affect the accuracy of the geometry-free phase combination observations. The BDS triple-frequency carrier-phase and code observations of different satellite types at 30 s sampling interval, which involve increased active ionospheric conditions in 1 day, are utilised to test the method. Results show that the proposed method can efficiently detect and accurately repair any cycle-slip combinations in real-time for different satellite types under active ionospheric conditions. No erroneous and leakage judgments are observed in the test.