A Partial Cycle-Slip Repair Method for BDS-3 Ultra-multi-frequency Observations

BDS-3 provides signals on six frequencies nowadays. In this contribution, five groups of geometry-free phase combinations and one group of geometry-free pseudo range phase combinations are combined to detect BDS-3 ultra-multi-frequency cycle slips. Considering the ill-conditioned problem of cycle-slip estimation equations, a condition-number principle for optimizing coefficient combinations is presented. Combined with the condition-number principle, final coefficient combinations with long combination wavelength, small ionospheric delay amplification factor and small standard deviation are determined, which consider both cycle-slip detection and repair performance. Nevertheless, it often causes a failed cycle-slip repair due to the poor accuracy of float estimates on some frequencies. Therefore, a partial cycle slip repair method based on the LAMBDA algorithm is presented. Firstly, the LAMBDA algorithm with a threshold of 3.0 for the ratio test is performed. If the ratio test fails, the variances of all cycle-slip estimates are sorted from the largest to smallest, then the cycle-slip float estimates corresponding to the maximum variance and its variance are removed and the LAMBDA algorithm is performed again. Subsequently, the above steps are repeated until the ratio test passes. Noted that the number of remaining frequencies must be larger than 2, otherwise, stop the algorithm. The ultra-multi-frequency observations provide more iterative redundancy, making the partial cycle-slip repair method more reasonable. The algorithm is verified by BDS-3 observations. The statistical results show that the averaged success rates of the rounding method, LAMBDA method and our method are 78.37%, 88.65% and 98.70%. The average improvements of our method are 20.33% and 10.38% respectively.