Enhanced BDS four-frequency cycle slip detection and repair using fuzzy clustering analysis

Cycle slip detection and repair is one of the key technologies for GNSS high-precision positioning. We introduce an enhanced methodology for detecting and repairing BDS four-frequency cycle slips, utilizing fuzzy clustering analysis. Firstly, based on fuzzy clustering analysis, the optimal combinations for the BDS four-frequency, including extra-wide lane (EWL), wide lane (WL), and narrow lane (NL), were selected. Secondly, the feasibility of this method was verified using actual static and dynamic observation data, and different types of cycle slips were simulated for further validation. Meanwhile, the proposed method was compared with the classical Turbo-Edit method through experiments. Finally, cycle slips were repaired using the least squares method. According to the experimental results, the optimal geometry-free phase combinations (−2, 2, 1, −1), (1, −1, 1, −1), (3, 2, −2, −3), and the pseudo-range phase combination (−1, 1, 1, −1), selected based on fuzzy clustering analysis, were used for cycle slip detection. The proposed method accurately detected small, large, and specific cycle slips simulated in the actual data. Compared with the Turbo-Edit method, the proposed method was able to detect specific cycle slips that Turbo-Edit could not. It is worth noting that during the repair process, the coefficients of the combined observation values are integers, preserving the integer cycle characteristic of the observation values, which allows cycle slips to be fixed directly, eliminating the need for complex searching procedures. Consequently, by enhancing the precision and reliability of the detection of BDS four-frequency cycle slips, our proposed method provides the support for the high-precision localization of BDS multi-frequency observations.