Real-Time Cycle Slip Detection in Single-Frequency GNSS Receivers Using Dual-Index Cross-Validation and Elevation-Dependent Thresholding

Cycle slips, abrupt discontinuities in carrier-phase measurements, pose a significant challenge for single-frequency GNSS receivers, particularly in real-time applications where rapid detection is critical. Unlike dual-frequency approaches, these receivers cannot rely on redundant combinations to isolate slips from other errors. This study proposes a real-time cycle slip detection algorithm for single-frequency GNSS receivers based solely on short-term differencing of pseudorange and carrier-phase observables. The method employs a two-step logic: first-order differencing of code-minus-carrier and second-order differencing of carrier phase. Both steps employ satellite elevation-dependent adaptive thresholds, enabling robust detection under diverse signal conditions. The method requires no user position, receiver-generated tracking flags, or additional sensor data. Experimental results reveal that the algorithm achieves over 98% detection accuracy for slips exceeding 10 cycles, with no false positives in artificial slip testing, and 87.93% agreement with Loss of Lock Indicators (LLI) during periods in which the receiver indicated signal instability.