Two-Step Algorithm for Real-Time Cycle Slip Detection in Single-Frequency GNSS

Mireia Carvajal Librado*, Kwan-Dong Park

Cycle slips, abrupt discontinuities in Global Navigation Satellite System (GNSS) carrier-phase observations, can severely degrade the accuracy and reliability of high-precision positioning techniques. For single-frequency receivers, the detection of such slips remains especially challenging due to the absence of redundant frequency combinations commonly used in dual-frequency systems. This study introduces a lightweight, real-time cycle slip detection algorithm tailored for single-frequency GNSS receivers. The method operates without position solutions, aiding data, or receiver-dependent flags, making it suitable for embedded or low-cost platforms. The approach uses a two-step logic: the first stage flags potential slips using the first-order time difference of the code-minus-carrier observable, while the second stage confirms detections via the second-order time difference of the carrier-phase observable. To ensure robustness under varying signal conditions, elevation-dependent thresholds are implemented using empirical residual modeling. The algorithm was validated in static open-sky, forested, and low-speed dynamic scenarios using GPS and Galileo data. It achieved over 98% detection accuracy for slips exceeding 10 cycles in artificial injection tests and showed strong correlation (87.93%) with receiver-provided Loss of Lock Indicators (LLI). No false positives were recorded during controlled testing. The algorithm demonstrated reliable performance in real-world degraded environments, offering a practical solution for real-time cycle slip detection in single-frequency applications where robustness, efficiency, and independence from external data are essential.

Keywords: cycle slip detection, GNSS, single-frequency, real-time algorithm