Deep learning and adaptive carrier Phase–Doppler weighted fusion for GNSS cycle slip detection and repair

Abstract Cycle-slip detection and repair is a critical preprocessing step in high-precision Global Navigation Satellite System (GNSS) positioning. Under varying cycle-slip ratios, detection thresholds are difficult to determine adaptively, leading to missed detections, false alarms, and suboptimal repair. This paper proposes a deep-learning cycle-slip detection and repair method based on Satellite- and Epoch-Differenced (SDED) observations and develops an adaptive Phase-Doppler (PD) weighted fusion mechanism for kinematic observations. The SDED representation suppresses common-mode errors and highlights cycle-slip signatures. A cycle slip is detected when the prediction residual exceeds the detection threshold, and the rounded residual is used directly as the repair correction. For kinematic observations, PD residuals provide complementary physical consistency information and are adaptively fused with the deep-learning decision through a noise quality factor weighting scheme to suppress false alarms. Bayesian optimization is used to tune the model parameters, and the Transformer, CNN, and LSTM are benchmarked against the Time-Differenced Carrier Phase (TDCP) method across different frequencies, observation modes, and cycle-slip ratios. The Transformer achieves the best overall performance, with detection success rates consistently above 99% and repair success rates above 97% under static conditions, and mean repair errors below 0.11 cycles. Under kinematic conditions, the TF-PD fusion model achieves detection rates above 98.6%, repair rates above 96%, and precision and F1 scores above 94% and 96%, respectively. In real-world PPP experiments, TF-PD reduces the shipborne 3D RMSE by 11.70%, 7.12%, and 6.67% relative to polynomial fitting, PD, and TDCP, respectively, and reduces the vehicular 3D RMSE by 37.30%, 16.15%, and 9.14%, demonstrating enhanced stability and reliability of cycle-slip processing.