GNSS RTK Bridge Deformation Monitoring Algorithm Considering Relative Gradient in Regional Tropospheric Anomalies

Objectives: Real-Time Kinematic (RTK) positioning is a prevalent method for bridge health monitoring (BHM) due to its high accuracy and automation. As demonstrated in our previous research, a Fusion Weather Estimation (FWE) RTK method was developed to mitigate tropospheric delays in mountainous areas. However, it was observed that the performance of this method deteriorates in the presence of Regional Tropospheric Anomaly (RTA) conditions, such as heavy rainfall. During RTA, significant horizontal variations in tropospheric delay introduce directional residuals even in short-baseline measurements, leading to reduced vertical accuracy and unstable ambiguity resolution. The objective of this study is to address this limitation by developing an enhanced RTK algorithm tailored for RTA scenarios to improve the robustness and precision of structural displacement monitoring. Methods: An RTK algorithm is proposed that incorporates relative tropospheric delay gradients derived from high-resolution Numerical Weather Prediction (NWP) data. Firstly, a three-dimensional, time-varying tropospheric delay field is constructed using NWP and ray tracing to enhance un-difference delay corrections. Secondly, relative tropospheric gradient parameters are incorporated into the double-difference observation model to explicitly account for horizontal delay non-isotropy. In conclusion, an extended kalman filter has been developed which estimates coordinates, integer ambiguities and tropospheric parameters, including these gradients. This is achieved using a soft-constraint strategy to balance model stability and sensitivity to atmospheric anomalies. Results: The efficacy of the algorithm was demonstrated through field validation during a heavy rainfall event. A comparison of the proposed method with both the conventional GPT3 model and the FWE method reveals an enhancement in vertical (U) positioning accuracy of approximately 19.8% and 8.3%, respectively, for the BDS system. The accuracy of northward (N) direction has also shown an average improvement of approximately 8%. Residual analysis reveals a quantifiable mitigation of directional error: the introduced "circularity" index shows residual point clouds shifting from an "elliptical" to a "near-circular" distribution. The total circularity for the combined BDS+GPS system increased by approximately 14.9%, directly indicating a reduction in azimuthally dominant residuals. Conclusions: The proposed NWP-driven, gradient-considered RTK algorithm successfully mitigates the detrimental effects of directional tropospheric residuals during RTA events. The enhancement of both the accuracy (particularly in the vertical component) and the non-isotropy of residuals has been demonstrated to significantly improve the robustness and reliability of GNSS-based bridge displacement monitoring under complex meteorological conditions, offering strong potential for engineering applications.