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

LIU Guolin; HUANG Guanwen; GAO Yang; JING Ce; LIN Maijin

doi:10.13203/j.whugis20260047

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

CPGNSS 25th Anniversary Column | 更新时间：2026-11-05

- GNSS RTK Bridge Deformation Monitoring Algorithm Considering Relative Gradient in Regional Tropospheric Anomalies
- Geomatics and Information Science of Wuhan University Vol. 51, Issue 7, Pages: 1324-1335(2026)
- 作者机构：
  
  1.长安大学地质工程与测绘学院，陕西西安，710054
  2.卡尔加里大学舒利克工程学院，阿尔伯塔卡尔加里，T2N 1N4
  3.智能北斗陕西省高校工程研究中心，陕西西安，710054
- 作者简介：
- 基金信息：
- DOI：10.13203/j.whugis20260047
  CLC： P228
- Received：24 April 2026，
  
  Published：05 July 2026
- 稿件说明：
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刘国林,黄观文,高扬，等.区域对流层异常下顾及相对梯度的GNSS RTK桥梁变形监测算法[J].武汉大学学报（信息科学版）,2026,51(7):1324-1335.

LIU Guolin,HUANG Guanwen,GAO Yang,et al.GNSS RTK Bridge Deformation Monitoring Algorithm Considering Relative Gradient in Regional Tropospheric Anomalies[J].Geomatics and Information Science of Wuhan University,2026,51(7):1324-1335.
刘国林,黄观文,高扬，等.区域对流层异常下顾及相对梯度的GNSS RTK桥梁变形监测算法[J].武汉大学学报（信息科学版）,2026,51(7):1324-1335. DOI：10.13203/j.whugis20260047

LIU Guolin,HUANG Guanwen,GAO Yang,et al.GNSS RTK Bridge Deformation Monitoring Algorithm Considering Relative Gradient in Regional Tropospheric Anomalies[J].Geomatics and Information Science of Wuhan University,2026,51(7):1324-1335. DOI：10.13203/j.whugis20260047

摘要

在全球导航卫星系统（global navigation satellite system

GNSS）桥梁监测中，实时动态定位（real time kinematic

RTK）技术因高精度与实时快速等优势而被广泛应用。在暴雨等区域对流层异常（regional tropospheric anomaly

RTA）条件下，针对山区大高差环境下融合气象估计（fusion weather estimation

FWE）方法存在水平延迟差异显著、差分残差较大的问题，提出一种面向RTA的顾及相对梯度的GNSS RTK监测方法。利用数值气象预报与射线追踪技术反演高精度三维延迟场，通过引入相对对流层延迟梯度参数增强对方向性残差的建模能力，并采用卡尔曼滤波实现坐标、模糊度与对流层参数的联合估计。实测暴雨数据验证表明，在RTA时段，相比于GPT3模型与FWE方法，所提方法使北斗卫星导航系统（BeiDou navigation satellite system

BDS）RTK垂向精度分别提升约19.8%与8.3%，北向精度平均提升约8%。残差分析结果显示，所提方法的圆度指标显著提高，残差点云形态由椭圆向近圆转变，BDS/GPS双系统卫星总圆度提升了14.9%。所提方法有效削弱了对流层的方位向残差，显著提升了RTA条件下桥梁变形监测的鲁棒性与工程适用性。

Abstract

Objectives

Real-time kinematic (RTK) positioning is a prevalent method for bridge health monitoring due to its high accuracy and automation. As demonstrated in the previous research

a fusion weather estimation (FWE) method is developed to mitigate tropospheric delays in mountainous areas. However

it is observed that the performance of FWE method deteriorates in the presence of regional tropospheric anomaly (RTA) conditions

such as heavy rainfall. In RTA scenarios

significant horizontal variations in tropospheric delay introduce directional residuals even in short-baseline measurements

leading to reduced vertical accuracy and unstable ambiguity resolution. A key objective here 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. First

a 3-D

time-varying tropospheric delay field is constructed using NWP and ray tracing to enhance un-difference delay corrections. Second

relative tropospheric gradient parameters are incorporated into the double-difference observation model to explicitly account for horizontal delay non-isotropy. Finally

an extended Kalman filter is developed to jointly estimate coordinates

integer ambiguities and tropospheric parameters

including these gradients

using constraint strategy to balance model stability and sensitivity to atmospheric anomalies.

Results

The efficacy of the proposed method is demonstrated through field validation during a heavy rainfall event. Compared with both the conventional GPT3 model and FWE method

the proposed method improves vertical positioning accuracy for BDS by approximately 19.8% and 8.3%

respectively. The accuracy in north direction is also improved by an average of about 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

and the total circularity for the combined BDS+GPS system increases by approximately 14.9%

directly indicating a reduction in azimuthally dominant residuals.

Conclusions

The proposed 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 isotropy of residuals significantly improves the robustness and reliability of GNSS-based bridge displacement monitoring under complex meteorological conditions

offering strong potential for engineering applications.

关键词

Keywords

references

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