Long-distance RTK positioning method with atmospheric error constraints

Real-time kinematic (RTK) positioning has become a crucial technique for real-time displacement monitoring due to its low cost and high real-time performance. However, as the demand for high-precision real-time displacement monitoring of long-distance infrastructure such as cross-sea bridges and offshore platforms increasing continuously. Conventional RTK technology suffers from reduced spatial correlation of atmospheric errors (tropospheric and ionospheric delays) during long-distance operations due to increased distances between measurement stations. This makes residual atmospheric errors difficult to fully eliminate after differential correction, severely impacting ambiguity resolution and consequently compromising positioning accuracy. To address this issue, a long-distance RTK positioning method with atmospheric error constraints is proposed: 1) Parameterize the residual tropospheric and ionospheric delays after prior model correction and differential processing, and incorporate them into the estimation model. Establish prior constraints for residual errors: construct prior variance for tropospheric residual based on differences between stations and station distances to more comprehensively characterize tropospheric residual uncertainty under long-distance conditions. Ionospheric residuals incorporate latitude-dependent prior variance to impose robust constraint on positioning parameter solutions. 2) To account for the time-varying nature of atmospheric errors, dynamic estimation of tropospheric and ionospheric parameters employs a random walk process. Given the significant variability in ionospheric activity, the random walk noise model considers baseline length and satellite elevation angle variations, ensuring the dynamic estimation better reflects real-world conditions. Experiments were conducted using data from International GNSS Service (IGS) stations and offshore platform measurements. Results demonstrate that compared to the conventional RTK method, the proposed method achieves faster convergence and reduces the time to first fix in different observation environments, enhances the ambiguity fixing rate, and achieves measurable improvements in both horizontal and vertical positioning accuracy.