大高差阵列GNSS拓扑约束解耦的形变提取模型

A Deformation Extraction Model for Large Height-Difference Array GNSS Decoupled by Topological Constraints

  • 摘要: 针对超高层建筑施工期受限空间下全球定位导航系统(Global Navigation Satellite System, GNSS)动态解算发散与参数恶性耦合的难题,笔者提出一种大高差阵列GNSS拓扑约束解耦的形变提取模型,在观测域,构建融合预测新息残差、高度角与信噪比的抗差观测模型;在状态域,通过对阵列GNSS共享残余对流层延迟参数建模,将结构先验物理信息通过增广矩阵约束滤波量测更新环节,实现误差脱耦。结果表明,多维特征定权模型能将高仰角下的畸变信号标准差自适应放大1.8至2.0倍;四天线阵列协同残余对流层延迟的标准差下降至0.179 mm/s,较单节点下降了44.06%,模糊度固定率提高了14.02%;三维形变的平面95%误差概率圆半径缩减49.88%,高程最大误差较线状约束降低37.78%,为大型复杂工程的受限空间长周期动态安全监测提供了稳定的算法引擎。

     

    Abstract: Objectives:The climbing formwork system of super-tall buildings provides an ideal carrier for deploying Global Navigation Satellite System (GNSS) sensors and has become an important monitoring object in intelligent construction and structural health monitoring. However, GNSS observations in this scenario are frequently contaminated by severe signal blockage, diffraction, and multipath interference due to reinforced concrete core walls, steel protection fences, tower cranes, lifting equipment, and the large height difference between the ground reference station and the high-rise monitoring array. In addition, the residual zenith tropospheric delay (ZTD) caused by the large height difference is strongly coupled with the vertical displacement component in the observation model, resulting in ambiguity fixing degradation and pseudo-deformation extraction. Traditional single-node RTK solutions cannot effectively suppress these errors, leading to unstable positioning performance and reduced monitoring reliability. To address these challenges, this study proposes a large height-difference array GNSS deformation extraction model based on topological constraint-assisted parameter decoupling. The objective is to suppress hidden multipath interference, mitigate the coupling between residual tropospheric delay and vertical deformation parameters, improve ambiguity fixing reliability, and achieve high-precision deformation monitoring in confined construction environments.Methods:The proposed framework consists of a multidimensional adaptive weighting model and a topology-constrained parameter decoupling model. First, to address severe multipath interference in confined construction environments, a multidimensional stochastic model is established by integrating satellite elevation angle, signal-to-noise ratio (SNR), and innovation residual information. Unlike conventional elevation-dependent weighting strategies, the proposed method dynamically adjusts the observation variance according to satellite observation quality, enabling real-time suppression of hidden multipath-contaminated observations. Second, considering that all GNSS antennas are installed on the same climbing formwork platform and experience nearly identical atmospheric conditions, a shared residual tropospheric parameter is introduced into the state vector. This strategy reduces parameter redundancy and improves model observability. Third, according to the physical topology characteristics of the climbing formwork system, rigid-body geometric constraints and relative deformation constraints are incorporated into the Extended Kalman Filter (EKF) through virtual observations. The proposed heterogeneous rigid-flexible topology model effectively constrains common-mode drift and suppresses the propagation of multipath-induced errors into deformation parameters. Finally, ambiguity resolution is performed using the LAMBDA algorithm together with quality-control indicators, including ambiguity ratio tests, fixed-satellite thresholds, and PDOP constraints, ensuring reliable ambiguity-fixed solutions under severe obstruction conditions.Results:Experimental validation was conducted using a four-antenna GNSS monitoring array deployed on the climbing formwork system of a super-tall building under construction in Tianjin, China. A two-hour dataset sampled at 1 Hz under quasi-static conditions was selected for analysis. Satellite visibility analysis showed that individual antennas experienced severe sky-view limitations and frequent satellite interruptions. By exploiting complementary observation information among multiple antennas, the proposed array configuration maintained significantly improved satellite availability and observation redundancy. Multipath analysis based on the Code-Minus-Carrier (CMC) combination revealed strong spatial heterogeneity among array nodes. Several representative satellites exhibited severe multipath contamination, with maximum absolute CMC multipath errors exceeding 14 m and RMS values reaching 6.95 m. Experimental results demonstrated that the proposed multidimensional feature-weighting model successfully identified abnormal observations and adaptively enlarged the observation standard deviation of contaminated satellites by approximately 1.8-2.0 times, thereby preventing multipath errors from propagating into the filter state domain. To evaluate the effectiveness of parameter decoupling, four positioning schemes were compared: single-node positioning, two-antenna linear constraint, three-antenna planar constraint, and the proposed four-antenna heterogeneous topology-constrained model. Results showed that the residual ZTD time-series smoothness improved significantly after introducing array topology constraints. The STD of the residual ZTD sequence decreased from 0.320 mm/s for the single-node solution to 0.179 mm/s for the proposed method, corresponding to a reduction of 44.06%. Meanwhile, the ambiguity fixing rate increased from 75.52% for the single-node solution to 89.54% for the proposed method, representing an improvement of 14.02%. These results indicate that array redundancy and topological constraints effectively weaken the coupling between vertical displacement and residual tropospheric parameters, thereby improving float-solution quality and ambiguity fixing reliability. In terms of deformation monitoring performance, the proposed method achieved significant improvements in horizontal positioning accuracy. The CEP95 radius decreased from 36.93 mm to 18.51 mm, corresponding to a reduction of 49.88%, while the 2D-RMS decreased from 18.48 mm to 10.49 mm, representing an accuracy improvement of 43.24%. For vertical deformation extraction, the proposed topology-constrained model effectively suppressed pseudo-deformation caused by residual tropospheric delay coupling. Compared with the two-antenna linear-constraint solution, the maximum vertical deformation error decreased from 12.52 mm to 7.79 mm, corresponding to a reduction of 37.78%, while the vertical RMS error decreased from 2.73 mm to 2.26 mm, corresponding to a reduction of 17.22%.Conclusions:A topology-constrained array GNSS deformation extraction model is proposed for large height-difference monitoring environments in super-tall building construction. By integrating multidimensional adaptive weighting, shared residual tropospheric delay estimation, and heterogeneous rigid-flexible topology constraints, the proposed method effectively suppresses hidden multipath interference and mitigates the strong coupling between residual ZTD and vertical deformation parameters. Experimental results from a real super-tall construction project demonstrate that the proposed approach significantly improves residual ZTD stability, ambiguity fixing reliability, and three-dimensional deformation monitoring accuracy. Compared with single-node positioning, the proposed method reduces the residual ZTD STD by 44.06%, increases the ambiguity fixing rate by 14.02%, reduces the horizontal CEP95 radius by 49.88%, and improves the horizontal 2D-RMS accuracy by 43.24%. Compared with the two-antenna linear-constraint solution, the maximum vertical deformation error is reduced by 37.78%, and the vertical RMS error is reduced by 17.22%. The proposed framework provides a reliable and physically consistent solution for GNSS-based structural health monitoring in confined construction environments and offers technical support for intelligent monitoring and digital twin applications in super-tall building construction.

     

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