Modeling Azimuthal Steel-Track Deformation to Determine the Reference Point of Wheel-Track VLBI Antenna
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摘要: 为在本地测量中更精确地测定VLBI（very long baseline interferometry）天线参考点（reference point，RP）点位，分析了水平钢轨残余形变对四轮座架式天线的影响，首次提出并推导了用以改正归心解算靶标点（target point，TP）坐标的水平钢轨残余形变模型，结合实测靶标坐标与钢轨水准数据，解释了TP坐标残差中的系统性效应，精化了TP理论坐标，显著提高了参考点测定精度。结果表明，采用水平钢轨残余形变改正模型与估算模型可分别使靶标坐标归心拟后残差中误差提高50%和65%，归心精度均可提高约30%。此外，本钢轨残余形变估算模型还可有效用于该类天线钢轨形变的监测。Abstract: To determine a more precise reference point (RP) coordinate of Very Long Baseline Interfero-metry (VLBI) antenna in a local surveying, the effects of azimuthal track deformations in four-wheels and pedestal-based radio telescopes are analyzed, and an azimuthal steel-track residual deformation correction model is firstly proposed and derived to correct the coordinates of target points (TPs), which are used to determine the RP position. Using the real measurements of TPs and the leveling data of the steel track, systematic effects in residual of TP coordinates are explained and theoretical TP coordinates are corrected so that the corresponding RP precision is significantly improved. The results show that applying azimuthal steel-track residual deformation correction and estimation models can improve the standard error of post-fit TP residuals by 50% and 65%, respectively. The RP precision can improve about 30%. Moreover, the proposed steel-track residual deformation estimation model can be well applied to monitor the azimuth steel-track deformation of four-wheels and pedestal-based antenna.
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Keywords:
- reference point /
- VLBI /
- local surrey /
- steel-track deformation correction /
- wheel-track mount
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图 4 利用3类模型拟合7个靶标所得TP拟后残差
Figure 4. Post-Residuals to Observations of 7 Targets Fitted by 3 Different IMs
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图 5 未加入钢轨残余形变改正的靶标分量残差(点)和钢轨残余形变模型所计算的改正值(线)
Figure 5. Component Residuals (Dots) Without Steel-Track Residual Deformation Correction and Corrections (Lines) Calculated by Steel-Track Residual Deformation
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图 7 钢轨不平度的反演与实测结果对比图
Figure 7. Comparison Between Inversion and Real Steel-Track Unevenness
表 1 观测靶标信息统计
Table 1 Statistics of Observed Targets
项目 第1组 第2组 靶标名称 Tc1~Tc5 Ta、Tb 靶标数目 5 2 方位定向/(°) 0, 15, 30…360 10, 70, 130…310 方位步进/(°) 15 60 俯仰定向/(°) 88 10, 20, 30…80, 88 俯仰步进/(°) - 10或8 TP观测量数目 125 108 TP分量(1σ/mm) 1.0, 1.0, 1.7 0.3, 0.3, 0.2 
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表 2 不同归心与改正算法所解算参考点点位坐标(1 σ精度)以及模型拟合优度
Table 2 RP Coordinates (1 σ Precision) and Goodness of Fit Based on the Different IMs and Corrections
模型 Δx/mm Δy/mm Δz/mm $\frac{{{\chi ^2}}}{{{\mathop{\rm dof}\nolimits} }} $ A -0.09(0.09) -0.11(0.11) 0.07(0.18) 6.9 B -0.23(0.07) 0.11(0.08) -0.08(0.15) 4.4 C 0(0.07) 0(0.07) 0(0.13) 3.5 注：表中所给值为各模型所解算参考点坐标与(63 365.95, -12 396.01, 8 695.44)mm的差值
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