Application of Helmert variance component estimation in GPS/GLONASS/BDS/Galileo combined precise point positioning weight determination
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摘要: 多星座组合定位可以提升导航定位性能，但不同星座观测量组合时需要考虑合适的随机模型. 传统方法是根据经验直接设定各系统的等价权重，但会导致随机模型确定不精确，从而影响组合系统的性能提升. 将Helmert方差分量估计方法应用于GPS/GLONASS/BDS/Galileo组合精密单点定位(PPP)中，以自适应确定各系统间权比. 采用国际GNSS服务(IGS) MGEX (Multi-GNSS Experiment)观测网的10个测站一周的观测数据进行静态和仿动态试验. 结果表明：采用Helmert方差分量估计定权方法可显著提高GPS/GLONASS/BDS/Galileo组合 PPP的收敛速度，与等权定权方案比较，静态模式下平均提高52%，仿动态模式下平均提高64%. 因定位精度主要由载波相位观测值精度和误差修正水平决定，在静态和仿动态测试中Helmert方差分量估计方法对定位精度没有明显改善.
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关键词:
- 精密单点定位(PPP) /
- Helmert方差分量估计 /
- 定权 /
- 精度 /
- 收敛速度
Abstract: Multi-constellation combined positioning can improve the performance of navigation and positioning, but a suitable stochastic model needs to be considered when combining observations from different constellations. The traditional method is to directly set the equivalent weight of each system based on experience, which will lead to inaccurate determination of the stochastic model, and thus affect the performance improvement of the combined system. In this paper, Helmert variance component estimation method is applied to GPS/GLONASS/BDS/Galileo combined precise point positioning to adaptively determine the weight ratio between systems. The static and pseudo-dynamic tests were carried out using the daily observation dataset collected at 10 stations in the global International GNSS Service (IGS) Multi-GNSS experiment (MGEX) observation network over one week of February 8 to February 14, 2021. The results show that the Helmert variance component estimation weighting method can significantly improve the convergence speed of GPS/GLONASS/BDS/Galileo combined precise point positioning (PPP), with an average increase of 52% in static mode and 64% in pseudo-dynamic mode. Because the positioning accuracy is mainly determined by the carrier phase observation accuracy and error correction level, the Helmert variance component estimation method has no obvious improvement on positioning accuracy in static and pseudo-dynamic tests. -
表 1 多星座组合精密单点定位数据处理策略
项目 处理策略 卫星系统及信号 GPS:L1/L2 GLONASS:G1/G2
BDS:B1/B2b Galileo:El/E5a观测值组合类型 无电离层组合 截至高度角/° 7 采样间隔/s 30 卫星轨道、钟差 GFZ 精密产品 对流层干分量 Saastmoinen模型+GMF投影函数 接收机/卫星天线相位中心
偏差及其变化IGS绝对天线模型(igs14.atx) 其余误差 模型改正 接收机坐标 常数(静态)，白噪声(动态) 对流层天顶湿分量 随机游走 接收机钟差 白噪声 模糊度 常数、浮点解 
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表 2 静态模式下所有站点两种定权方案的定位误差和收敛时间对比
测站 定权方案 E/m N/m U/m 3D/m 收敛时间/min SOD3 等权 0.002 0.002 0.014 0.015 27.786 Helmert方差分量估计 0.001 0.002 0.016 0.016 11.929 FFMJ 等权 0.003 0.003 0.060 0.061 32.857 Helmert方差分量估计 0.002 0.002 0.048 0.048 7.429 MET3 等权 0.002 0.003 0.020 0.021 34.286 Helmert方差分量估计 0.003 0.003 0.025 0.025 13.071 RGDG 等权 0.004 0.002 0.025 0.026 10.929 Helmert方差分量估计 0.004 0.003 0.032 0.032 10.071 DAV1 等权 0.001 0.002 0.076 0.076 10.357 Helmert方差分量估计 0.001 0.001 0.073 0.073 7.143 UNB3 等权 0.003 0.001 0.007 0.009 16.857 Helmert方差分量估计 0.004 0.002 0.004 0.007 19.071 POL2 等权 0.003 0.001 0.017 0.017 29.286 Helmert方差分量估计 0.002 0.001 0.025 0.025 8.286 YEL2 等权 0.009 0.007 0.037 0.040 14.000 Helmert方差分量估计 0.004 0.005 0.031 0.032 5.429 SUTM 等权 0.005 0.004 0.006 0.009 36.500 Helmert方差分量估计 0.005 0.005 0.010 0.014 18.000 SEYG 等权 0.005 0.005 0.014 0.016 19.071 Helmert方差分量估计 0.002 0.004 0.018 0.019 10.714
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表 3 静态仿动态模式下所有站点两种定权方案的定位误差和收敛时间对比
测站 定权方案 E/m N/m U/m 3D/m 收敛时间/min SOD3 等权 0.024 0.031 0.054 0.069 28.643 Helmert方差分量估计 0.021 0.018 0.047 0.055 8.214 FFMJ 等权 0.026 0.018 0.072 0.079 36.143 Helmert方差分量估计 0.020 0.016 0.061 0.066 4.357 MET3 等权 0.027 0.018 0.036 0.049 31.643 Helmert方差分量估计 0.023 0.020 0.038 0.049 10.071 RGDG 等权 0.018 0.018 0.052 0.058 9.571 Helmert方差分量估计 0.021 0.020 0.054 0.061 5.929 DAV1 等权 0.028 0.016 0.087 0.095 12.571 Helmert方差分量估计 0.022 0.018 0.084 0.091 6.571 UNB3 等权 0.019 0.014 0.028 0.037 14.714 Helmert方差分量估计 0.019 0.017 0.034 0.042 8.000 POL2 等权 0.025 0.020 0.048 0.058 29.571 Helmert方差分量估计 0.015 0.020 0.060 0.065 11.143 YEL2 等权 0.063 0.040 0.112 0.136 13.214 Helmert方差分量估计 0.039 0.032 0.078 0.093 3.286 SUTM 等权 0.037 0.030 0.075 0.090 30.071 Helmert方差分量估计 0.031 0.025 0.074 0.085 16.571 SEYG 等权 0.034 0.015 0.045 0.059 13.929 Helmert方差分量估计 0.021 0.014 0.043 0.050 6.143
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