﻿ 多频BDS-3/Galileo/GPS长基线相对定位性能分析
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 大地测量与地球动力学  2023, Vol. 43 Issue (5): 452-458, 550  DOI: 10.14075/j.jgg.2023.05.003

### 引用本文

LÜ Zhen, WANG Zhenjie, LIU Jinping, et al. Analysis on the Performance of Multi-Frequency BDS-3/Galileo/GPS Long-Baseline Relative Positioning[J]. Journal of Geodesy and Geodynamics, 2023, 43(5): 452-458, 550.

### Foundation support

Sinopec Science and Technology Project, No. JP21004.

### 第一作者简介

LÜ Zhen, postgraduate, major in GNSS data processing, E-mail: 17864293627@163.com.

### 文章历史

1. 中国石油大学(华东)海洋与空间信息学院，青岛市长江西路66号，266580;
2. 中石化石油工程地球物理有限公司胜利分公司，山东省东营市镇前街173号，257100;
3. 青岛北斗陆海科技有限公司，青岛市江山南路480号，266555

1 多频GNSS观测模型

 $\begin{gathered} \nabla \Delta P_{\left(i_1, i_2, \cdots, i_k\right)}=\nabla \Delta \rho+\nabla \Delta T+\beta_{\left(i_1, i_2, \cdots, i_k\right)} \nabla \Delta I_1+ \\ \theta_{\left(i_1, i_2, \cdots, i_k\right)} \nabla \Delta I_2+\varepsilon_{\nabla \Delta P\left(i_1, i_2, \cdots, i_k\right)} \end{gathered}$ (1)
 $\begin{gathered} \nabla \Delta \varPhi_{\left(i_1, i_2, \cdots, i_k\right)}=\nabla \Delta \rho+\nabla \Delta T-\beta_{\left(i_1, i_2, \cdots, i_k\right)} \nabla \Delta I_1- \\ \theta_{\left(i_1, i_2, \cdots, i_k\right)} \nabla \Delta I_2- \\ \lambda_{\left(i_1, i_2, \cdots, i_k\right)} \nabla \Delta N_{\left(i_1, i_2, \cdots, i_k\right)}+\varepsilon_{\nabla \Delta \varPhi\left(i_1, i_2, \cdots, i_k\right)} \end{gathered}$ (2)

 $\sigma_{\varepsilon \nabla \Delta P\left(i_1, i_2, \cdots, i_k\right)}^2=\eta_{\left(i_1, i_2, \cdots, i_k\right)}^2 \sigma_{\varepsilon \nabla \Delta P}^2$ (10)
 $\sigma_{\varepsilon \nabla \Delta \varPhi\left(i_1, i_2, \cdots, i_k\right)}^2=\eta_{\left(i_1, i_2, \cdots, i_k\right)}^2 \sigma_{\varepsilon \nabla \Delta \varPhi}^2$ (11)

3 单系统及多系统组合相对定位模型

 $\nabla \Delta N_{\varPhi_1}=\left[\frac{\nabla \Delta P-\nabla \Delta \varPhi_1}{\lambda_{\varPhi_1}}\right]_{\mathrm{round}}$ (14)

 \left[\begin{array}{c} \nabla \Delta \widetilde{\varPhi}_2^{\mathrm{C}} \\ \nabla \Delta \widetilde{\varPhi}_2^{\mathrm{E}} \\ \nabla \Delta \widetilde{\varPhi}_{(1, -1)}^{\mathrm{G}} \end{array}\right]=\left[\begin{array}{c} \nabla \Delta \varPhi_2^{\mathrm{C}}+\lambda_{\varPhi_2}^{\mathrm{C}} \nabla \Delta N_{\varPhi_2}^{\mathrm{C}} \\ \nabla \Delta \varPhi_2^{\mathrm{E}}+\lambda_{\varPhi_2}^{\mathrm{E}} \nabla \Delta N_{\varPhi_2}^{\mathrm{E}} \\ \nabla \Delta \varPhi_{(1, -1)}^{\mathrm{G}}+\lambda_{\varPhi_{(1, -1)}^{\mathrm{G}}} \nabla \Delta N_{\varPhi_{(1, -1)}^{\mathrm{G}}}^{\mathrm{G}} \end{array}\right]=\\ \begin{aligned} & {\left[\begin{array}{cccc} -\nabla \Delta l-\nabla \Delta m & -\nabla \Delta n & -\beta_{\varPhi_2}^{\mathrm{C}} \\ -\nabla \Delta l-\nabla \Delta m & -\nabla \Delta n & -\beta_{\varPhi_2}^{\mathrm{E}} \\ -\nabla \Delta l-\nabla \Delta m & -\nabla \Delta n & -\beta_{\varPhi_{(1, -1)}}^{\mathrm{G}} \end{array}\right]\left[\begin{array}{c} \delta X \\ \delta Y \\ \delta Z \\ \nabla \Delta \iota^{\mathrm{C}} \\ \nabla \Delta \iota^{\mathrm{E}} \\ \nabla \Delta \iota^{\mathrm{G}} \end{array}\right]} \\ & \end{aligned} (22)

4 实验分析

 图 1 基线1卫星可见数与PDOP值 Fig. 1 The number of visible satellites and PDOP of baseline 1

 图 2 基线2卫星可见数与PDOP值 Fig. 2 The number of visible satellites and PDOP of baseline 2

 图 3 基线1定位结果偏差 Fig. 3 The positioning errors of baseline 1

 图 4 基线2定位结果偏差 Fig. 4 The positioning errors of baseline 2

 图 5 基线1单天定位结果均方根误差 Fig. 5 The RMSE of single day positioning results of baseline 1

 图 6 基线2单天定位结果均方根误差 Fig. 6 The RMSE of single day positioning results of baseline 2
5 结语

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Analysis on the Performance of Multi-Frequency BDS-3/Galileo/GPS Long-Baseline Relative Positioning
LÜ Zhen1     WANG Zhenjie1     LIU Jinping2     WANG Hongqiang2     ZHOU Hao3
1. College of Oceanography and Space Informatics, China University of Petroleum, 66 West-Changjiang Road, Qingdao 266580, China;
2. Shengli Branch of SINOPEC Geophysical Co Ltd, 173 Zhenqian Road, Dongying 257100, China;
3. Qingdao Beidou Land-Sea Technology Co Ltd, 480 South-Jiangshan Road, Qingdao 266555, China
Abstract: To take full advantage of BDS-3 and Galileo multi-frequency signals on positioning, we make a proper selection of BDS-3 and Galileo four-frequency wide-lane combinations, and construct multi-frequency positioning models which are suitable for BDS-3 single-system, Galileo single-system, BDS-3/Galileo dual-system as well as BDS-3/Galileo/GPS triple-system, based on the proper combinations. We compare and analyze the multi-frequency long baseline data, positioning accuracy and stability of four positioning models. The results show that when the long-baseline is over 500 km, the positioning accuracy of the BDS-3 single-system is better than that of the Galileo single-system. The positioning accuracy of the BDS-3/Galileo dual-system can reach the decimeter level in both the horizontal and vertical directions, which is more than 10% and 25% higher than that of the BDS-3 single-system, and the stability is also significantly improved. Compared with the dual-system, the positioning accuracy of the BDS-3/Galileo/GPS triple-system is improved by about 10%. The relative positioning accuracy of the dual-system and the triple-system reaches 1×10-9 m, which can meet long-baseline precise positioning requirements. The increase of satellite systems not only increases the number of visible satellites, but also enhances the geometry of the satellites, which improves the positioning accuracy and stability effectively.
Key words: BDS-3; Galileo; multi-frequency; long-baseline; combination positioning