﻿ GEO卫星对BDS相对定位性能的影响分析
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 大地测量与地球动力学  2021, Vol. 41 Issue (8): 795-799  DOI: 10.14075/j.jgg.2021.08.005

### 引用本文

ZHU Huizhong, ZHANG Xinyang, YANG Hu, et al. Analysis of GEO Satellites on BDS High-Precision Relative Positioning Performance[J]. Journal of Geodesy and Geodynamics, 2021, 41(8): 795-799.

### Foundation support

National Natural Science Foundation of China, No.42030109, 42074012; Liaoning Revitalization Talents Prograrn, No.XLYC2002101, XLYC2008034, XLYC2002098.

### 第一作者简介

ZHU Huizhong, PhD, associate professor, majors in GNSS high-precision positioning algorithm, E-mail: zhuhuizhong@whu.edu.cn.

### 文章历史

GEO卫星对BDS相对定位性能的影响分析

1. 辽宁工程技术大学测绘与地理科学学院，辽宁省阜新市中华路47号，123000

1 BDS基本观测模型 1.1 BDS非差观测模型

 $\begin{array}{l} {\lambda _i} \cdot \mathit{\Phi }_i^s = {{\boldsymbol{H}}^s} \cdot \delta {\boldsymbol{X}} + \rho _0^s - {\lambda _i} \cdot N_i^s - I_i^s + \\ \;\;\;\;\;\;\;\;\;\;\;{T^s} + {O^s} + {t_R} - {t^s} + \varepsilon _i^s \end{array}$ (1)
 $P_i^s = {{\boldsymbol{H}}^s} \cdot \delta {\boldsymbol{X}} + \rho _0^s + I_i^s + {T^s} + {O^s} + {t_R} - {t^s} + \varepsilon _{ic}^s$ (2)

1.2 随机模型

BDS相对定位中，多项误差对观测值的影响与高度角有关[7]。本文根据卫星高度角大小来确定观测值的权重，采用基于高度角的随机模型：

 ${\sigma ^2} = \left\{ \begin{array}{l} {a^2}, E \ge 30^\circ \\ 2{\sin ^2}E, 10^\circ < E < 30^\circ \end{array} \right.$ (3)

 $P\left( E \right) = \left\{ \begin{array}{l} 1.0, E \ge 30^\circ \\ 2\sin E, 10^\circ < E < 30^\circ \end{array} \right.$ (4)
2 BDS相对定位观测模型 2.1 由非差观测模型确定相对定位模型

 $L_{iR}^s = \rho _R^s - {\lambda _i}N_{iR}^p + {t_R} - {t^s} - I_R^s + T_R^s + \varepsilon _{iR}^s$ (5)

 $\begin{array}{l} {\rm{cor}}_{iR}^s = L_{iR}^s - \rho _R^s = - {\lambda _i}N_{iR}^s + {t_R} - \\ \;\;\;\;\;\;\;\;\;\;{t^s} - I_{iR}^s + T_R^s + \varepsilon _{iR}^s \end{array}$ (6)

 $\begin{array}{l} L_{iU}^s - {\rm{cor}}_{iR}^s = {\boldsymbol{H}}_U^s\delta {\boldsymbol{X}} + \rho _{oU}^s - \\ \;\;\;\;{\lambda _i}N_{iR}^s + t - \delta {I^s} + \delta {T^s} \end{array}$ (7)

2.2 残余误差的处理

 ${\rm{map = }}\frac{{1.001}}{{\sqrt {0.002001 + {\rm{si}}{{\rm{n}}^2}E} }}$ (8)

 $\delta {T^s} = {\rm{ma}}{{\rm{p}}^s} \cdot {\rm{RZTD}}$ (9)

3 实验与结果分析

 图 1 测站分布 Fig. 1 Distribution of the stations

3.1 静态相对定位结果分析

 图 2 可见卫星数量和PDOP值 Fig. 2 The visible satellite numbers and PDOP values

 图 3 静态基线单天解偏差 Fig. 3 The bias of single day solution of static baselines

 图 4 2 h静态基线误差对比 Fig. 4 Comparison of static baselines errors with 2 h

3.2 动态相对定位结果分析

 图 5 动态基线误差比较 Fig. 5 Comparison of dynamic baselines errors

 图 6 第1时段BDS动态相对定位偏差 Fig. 6 BDS dynamic relative positioning bias in period 1

4 结语

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Analysis of GEO Satellites on BDS High-Precision Relative Positioning Performance
ZHU Huizhong1     ZHANG Xinyang1     YANG Hu1     TANG Longjiang1     LI Jun1
1. School of Geomatics, Liaoning Technical University, 47 Zhonghua Road, Fuxin 123000, China
Abstract: The influence of GEO satellites in BDS high precision relative positioning is studied and analyzed. First, the BDS un-differential observation model is realized, the high precision relative positioning solution model of BDS is derived on this basis. Then, the whole constellation satellites and IGSO+MEO satellites combination are used to carry out in high precision relative positioning processing. Finally, the influence of GEO satellites on BDS relative positioning convergence time, positioning accuracy and PDOP values are further analyzed. The results show that the BDS GEO satellites are beneficial to increase the number of observation satellites, and significantly improve the geometry of the observation satellites and the positioning convergence speed and accuracy. Both the static and dynamic results of the whole constellation satellites of high precision relative positioning are at or better than centimeter level.
Key words: BDS; GEO satellites; long range; relative positioning; position accuracy; convergence rate