﻿ 不同系统间偏差模型对GPS/BDS/Galileo精密单点定位的影响
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 大地测量与地球动力学  2020, Vol. 40 Issue (10): 1017-1021  DOI: 10.14075/j.jgg.2020.10.005

### 引用本文

QI Wenlong, CHAI Hongzhou, YIN Xiao, et al. The Influence of Different ISB Models on GPS/BDS/Galileo Precise Point Positioning[J]. Journal of Geodesy and Geodynamics, 2020, 40(10): 1017-1021.

### Foundation support

National Natural Science Foundation of China, No.41574010, 41604013; Open Fund of Guangxi Key Laboratory of Spatial Information and Geomatics, No.19-050-11-05.

### About the first author

QI Wenlong, postgraduate, majors in multi-GNSS undifferential and uncombined precise point positioning, E-mail: 13653824137@163.com.

### 文章历史

1. 信息工程大学地理空间信息学院，郑州市科学大道62号，450001

1 非组合精密单点定位及参数处理策略 1.1 GPS/BDS/Galileo非组合精密单点定位模型

 $\left\{ \begin{array}{l} P_{1,r}^{{\rm G},j} = \rho _r^{{\rm G},j} + c\delta \tilde t_r^{\rm G} - c\tilde \delta {t^{{\rm G},j}} + M_r^{{\rm G},j}{T_{{\rm trop}}} + \tilde I_{1,r}^{{\rm G},j} + \varepsilon (P_{1,r}^{{\rm G},j})\\ P_{2,r}^{{\rm G},j} = \rho _r^{{\rm G},j} + c\tilde \delta t_r^{\rm G} - c\tilde \delta {t^{{\rm G},j}} + M_r^{{\rm G},j}{T_{{\rm trop}}} + {\gamma _G}\tilde I_{1,r}^{{\rm G},j} + \varepsilon (P_{,r}^{{\rm G},j})\\ L_{1,r}^{{\rm G},j} = \rho _r^{{\rm G},j} + c\tilde \delta t_r^{\rm G} - c\tilde \delta {t^{{\rm G},j}} + M_r^{{\rm G},j}{T_{{\rm trop}}} - \tilde I_{1,r}^{{\rm G},j} + \lambda _1^{\rm G}\tilde N_1^{\rm G} + \varepsilon (L_{1,r}^{{\rm G},j})\\ L_{2,r}^{{\rm G},j} = \rho _r^{{\rm G},j} + c\tilde \delta t_r^{\rm G} - c\tilde \delta {t^{{\rm G},j}} + M_r^{{\rm G},j}{T_{{\rm trop}}} - {\gamma _G}\tilde I_{1,r}^{{\rm G},j} + \lambda _2^{\rm G}\tilde N_2^{\rm G} + \varepsilon (L_{2,r}^{{\rm G},j})\\ P_{1,r}^{{\rm C},j} = \rho _r^{{\rm C},j} + c\tilde \delta t_r^{\rm G} + {\rm ISB}_r^{\rm C} - c\tilde \delta {t^{{\rm C},j}} + M_r^{{\rm C},j}{T_{{\rm trop}}} + \tilde I_{1,r}^{{\rm C},j} + \varepsilon (P_{1,r}^{{\rm C},j})\\ P_{2,r}^{{\rm C},j} = \rho _r^{{\rm C},j} + c\tilde \delta t_r^{\rm G} + {\rm ISB}_r^{\rm C} - c\tilde \delta {t^{{\rm C},j}} + M_r^{{\rm C},j}{T_{{\rm trop}}} + {\gamma _C}\tilde I_{1,r}^{{\rm C},j} + \varepsilon (P_{2,r}^{{\rm C},j})\\ L_{1,r}^{{\rm C},j} = \rho _r^{{\rm C},j} + c\tilde \delta t_r^{\rm G} + {\rm ISB}_r^{\rm C} - c\tilde \delta {t^{{\rm C},j}} + M_r^{{\rm C},j}{T_{{\rm trop}}} - \tilde I_{1,r}^{{\rm C},j} + \lambda _1^{\rm C}\tilde N_1^{\rm C} + \varepsilon (L_{1,r}^{{\rm C},j})\\ L_{2,r}^{{\rm C},j} = \rho _r^{{\rm C},j} + c\tilde \delta t_r^{\rm G} + {\rm ISB}_r^{\rm C} - c\tilde \delta {t^{{\rm C},j}} + M_r^{{\rm C},j}{T_{{\rm trop}}} - {\gamma _C}\tilde I_{1,r}^{{\rm C},j} + \lambda _2^{\rm C}\tilde N_2^{\rm C} + \varepsilon (L_{2,r}^{{\rm C},j})\\ P_{1,r}^{{\rm E},j} = \rho _r^{{\rm E},j} + c\tilde \delta t_r^{\rm G} + {\rm ISB}_r^{\rm E} - c\tilde \delta {t^{{\rm E},j}} + T_{{\rm trop}}^{{\rm E},j} + \tilde I_{1,r}^{{\rm E},j} + \varepsilon (P_{1,r}^{{\rm E},j})\\ P_{2,r}^{{\rm E},j} = \rho _r^{{\rm E},j} + c\tilde \delta t_r^{\rm G} + {\rm ISB}_r^{\rm E} - c\tilde \delta {t^{{\rm E},j}} + M_r^{{\rm E},j}{T_{{\rm trop}}} + {\gamma _C}\tilde I_{1,r}^{{\rm E},j} + \varepsilon (P_{2,r}^{{\rm E},j})\\ L_{1,r}^{{\rm E},j} = \rho _r^{{\rm E},j} + c\tilde \delta t_r^{\rm G} + {\rm ISB}_r^{\rm E} - c\tilde \delta {t^{{\rm E},j}} + M_r^{{\rm E},j}{T_{{\rm trop}}} - \tilde I_{1,r}^{{\rm E},j} + \lambda _1^{\rm E}\tilde N_1^{\rm E} + \varepsilon (L_{1,r}^{{\rm E},j})\\ L_{2,r}^{{\rm E},j} = \rho _r^{{\rm E},j} + c\tilde \delta t_r^{\rm G} + {\rm ISB}_r^{\rm E} - c\tilde \delta {t^{{\rm E},j}} + M_r^{{\rm E},j}{T_{{\rm trop}}} - {\gamma _E}\tilde I_{1,r}^{{\rm E},j} + \lambda _2^{\rm E}\tilde N_2^{\rm E} + \varepsilon (L_{2,r}^{{\rm E},j}) \end{array} \right.$ (1)

 $\left\{ \begin{array}{l} \tilde \delta t_r^S = \delta t_r^S + d_{{\rm IF},r}^s\\ \tilde \delta {t^{S,j}} = \delta {t^{S,j}} + d_{{\rm IF}}^{S,j}\\ {\rm ISB}_r^S = {\rm d}t_r^S - {\rm d}t_r^{\rm G} + d_{{\rm IF}}^S - d_{{\rm IF}}^{\rm G}\\ {\gamma _i}\tilde I_{i,r}^{S,j} = {\gamma _i}I_{i,r}^{S,j} + d_{{\rm IF}}^{s,j} - d_i^{s,j} - \\ \;\;\;\;(d_{{\rm IF},r}^s - d_{i,r}^s)\\ \lambda _i^s\tilde N_i^S = \lambda _i^sN_{i,r}^{s,j} + 2(d_{{\rm IF}}^{s,j} - d_{{\rm IF},r}^s) + \\ \;\;\;\;\;(d_{i,r}^s - d_i^{s,j}) + (b_{i,r}^s - b_j^{s,j}) \end{array} \right.$ (2)

 $\left\{ \begin{array}{l} \mathit{\boldsymbol{X}} = [x,y,z,{\rm MT},c{\rm d}{t_r},({\rm ISB}_r^S),(\tilde I_{r,1}^{S,j}),\\ \;(\tilde N_{r,1}^{S,j}),(\tilde N_{r,2}^{S,j})]\\ ({\rm ISB}_r^S) = [{\rm ISB}_r^{\rm E},{\rm ISB}_r^{\rm C}]\\ (\tilde I_{r,1}^{S,j}) = [\tilde I_{r,1}^{{\rm G},1} \cdots \tilde I_{r,1}^{{\rm G},{N_{\rm G}}},\tilde I_{r,1}^{{\rm C},1} \cdots \tilde I_{r,1}^{{\rm C},{N_{\rm C}}},\\ \;\;\tilde I_{r,1}^{{\rm E},1} \cdots \tilde I_{r,1}^{{\rm E},{N_{\rm E}}}]\\ (\tilde N_{r,1}^{S,j}) = [\tilde N_{r,1}^{{\rm G},1} \cdots \tilde N_{r,1}^{{\rm G},{N_{\rm G}}},\tilde N_{r,1}^{{\rm C},1} \cdots \tilde N_{r,1}^{{\rm C},{N_{\rm C}}},\\ \;\;\;\tilde N_{r,1}^{1,{N_{\rm E}}} \cdots \tilde N_{r,1}^{{\rm E},{N_{\rm E}}}] \end{array} \right.$ (3)

1.2 ISB模型处理策略

1) 将ISB作为常量模型时可不考虑ISB随时间变化的部分，即σK2=0(记为PPP-CV模型)，具体表达示为：

 ${\rm{ISB}}_r^{\rm{S}}K{\rm{ = ISB}}_r^{\rm{S}}K - 1\;\sigma _K^2 = 0$ (4)

2) 将ISB作为随机游走模型时，传递上一历元Kalman滤波解ISBrS(K－1)，并考虑ISB随时间变化的部分ωK，该部分服从高斯正态分布。本文将σ2设置为0.01 m2(记为PPP-RW模型)，具体表达示为：

 ${\rm{ISB}}_r^{\rm{S}}(K){\rm{ = ISB}}_r^{\rm{S}}(K - 1) + {\omega _K},{\omega _k} \sim N(0,{\sigma ^2})$ (5)

3) 将ISB作为白噪声模型进行处理时，认为相邻历元间ISB相互独立，在进行Kalman滤波时对ISB过程噪声赋予较大方差。本文将σ2设置为109 m2(记为PPP-WN模型)，具体表达示为：

 ${\rm{ISB}}_r^S \sim N(0,{\sigma ^2})$ (6)
2 数据处理流程及参数处理策略

 图 1 数据处理流程 Fig. 1 Flow chart of data processing

3 实验分析 3.1 不同模型ISB特性分析

 图 2 HKWS测站卫星可见数与PDOP值 Fig. 2 Number of visible satellites and PDOP of HKWS station

 图 3 3种ISB模型静态PPP误差 Fig. 3 Static PPP errors of three different ISB models

 图 4 3种ISB模型日跳变量 Fig. 4 Daily variation of three different ISB models
3.2 静态实验分析

 图 5 各测站静态收敛时间 Fig. 5 Static convergence time of each stations

3.3 仿动态实验分析

 图 6 各测站仿动态PPP收敛时间 Fig. 6 Simulated dynamic PPP convergence time of each stations

 图 7 HKWS仿动态定位精度 Fig. 7 Simulated dynamic positioning accuracy of HKWS station

4 结语

1) 相比于G/B ISB模型，G/E ISB模型的日跳变量变化较小，表明GPS与Galileo系统的ISB模型更加稳定。

2) 在收敛时间方面，PPP-RW模型和PPP-WN模型的收敛时间相当，总体上优于PPP-CV模型，在静态模式下可提升15.4%，在仿动态模式下可提升29.4%。

3) 在定位精度方面，PPP-RW模型和PPP-WN模型的定位精度与静态模式基本一致，但均优于PPP-CV模型，EU方向的定位精度分别提升约77.7%和32.2%。在仿动态条件下，相比于PPP-CV模型，PPP-RW模型和PPP-WN模型在EU方向提升约66%和43.5%。在静态模式和仿动态模式下，3种ISB模型在N方向的定位精度相当。

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The Influence of Different ISB Models on GPS/BDS/Galileo Precise Point Positioning
QI Wenlong     CHAI Hongzhou     YIN Xiao     DU Zhenqiang     SHI Mingchen
1. School of Surveying and Mapping, Information Engineering University, 62 Kexue Road, Zhengzhou 450001, China
Abstract: Based on the dual frequency uncombined PPP model, ISB parameters are processed by constant, white noise and random walk models respectively. Static and simulated dynamic experiments are carried out by using 10 days data of 7 MGEX stations to analyze convergence time and positioning accuracy of 3 models. The results show that in terms of convergence time, the effect of the random walk and white noise models are the same, both of which are superior to the constant model; static and simulated dynamic methods increase by 15.4% and 29.4% respectively. In terms of positioning accuracy, the effect of the random walk model and white noise method are equivalent. Compared with constant method, the accuracy of E and U direction improve most obviously, increasing by about 77.7% and 32.2% in static state, and by about 66% and 43.5% in simulated dynamic positioning.
Key words: inter-system bias; uncombined precise point positioning; white noise; random walk; static; simulated dynamic