﻿ 基于空间几何原理的北斗三频IF-PPP建模和验证
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 大地测量与地球动力学  2020, Vol. 40 Issue (12): 1290-1293, 1320  DOI: 10.14075/j.jgg.2020.12.016

### 引用本文

HE Maihang, SUN Fuping, XIAO Kai, et al. Model and Verification of Beidou Triple-Frequency IF-PPP Based on Space Geometric Principle[J]. Journal of Geodesy and Geodynamics, 2020, 40(12): 1290-1293, 1320.

### Foundation support

National Natural Science Foundation of China, No.41374027, 41804018, 41674027.

### About the first author

HE Maihang, postgraduate, majors in GNSS/INS integrated navigation, E-mail: hemaihang@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 北斗三频IF-PPP模型 1.1 观测模型

 $\left\{ \begin{array}{l} P_j^s = {\rho ^{\rm{s}}} + c{\rm{d}}{t_{\rm{r}}} - c{\rm{d}}{t^{\rm{s}}} + {T^{\rm{s}}} + {\gamma _j}{I^{\rm{s}}} + \\ {B_{{\rm{r}}, {P_j}}} - B_{{P_j}}^{\rm{s}} + \varepsilon _{{P_j}}^{\rm{s}}\\ L_j^{\rm{s}} = {\lambda _j}\Phi _j^{\rm{s}} = {\rho ^{\rm{s}}} + c{\rm{d}}{t_{\rm{r}}} - c{\rm{d}}{t^{\rm{s}}} + {T^{\rm{s}}} - \\ {\gamma _j}{I^{\rm{s}}} + {\lambda _j}N_j^{\rm{s}} + {B_{{\rm{r}}, {L_j}}} - B_{{L_j}}^{\rm{s}} + \varepsilon _{{L_j}}^{\rm{s}} \end{array} \right.$ (1)

 $\left\{ {\begin{array}{*{20}{l}} {P_{{\rm{IF}}}^{\rm{s}} = \alpha P_1^{\rm{s}} + \beta P_2^{\rm{s}} + \gamma P_3^{\rm{s}}}\\ {L_{{\rm{IF}}}^{\rm{s}} = \alpha L_1^{\rm{s}} + \beta L_2^{\rm{s}} + \gamma L_3^{\rm{s}}} \end{array}} \right.$ (2)

 $\alpha + \beta + \gamma = 1$ (3)

 $\alpha + 1.672\;4\beta + 1.514\;5\gamma = 1$ (4)

 图 1 消电离层系数平面及系数和为1平面 Fig. 1 Planes of ionospheric-free and coefficient sum is 1

 $\left\{ {\begin{array}{*{20}{l}} {{\sigma _{{P_{{\rm{IF}}}}}} = {\sigma _P}\;\;\;{\kern 1pt} \sqrt {{\alpha ^2} + {\beta ^2} + {\gamma ^2}} }\\ {{\sigma _{{L_{{\rm{IF}}}}}} = {\sigma _L}\sqrt {{\alpha ^2} + {\beta ^2} + {\gamma ^2}} } \end{array}} \right.$ (5)

 $\sqrt {{\alpha ^2} + {\beta ^2} + {\gamma ^2}} \to \min$ (6)

 $\frac{x}{{ - 0.1579}} = \frac{{y + 9.5915}}{{ - 0.5145}} = \frac{{z - 10.5915}}{{0.6724}}$ (7)

1.2 观测量随机模型

2 参数处理策略

3 实验分析 3.1 静态实验

3.1.1 定位精度分析

 图 2 测站位置误差统计 Fig. 2 Statistic of station position error

 图 3 CUTC站位置误差序列 Fig. 3 Position error series of CUTC station
3.1.2 收敛时间分析

 图 4 测站收敛时间 Fig. 4 Convergence time of the stations

3.2 动态实验

 图 5 跑车轨迹 Fig. 5 Track of car

 图 6 观测卫星工作状态 Fig. 6 Working condition of observed satellites

 图 7 动态PPP位置误差序列 Fig. 7 Position error series of dynamic PPP
4 结语

1) 三频PPP的定位精度和收敛速度均明显优于双频PPP。静态条件下，三频PPP的位置误差为3.75 cm，标准差为2.06 cm，平均收敛时间为109.6 min，较双频PPP分别提升22.3%、19.8%、22.1%；动态条件下，三频PPP的位置误差为15.21 cm，标准差为12.89 cm，较双频PPP分别提升42.4%、26.8%，且收敛速度也更优。

2) 频率观测粗差会严重影响双频PPP的定位精度和收敛速度，三频PPP可有效减弱单频率粗差的影响，提高定位可靠性和稳定性。

3) 对比静态和动态实验可以看出，BDS PPP的位置误差较大，收敛速度慢而导致收敛时间较长，其原因为BDS卫星以GEO/IGSO为主，卫星几何结构变化较慢，伪距观测精度低，且GEO卫星精密星历精度比MEO卫星低。

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Model and Verification of Beidou Triple-Frequency IF-PPP Based on Space Geometric Principle
HE Maihang1     SUN Fuping1     XIAO Kai1     ZHANG Lundong1     ZHU Xinhui1
1. School of Surveying and Mapping, Information Engineering University, 62 Kexue Road, Zhengzhou 450001, China
Abstract: We derive the triple-frequency ionospheric-free parameters and minimum noise line expression using the space geometric principle. We compare the positioning accuracy and convergence speed of triple-frequency and dual-frequency ionospheric-free models using data from five static observation stations and Beidou triple-frequency observation data of measured sports car. The results show that under static conditions, the position error of triple-frequency PPP is 3.75 cm, the standard deviation is 2.06 cm, and convergence time is 109.6 min, which is 22.3%, 19.8% and 22.1% higher than the performance of dual-frequency PPP, respectively. Under dynamic conditions, the position error of triple-frequency PPP is 15.21 cm and the standard deviation is 12.89 cm, which is 42.4% and 26.8% higher than the dual-frequency PPP, and the convergence speed is better than that.
Key words: Beidou satellite navigation system; triple-frequency ionospheric-free model; minimum noise line; static and dynamic PPP; positioning performance