﻿ 一种差分码偏差估计的简化模型及其评估分析
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 大地测量与地球动力学  2022, Vol. 42 Issue (8): 840-845  DOI: 10.14075/j.jgg.2022.08.013

### 引用本文

WANG Qisheng. A Simplified Model for DCB Estimation and Its Assessment Analysis[J]. Journal of Geodesy and Geodynamics, 2022, 42(8): 840-845.

### Foundation support

Scientific Research Foundation for Doctors of Xiangtan University, No.21QDZ55.

### 第一作者简介

WANG Qisheng, PhD, Lecturer, majors in geodetic data processing, E-mail: wangqisheng0702@163.com.

### 文章历史

1. 湘潭大学土木工程与力学学院，湖南省湘潭市北二环路，411105

1 差分码偏差估计方法 1.1 电离层TEC观测值

GPS和GLONASS的伪距和载波相位观测值可以表示为[10]

 \begin{aligned} &P_{k, j}^{i}=\rho_{0, j}^{i}+d_{\text {ion }, k, j}^{i}+d_{\text {trop }, j}^{i}+ \\ &\quad c\left(\tau^{i}-\tau_{j}\right)+d_{k}^{i}+d_{k, j}+\varepsilon_{P, k, j}^{i} \\ &L_{k, j}^{i}=\rho_{0, j}^{i}-d_{\text {ion }, k, j}^{i}+d_{\text {trop }, j}^{i}+ \\ &\quad c\left(\tau^{i}-\tau_{j}\right)-\lambda\left(b_{k, j}^{i}+N_{k, j}^{i}\right)+\varepsilon_{L, k, j}^{i} \end{aligned} (1)

 \begin{aligned} P_{4, s m}=& 40.3\left(\frac{1}{f_{1}^{2}}-\frac{1}{f_{2}^{2}}\right) \mathrm{STEC}+\\ & c \mathrm{DCB}^{i}+c \mathrm{DCB}_{j} \end{aligned} (2)

 $\begin{gathered} \mathrm{STEC}=M(z) \cdot \mathrm{VTEC}= \\ 1 / \cos \left(\arcsin \left(\frac{R}{R+H} \sin (\alpha z)\right)\right) \cdot \mathrm{VTEC} \end{gathered}$ (3)

 $\begin{gathered} P_{4, s m}=F(f) \cdot M(z) \\ \mathrm{VTEC}+{c} \mathrm{DCB}^{i}+c \mathrm{DCB}_{j} \end{gathered}$ (4)

1.2 球谐函数建模求解DCB

 $\begin{array}{l} \sum\limits_{n = 0}^{{n_{\max }}} {\sum\limits_{m = 0}^n {{{\tilde P}_{nm}}} } (\sin \beta )\left( {{a_{nm}}\cos ms + {b_{nm}}\sin ms} \right)\\ F(f) \cdot M(z) + c{\rm{DC}}{{\rm{B}}_j} + c{\rm{DC}}{{\rm{B}}^i} = {P_{4, sm}} \end{array}$ (5)

 $\boldsymbol{X}=\left(\mathrm{DCB}_{\mathrm{r}}^{\mathrm{G}}, \mathrm{DCB}^{\mathrm{G}, \mathrm{i}}, \mathrm{DCB}_{\mathrm{r}}^{\mathrm{R}}, \mathrm{DCB}^{\mathrm{R}, \mathrm{i}}, a_{n m}, b_{n m}\right)^{\mathrm{T}}$ (6)

 $\sum\limits_{j = 1}^{{N_{\rm{G}}}} {{\rm{DC}}{{\rm{B}}^{{\rm{G}}, {\rm{i}}}}} = 0, \sum\limits_{j = 1}^{{N_{\rm{R}}}} {{\rm{DC}}{{\rm{B}}^{{\rm{R}}, {\rm{i}}}}} = 0$ (7)
1.3 基于GIM建模求解DCB

 $\begin{array}{*{20}{c}} {c{\rm{DC}}{{\rm{B}}_{\rm{r}}} + c{\rm{DC}}{{\rm{B}}^{\rm{i}}} = }\\ {\frac{1}{N}\sum\limits_{k = 1}^N {\left[ {{P_{4, sm}} - {\rm{VTEC}}_{\rm{r}}^{\rm{i}} \cdot F(f) \cdot M\left( {z_{\rm{r}}^{\rm{i}}} \right)} \right]} } \end{array}$ (8)

1.4 简化模型建模求解DCB

 $\begin{array}{l} F(f) \cdot F\left( {z_{\rm{r}}^{\rm{i}}} \right) \cdot {\rm{VTE}}{{\rm{C}}_{{\rm{r}}, t}} + \\ c{\rm{DC}}{{\rm{B}}^{\rm{i}}} + c{\rm{DC}}{{\rm{B}}_{\rm{r}}} = {P_{4, sm}} \end{array}$ (9)

2 实验数据

3 结果讨论与分析 3.1 卫星DCB估计结果

 图 1 GPS卫星P1-P2 DCB估值 Fig. 1 The estimated P1-P2 DCB of GPS satellite

 图 2 GLONASS卫星P1-P2 DCB估值 Fig. 2 The estimated P1-P2 DCB of GLONASS satellite

 图 3 GPS卫星P1-P2 DCB偏差和标准差 Fig. 3 The bias and STD of GPS satellite P1-P2 DCB

 图 4 GLONASS卫星P1-P2 DCB偏差和标准差 Fig. 4 The bias and STD of GLONSSS satellite P1-P2 DCB

3.2 接收机DCB估计结果

 图 5 GPS接收机P1-P2 DCB估值 Fig. 5 The estimated P1-P2 DCB of GPS receiver

 图 6 GLONASS接收机P1-P2 DCB估值 Fig. 6 The estimated P1-P2 DCB of GLONASS receiver

 图 7 GPS接收机P1-P2 DCB平均偏差和标准差 Fig. 7 The bias and STD of GPS receiver P1-P2 DCB

 图 8 GLONASS接收机P1-P2 DCB平均偏差和标准差 Fig. 8 The bias and STD of GLONASS receiver P1-P2 DCB

4 结语

1) 对于GPS和GLONASS卫星DCB，本文方法与其他2种方法的估计结果比较接近，且GPS和GLONASS卫星DCB与CODE产品相比的平均偏差分别为-0.3~0.5 ns、-1.3~0.7 ns，标准差分别为0.05~0.20 ns、0.14~1.10 ns。

2) 对于接收机DCB，3种方法与CODE产品的平均偏差分别为-0.6~0.7 ns (GPS)和-1.5~1.5 ns (GLONASS)。

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A Simplified Model for DCB Estimation and Its Assessment Analysis
WANG Qisheng1
1. College of Civil Engineering and Mechanics, Xiangtan University, North-Erhuan Road, Xiangtan 411105, China
Abstract: We propose a simplified model for differential code bias estimation, which simplifies the VTEC of each puncture point in the direction of the station into a parametric sub-period for direct estimation. To verify the validity of the method, a comparative analysis is performed using the spherical harmonic function modeling and the GIM estimation-based method. GPS+GLONASS data from nearly 200 IGS stations in January 2016 were selected for the experiments and validated with the products provided by CODE. The results show that for GPS(GLONASS) satellite DCB, the method is relatively close to the results estimated by the other two methods, and the mean deviation and standard deviation compared with the products of CODE are -0.3-0.5 ns (GPS)、-1.3-0.7 ns(GLONASS) and 0.05-0.20 ns (GPS)、0.14-1.10 ns(GLONASS), respectively. For receiver DCB, the mean deviation of the three methods compared with the products of CODE are -0.6-0.7 ns (GPS) and -1.5-1.5 ns (GLONASS), respectively. The experimental results verified the validity of the simplified model of DCB.
Key words: DCB; GPS; GLONASS; ionospheric