﻿ BDS-3多频PPP模型性能分析
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 大地测量与地球动力学  2022, Vol. 42 Issue (8): 846-851  DOI: 10.14075/j.jgg.2022.08.014

### 引用本文

WU Zhiyuan, WANG Qianxin, HU Chao, et al. Performance Analysis of BDS-3 Multi-Frequency PPP Model[J]. Journal of Geodesy and Geodynamics, 2022, 42(8): 846-851.

### Foundation support

National Key Research and Development Program of China, No.2020YFA0713502.

### 第一作者简介

WU Zhiyuan, postgraduate, majors in satellite positioning and navigation location service, E-mail: 3032853051@qq.com.

### 文章历史

BDS-3多频PPP模型性能分析

1. 中国矿业大学环境与测绘学院，江苏省徐州市大学路1号，221116;
2. 安徽理工大学空间信息与测绘工程学院，安徽省淮南市泰丰大街168号，232001

1 三频PPP函数模型

 \left\{ \begin{align} & P_{\text{r}, j}^{\text{s}}=\rho _{\text{r}}^{\text{s}}+c\cdot \text{d}{{t}_{\text{r}}}-c\cdot \text{d}{{t}^{\text{s}}}+{{T}_{\text{r}}}+ \\ & \ \ \ \ {{\gamma }_{j}}\cdot I_{\text{r}, 1}^{\text{s}}+c\left( d_{\text{r}, j}^{\text{s}}-d_{j}^{\text{s}} \right)+\varepsilon _{\text{r}, {{P}_{j}}}^{\text{s}, T} \\ & L_{\text{r}, j}^{\text{s}}=\rho _{\text{r}}^{\text{s}}+c\cdot \text{d}{{t}_{\text{r}}}-c\cdot \text{d}{{t}^{\text{s}}}+{{T}_{\text{r}}}- \\ & \ \ \ \ {{\gamma }_{j}}\cdot I_{\text{r}, 1}^{\text{s}}+\lambda _{j}^{\text{s}}\left( N_{\text{r}, j}^{\text{s}}+b_{\text{r}, j}^{\text{s}}-b_{j}^{\text{s}} \right)+\xi _{\text{r}, {{L}_{j}}}^{\text{s}} \\ \end{align} \right. (1)

 $\left\{\begin{array}{l} \alpha_{m n}=\frac{f_{m}^{2}}{f_{m}^{2}-f_{n}^{2}}, \beta_{m n}=-\frac{f_{n}^{2}}{f_{m}^{2}-f_{n}^{2}} \\ \mathrm{DCB}_{P_{m} P_{n}}^{\mathrm{s}}=d_{m}^{\mathrm{s}}-d_{n}^{\mathrm{s}} \\ \mathrm{DCB}_{\mathrm{r}, P_{m} P_{n}}^{\mathrm{s}}=d_{\mathrm{r}, m}^{\mathrm{s}}-d_{\mathrm{r}, n}^{\mathrm{s}} \\ d_{\mathrm{IF}_{m n}}^{\mathrm{s}}=\alpha_{m n} \cdot d_{m}^{\mathrm{s}}+\beta_{m n} \cdot d_{n}^{\mathrm{s}}, d_{\mathrm{r}, \mathrm{F}_{m n}}^{\mathrm{s}}= \\ \;\;\;\; \alpha_{m n} \cdot d_{\mathrm{r}, m}^{\mathrm{s}}+\beta_{m n} \cdot d_{\mathrm{r}, n}^{\mathrm{s}} \end{array}\right.$ (2)

 $\begin{matrix} c\cdot \text{d}t_{\text{I}{{\text{F}}_{12}}}^{\text{s}}=c\left[ ~\text{d}{{t}^{\text{s}}}+\left( {{\alpha }_{12}}\cdot d_{1}^{\text{s}}+{{\beta }_{12}}\cdot d_{2}^{\text{s}} \right) \right]= \\ c\left( ~\text{d}{{t}^{\text{s}}}+d_{\text{I}{{\text{F}}_{12}}}^{\text{s}} \right) \\ \end{matrix}$ (3)

 $\left\{\begin{array}{l} P_{\mathrm{r}, j}^{\mathrm{s}}=\rho_{\mathrm{r}}^{\mathrm{s}}+c \cdot \mathrm{d} t_{\mathrm{r}}-c \cdot \mathrm{d} t_{\mathrm{IF}_{12}}^{\mathrm{s}}+T_{\mathrm{r}}+\gamma_{j} \cdot \\ \;\;\;\; I_{\mathrm{r}, 1}^{\mathrm{s}}+c \cdot d_{\mathrm{r}, j}^{\mathrm{s}}+c\left(d_{\mathrm{IF}_{12}}^{\mathrm{s}}-d_{j}^{\mathrm{s}}\right)+\varepsilon_{\mathrm{r}, P_{j}}^{\mathrm{s}, T} \\ L_{\mathrm{r}, j}^{\mathrm{s}}=\rho_{\mathrm{r}}^{\mathrm{s}}+c \cdot \mathrm{d} t_{\mathrm{r}}-c \cdot \mathrm{d} t_{\mathrm{IF}_{12}}^{\mathrm{s}}+T_{\mathrm{r}}-\gamma_{j} \cdot \\ \;\;\;\; I_{\mathrm{r}, 1}^{\mathrm{s}}+\lambda_{j}^{\mathrm{s}}\left(N_{\mathrm{r}, j}^{\mathrm{s}}+b_{\mathrm{r}, j}^{\mathrm{s}}-b_{j}^{\mathrm{s}}\right)+c \cdot d_{\mathrm{IF}_{12}}^{\mathrm{s}}+\xi_{\mathrm{r}, L_{j}}^{\mathrm{s}} \end{array}\right.$ (4)

 $\left\{ \begin{array}{*{35}{l}} d_{\text{I}{{\text{F}}_{12}}}^{\text{s}}-d_{1}^{\text{s}}={{\alpha }_{\text{B1B3}}}\cdot \text{DCB}_{\text{B1IB1C}}^{\text{s}}+{{\beta }_{\text{B1B3}}}\cdot \text{DCB}_{\text{B3IB1C}}^{\text{s}} \\ d_{\text{I}{{\text{F}}_{12}}}^{\text{s}}-d_{2}^{\text{s}}={{\alpha }_{\text{B1B3}}}\cdot \text{DCB}_{\text{B1IB2a}}^{\text{s}}+{{\beta }_{\text{B1B3}}}\cdot \text{DCB}_{\text{B3IB2a}}^{\text{s}} \\ d_{\text{I}{{\text{F}}_{12}}}^{\text{s}}-d_{3}^{\text{s}}={{\alpha }_{\text{B1B3}}}\cdot \text{DCB}_{\text{B1IB2b}}^{\text{s}}+{{\beta }_{\text{B1B3}}}\cdot \text{DCB}_{\text{B3IB2b}}^{\text{s}} \\ {{\alpha }_{\text{B1B3}}}=\frac{f_{\text{B}11}^{2}}{f_{\text{B}11}^{2}-f_{\text{B}31}^{2}}, {{\beta }_{\text{B1B3}}}=-\frac{f_{\text{B}31}^{2}}{f_{\text{B}11}^{2}-f_{\text{B}3\text{I}}^{2}} \\ \end{array} \right.$ (5)

 $\left\{ \begin{array}{*{35}{l}} P_{\text{r}, j}^{\text{s}}=\rho _{\text{r}}^{\text{s}}+c\cdot \text{d}{{t}_{\text{r}}}+{{T}_{\text{r}}}+{{\gamma }_{j}}\cdot I_{\text{r}, 1}^{\text{s}}+ \\ \quad c\cdot d_{\text{r}, j}^{\text{s}}+\varepsilon _{\text{r}, {{P}_{j}}}^{\text{s}, T} \\ L_{\text{r}, j}^{\text{s}}=\rho _{\text{r}}^{\text{s}}+c\cdot \text{d}{{t}_{\text{r}}}+{{T}_{\text{r}}}-{{\gamma }_{j}}\cdot I_{\text{r}, 1}^{\text{s}}+ \\ \quad \lambda _{j}^{\text{s}}\left( N_{\text{r}, j}^{\text{s}}+b_{\text{r}, j}^{\text{s}}-b_{j}^{\text{s}} \right)+c\cdot d_{\text{I}{{\text{F}}_{12}}}^{\text{s}}+\xi _{\text{r}, {{L}_{j}}}^{\text{s}} \\ \end{array} \right.$ (6)
1.1 非差模型(TU)

TU模型不对三频数据作任何线性组合，而是直接使用原始伪距和相位观测方程，即

 $\left\{\begin{array}{l} P_{\mathrm{r}, j}^{\mathrm{s}}=\rho_{\mathrm{r}}^{\mathrm{s}}+c \cdot \mathrm{d} t_{\mathrm{r}}+T_{\mathrm{r}}+ \\ \;\;\;\; \gamma_{j} \cdot I_{\mathrm{r}, 1}^{\mathrm{s}}+c \cdot d_{\mathrm{r}, j}^{\mathrm{s}}+ \varepsilon_{\mathrm{r}, P_{j}}^{\mathrm{s}, T} \\ L_{\mathrm{r}, j}^{\mathrm{s}}=\rho_{\mathrm{r}}^{\mathrm{s}}+c \cdot \mathrm{d} t_{\mathrm{r}}+T_{\mathrm{r}}-\gamma_{j} \cdot I_{\mathrm{r}, 1}^{\mathrm{s}}+ \\ \;\;\;\; \lambda_{j}^{\mathrm{s}}\left(N_{\mathrm{r}, j}^{\mathrm{s}}+b_{\mathrm{r}, j}^{\mathrm{s}}-b_{j}^{\mathrm{s}}\right)+c \cdot d_{\mathrm{IF}_{12}}^{\mathrm{s}}+\xi_{\mathrm{r}, L_{j}}^{\mathrm{s}} \end{array}\right.$ (7)

 $\begin{array}{l} \left\{ {\begin{array}{*{20}{c}} {c \cdot d_{{\rm{r}}, 1}^{\rm{s}} = a + {\gamma _1} \cdot b}\\ {c \cdot d_{{\rm{r}}, 2}^{\rm{s}} = a + {\gamma _2} \cdot b} \end{array}} \right.\\ \qquad\qquad \Downarrow \\ \left\{ \begin{array}{l} a = {\alpha _{12}} \cdot c \cdot d_{{\rm{r}}, 1}^{\rm{s}} + {\beta _{12}} \cdot c \cdot d_{{\rm{r}}, 2}^{\rm{s}} = \\ \;\;\;\;c \cdot {d_{{\rm{r}}, {{\rm{F}}_{12}}}}\\ b = \frac{1}{{1 - {\gamma _2}}} \cdot c \cdot \left( {d_{{\rm{r}}, 1}^{\rm{s}} - d_{{\rm{r}}, 2}^{\rm{s}}} \right) = \\ \;\;\;\;{\beta _{12}} \cdot c \cdot {\rm{DC}}{{\rm{B}}_{{\rm{r}}, {P_1}{P_2}}} \end{array} \right. \end{array}$ (8)

 $\left\{\begin{array}{l} P_{\mathrm{r}, j}^{\mathrm{s}}=\rho_{\mathrm{r}}^{\mathrm{s}}+c \cdot \overline{\mathrm{d} t_{\mathrm{r}}}+T_{\mathrm{r}}+\gamma_{j} \cdot \\ \;\;\;\; \bar{I}_{\mathrm{r}, 1}^{\mathrm{s}}+\mathrm{IFB}_{\mathrm{r}, j}+\varepsilon_{\mathrm{r}, P_{j}}^{\mathrm{s}, T} \\ L_{\mathrm{r}, j}^{\mathrm{s}}=\rho_{\mathrm{r}}^{\mathrm{s}}+c \cdot \overline{\mathrm{d} t_{\mathrm{r}}}+T_{\mathrm{r}}-\gamma_{j} \cdot \\ \;\;\;\; \bar{I}_{\mathrm{r}, 1}^{\mathrm{s}}+\bar{N}_{\mathrm{r}, j}^{\mathrm{s}}+\xi_{\mathrm{r}, L_{j}}^{\mathrm{s}} \end{array}\right.$ (9)

 $\left\{ \begin{array}{l} \overline {{\rm{d}}{t_{\rm{r}}}} = {\rm{d}}{t_{\rm{r}}} + {d_{{\rm{r}}, {\rm{I}}{{\rm{F}}_{12}}}}\\ \bar I_{{\rm{r}}, 1}^{\rm{s}} = I_{{\rm{r}}, 1}^{\rm{s}} + c \cdot {\beta _{12}} \cdot {\rm{DC}}{{\rm{B}}_{{\rm{r}}, {P_1}{P_2}}}\\ \bar N_{{\rm{r}}, j}^{\rm{s}} = \lambda _j^{\rm{s}}\left( {N_{{\rm{r}}, j}^{\rm{s}} + b_{{\rm{r}}, j}^{\rm{s}} - b_j^{\rm{s}}} \right) + c\left( {d_{{\rm{I}}{{\rm{F}}_{12}}}^{\rm{s}} - } \right.\\ \left. {\;\;\;\;{d_{{\rm{r}}, {\rm{I}}{{\rm{F}}_{12}}}}} \right) + c \cdot {\gamma _j} \cdot {\beta _{12}} \cdot {\rm{DC}}{{\rm{B}}_{{\rm{r}}, {P_1}{P_2}}}\\ {\rm{IF}}{{\rm{B}}_{{\rm{r}}, 3}} = \left\{ {\begin{array}{*{20}{l}} {0, j < 3}\\ {c\left( {d_{{\rm{r}}, 3}^{\rm{s}} - {d_{{\rm{r}}, {\rm{I}}{{\rm{F}}_{12}}}}} \right) - c \cdot {\gamma _3} \cdot }\\ {\;\;\;{\beta _{12}} \cdot {\rm{DC}}{{\rm{B}}_{{\rm{r}}, {P_1}{P_2}}}, j = 3} \end{array}} \right. \end{array} \right.$ (10)
1.2 消电离层模型(TF)

TF模型是将三频数据组合成消去电离层一阶项的观测值，即

 $\left\{\begin{array}{l} P_{\mathrm{r}, \mathrm{IF}_{123}}^{\mathrm{s}} &=e_{1} \cdot P_{\mathrm{r}, 1}^{\mathrm{s}}+e_{2} \cdot P_{\mathrm{r}, 2}^{\mathrm{s}}+e_{3} \cdot \\ \;\;\;\; P_{\mathrm{r}, 3}^{\mathrm{s}} &=\rho_{\mathrm{r}}^{\mathrm{s}}+c \cdot \overline{\mathrm{d} t_{\mathrm{r}}}+T_{\mathrm{r}}+\varepsilon_{\mathrm{r}, \mathrm{IF}_{123}}^{\mathrm{s}} \\ L_{\mathrm{r}, \mathrm{IF}_{123}}^{\mathrm{s}}, &=e_{1} \cdot L_{\mathrm{r}, 1}^{\mathrm{s}}+e_{2} \cdot L_{\mathrm{r}, 2}^{\mathrm{s}}+e_{3} \\ \;\;\;\; L_{\mathrm{r}, 3}^{\mathrm{s}} &=\rho_{\mathrm{r}}^{\mathrm{s}}+c \cdot \overline{\mathrm{d} t_{\mathrm{r}}}+T_{\mathrm{r}}+\bar{N}_{\mathrm{r}, \mathrm{IF}_{123}}^{\mathrm{s}}+\xi_{\mathrm{r}, \mathrm{IF}_{123}}^{\mathrm{s}} \end{array}\right.$ (11)

 $\left\{\begin{array}{l} \overline{\mathrm{d} t_{\mathrm{r}}}=\mathrm{d} t_{\mathrm{r}}+d_{\mathrm{r}, \mathrm{IF}_{123}}^{\mathrm{s}} \\ \bar{N}_{\mathrm{r}, \mathrm{IF}_{123}}^{\mathrm{s}}=e_{1} \cdot \lambda_{1}^{\mathrm{s}}\left(N_{\mathrm{r}, 1}^{\mathrm{s}}+b_{\mathrm{r}, 1}^{\mathrm{s}}-b_{1}^{\mathrm{s}}\right)+ \\ \;\;\; e_{2} \cdot \lambda_{2}^{\mathrm{s}}\left(N_{\mathrm{r}, 2}^{\mathrm{s}}+b_{\mathrm{r}, 2}^{\mathrm{s}}-b_{2}^{\mathrm{s}}\right)+e_{3} \cdot \lambda_{3}^{\mathrm{s}} \cdot \\ \;\;\; \left(N_{\mathrm{r}, 3}^{\mathrm{s}}+b_{\mathrm{r}, 3}^{\mathrm{s}}-b_{3}^{\mathrm{s}}\right)+c\left(d_{\mathrm{IF}_{12}}^{\mathrm{s}}-d_{\mathrm{r}, \mathrm{IF}_{123}}^{\mathrm{s}}\right) \end{array}\right.$ (12)

 $\left\{\begin{array}{l} e_{1}=\frac{\gamma_{2}^{2}+\gamma_{3}^{2}-\gamma_{2}-\gamma_{3}}{2\left(\gamma_{2}^{2}+\gamma_{3}^{2}-\gamma_{2} \cdot \gamma_{3}-\gamma_{2}-\gamma_{3}+1\right)} \\ e_{2}=\frac{\gamma_{3}^{2}-\gamma_{2} \cdot \gamma_{3}-\gamma_{2}+1}{2\left(\gamma_{2}^{2}+\gamma_{3}^{2}-\gamma_{2} \cdot \gamma_{3}-\gamma_{2}-\gamma_{3}+1\right)} \\ e_{3}=\frac{\gamma_{2}^{2}-\gamma_{2} \cdot \gamma_{3}-\gamma_{3}+1}{2\left(\gamma_{2}^{2}+\gamma_{3}^{2}-\gamma_{2} \cdot \gamma_{3}-\gamma_{2}-\gamma_{3}+1\right)} \end{array}\right.$ (13)
1.3 无电离层两两组合模型(TDF)

BDS-3三频数据能够组合产生2个双频无电离层组合(B1C/B2a和B1C/B2b)[7]，组合后的观测方程为：

 $\left\{ \begin{array}{l} P_{{\rm{r}}, {\rm{I}}{{\rm{F}}_{12}}}^{\rm{s}} = {\alpha _{12}} \cdot P_{{\rm{r}}, 1}^{\rm{s}} + {\beta _{12}} \cdot P_{{\rm{r}}, 2}^{\rm{s}} = \\ \;\;\;\rho _{\rm{r}}^{\rm{s}} + c \cdot \overline {{\rm{d}}{t_{\rm{r}}}} + {T_{\rm{r}}} + \varepsilon _{{\rm{r}}, {\rm{I}}{{\rm{F}}_{12}}}^{\rm{s}}\\ P_{{\rm{r}}, {\rm{I}}{{\rm{F}}_{13}}}^{\rm{s}} = {\alpha _{13}} \cdot P_{{\rm{r}}, 1}^{\rm{s}} + {\beta _{13}} \cdot P_{{\rm{r}}, 3}^{\rm{s}} = \\ \;\;\;\rho _{\rm{r}}^{\rm{s}} + c \cdot \overline {{\rm{d}}{t_{\rm{r}}}} + {T_{\rm{r}}} + {\rm{IF}}{{\rm{B}}_{{\rm{r}}, {\rm{I}}{{\rm{F}}_{13}}}} + \varepsilon _{{\rm{r}}, {\rm{I}}{{\rm{F}}_{13}}}^{\rm{s}}\\ L_{{\rm{r}}, {\rm{I}}{{\rm{F}}_{12}}}^{\rm{s}} = {\alpha _{12}} \cdot L_{{\rm{r}}, 1}^{\rm{s}} + {\beta _{12}} \cdot L_{{\rm{r}}, 2}^{\rm{s}} = \\ \;\;\;\rho _{\rm{r}}^{\rm{s}} + c \cdot \overline {{\rm{d}}{t_{\rm{r}}}} + {T_{\rm{r}}} + \bar N_{{\rm{r}}, {\rm{I}}{{\rm{F}}_{12}}}^{{{\rm{s}}_{12}}} + \xi _{{\rm{r}}, {\rm{I}}{{\rm{F}}_{12}}}^{\rm{s}}\\ L_{{\rm{r}}, {\rm{I}}{{\rm{F}}_{13}}}^{\rm{s}} = {\alpha _{13}} \cdot L_{{\rm{r}}, 1}^{\rm{s}} + {\beta _{13}} \cdot L_{{\rm{r}}, 3}^{\rm{s}} = \\ \;\;\;\rho _{\rm{r}}^{\rm{s}} + c \cdot \overline {{\rm{d}}{t_{\rm{r}}}} + {T_{\rm{r}}} + \bar N_{{\rm{r}}, {\rm{I}}{{\rm{F}}_{13}}}^{\rm{s}} + \xi _{{\rm{r}}, {\rm{I}}{{\rm{F}}_{13}}}^{\rm{s}} \end{array} \right.$ (14)

 \begin{aligned} &\left\{\begin{array}{l} \overline{\mathrm{d} t_{\mathrm{r}}}=\mathrm{d} t_{\mathrm{r}}+d_{\mathrm{r}, \mathrm{IF}_{12}}^{\mathrm{s}} \\ \overline{N}_{\mathrm{r}, \mathrm{IF}_{12}}^{\mathrm{~s}}=\alpha_{12} \cdot \lambda_{1}^{\mathrm{s}}\left(N_{\mathrm{r}, 1}^{\mathrm{s}}+b_{\mathrm{r}, 1}^{\mathrm{s}}-b_{1}^{\mathrm{s}}\right)+\beta_{12} \cdot \\ \;\;\;\; \lambda_{2}^{\mathrm{s}}\left(N_{\mathrm{r}, 2}^{\mathrm{s}}+b_{\mathrm{r}, 2}^{\mathrm{s}}-b_{2}^{\mathrm{s}}\right)+c\left(d_{\mathrm{IF}_{12}}^{\mathrm{s}}-d_{\mathrm{r}, \mathrm{IF}_{12}}^{\mathrm{s}}\right) \\ \overline{N}_{\mathrm{r}, \mathrm{F}_{13}}^{\mathrm{~s}}=\alpha_{13} \cdot \lambda_{1}^{\mathrm{s}}\left(N_{\mathrm{r}, 1}^{\mathrm{s}}+b_{\mathrm{r}, 1}^{\mathrm{s}}-b_{1}^{\mathrm{s}}\right)+\beta_{13} \cdot \\ \;\;\;\; \lambda_{3}^{\mathrm{s}}\left(N_{\mathrm{r}, 3}^{\mathrm{s}}+b_{\mathrm{r}, 3}^{\mathrm{s}}-b_{3}^{\mathrm{s}}\right)+c\left(d_{\mathrm{IF}_{13}}^{\mathrm{s}}-d_{\mathrm{r}, \mathrm{IF}_{12}}^{\mathrm{s}}\right)\\ \mathrm{IFB}_{\mathrm{r}, \mathrm{IF}_{13}}=d_{\mathrm{r}, \mathrm{IF}_{13}}^{\mathrm{s}}-d_{\mathrm{r}, \mathrm{IF}_{12}}^{\mathrm{s}}=\left(1-\beta_{13}\right) d_{\mathrm{r}, 1}^{\mathrm{s}}+\\ \;\;\;\; \beta_{13} \cdot d_{\mathrm{r}, 3}^{\mathrm{s}}-\left(1-\beta_{12}\right) d_{\mathrm{r}, 1}^{\mathrm{s}}-\beta_{12} \cdot d_{\mathrm{r}, 2}^{\mathrm{s}}=\\ \;\;\;\; \beta_{12} \cdot \mathrm{DCB}_{\mathrm{r}, 12}^{\mathrm{s}}-\beta_{13} \cdot \mathrm{DCB}_{\mathrm{r}, 13}^{\mathrm{s}} \end{array}\right. \end{aligned} (15)
1.4 BDS-3新三频PPP特点

2 三频PPP随机模型

 $\sigma =f\left( E \right)=\sqrt{{{a}^{2}}+{{b}^{2}}/{{\sin }^{2}}E}$ (16)

 $\left\{ \begin{array}{l} {\varSigma _{{\rm{TU}}}} = \left[ {\begin{array}{*{20}{c}} {{\sigma _P}}&{}&{}&{}&{}&{}\\ {}&{{\sigma _L}}&{}&{}&{}&{}\\ {}&{}&{{\sigma _P}}&{}&{}&{}\\ {}&{}&{}&{{\sigma _L}}&{}&{}\\ {}&{}&{}&{}&{{\sigma _P}}&{}\\ {}&{}&{}&{}&{}&{{\sigma _L}} \end{array}} \right], {\varSigma _{{\rm{TF}}}} = \left[ {\begin{array}{*{20}{c}} {\left( {e_1^2 + e_2^2 + e_3^2} \right){\sigma _P}}&0\\ 0&{\left( {e_1^2 + e_2^2 + e_3^2} \right){\sigma _L}} \end{array}} \right]\\ {\varSigma _{{\rm{TDF}}}} = \left[ {\begin{array}{*{20}{c}} {\left( {\alpha _{12}^2 + \beta _{12}^2} \right){\sigma _P}}&0&{{\alpha _{12}} \cdot {\alpha _{13}} \cdot {\sigma _P}}&0\\ 0&{\left( {\alpha _{12}^2 + \beta _{12}^2} \right){\sigma _L}}&0&{{\alpha _{12}} \cdot {\alpha _{13}} \cdot {\sigma _L}}\\ {{\alpha _{12}} \cdot {\alpha _{13}} \cdot {\sigma _P}}&0&{\left( {\alpha _{13}^2 + \beta _{13}^2} \right){\sigma _P}}&0\\ 0&{{\alpha _{12}} \cdot {\alpha _{13}} \cdot {\sigma _L}}&0&{\left( {\alpha _{12}^2 + \beta _{12}^2} \right){\sigma _L}} \end{array}} \right] \end{array} \right.$ (17)
3 实验结果分析 3.1 实验数据及解算策略

3.2 静态PPP实验

 图 1 5种PPP模型静态定位误差 Fig. 1 Static positioning error of five PPP models

 图 2 14个测站5种PPP模型静态定位偏差和收敛时间平均值 Fig. 2 The average values of static positioning deviation and convergence time of five PPP models at fourteen stations

 图 3 5种PPP模型静态三维收敛时间和定位精度 Fig. 3 Static 3D convergence time and positioning accuracy of five PPP models

3.3 动态PPP实验

 图 4 5种PPP模型动态定位误差 Fig. 4 Dynamic positioning error of five PPP models

 图 5 14个测站5种PPP模型动态定位偏差和收敛时间平均值 Fig. 5 The average values of dynamic positioning deviation and convergence time of five PPP models at fourteen stations

 图 6 5种PPP模型动态三维收敛时间和定位精度 Fig. 6 Dynamic 3D convergence time and positioning accuracy of five PPP models

4 结语

1) BDS-3的DU2模型在静、动态定位中的收敛时间分别约为24 min和58 min；而B1C、B2a和B2b新频率组成的双频非差非组合模型和三频PPP模型在静、动态定位中的收敛时间可达约20 min和50 min，三维定位精度能达到2 cm和7 cm，提升较大。

2) 与传统B1I/B3I双频DU2模型相比，DU3、TU、TDF和TF模型的定位性能均有所提高。在收敛时间方面，TDF模型对静态定位的提升最大，略高于TF模型；TF模型对动态定位的提升最大，略高于TDF模型。在定位精度方面，TDF模型对静态和动态定位的提升最明显。

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Performance Analysis of BDS-3 Multi-Frequency PPP Model
WU Zhiyuan1     WANG Qianxin1     HU Chao2     WU Wei1
1. School of Environment and Spatial Informatics, China University of Mining and Technology, 1 Daxue Road, Xuzhou 221116, China;
2. School of Spatial Information and Geomatics Engineering, Anhui University of Science and Technology, 168 Taifeng Street, Huainan 232001, China
Abstract: In order to verify the positioning performance of the new triple-frequency PPP model of the BDS-3 system, we derive the new triple-frequency PPP model based on the original observation equation and derive the pseudorange deviation correction again in the model. Using BDS-3 data observed by 14 MGEX stations, we compare and analyze the static and dynamic positioning performances of three triple-frequency PPP models and two traditional dual-frequency uncombined models. Experimental results show that the new triple-frequency PPP model can improve convergence time and positioning accuracy, and the TDF model has the greatest improvement effect.
Key words: BDS-3; triple-frequency PPP model; dual-frequency uncombined model; pseudorange deviation correction; positioning performance