﻿ 基于历元差分原理的BDS测速模型及性能分析
 文章快速检索 高级检索
 大地测量与地球动力学  2019, Vol. 39 Issue (1): 7-12  DOI: 10.14075/j.jgg.2019.01.002

### 引用本文

WANG Xingxing, TU Rui, HONG Ju, et al. BDS Velocity Estimation and Performance Analysis Based on Time-Difference Model[J]. Journal of Geodesy and Geodynamics, 2019, 39(1): 7-12.

### Foundation support

National Key Research and Development Program of China, No. 2016YFB0501804; National Natural Science Foundation of China, No.41504006, 41674034; One Hundred Person Project and Frontier Science Research Project of CAS, No. QYZDB-SSW-DQC028.

### 第一作者简介

WANG Xingxing, postgraduate, majors in GNSS precise velocity estimation, E-mail: 961671525@qq.com.

### 文章历史

1. 中国科学院国家授时中心，西安市书院东路3号，710600;
2. 中国科学院大学，北京市玉泉路19号甲，100049

BDS作为中国自主研发的卫星导航系统，已于2012年底开始向亚太地区提供区域导航定位服务，并将在2020年实现全球服务。但针对北斗单点测速分析的文献相对较少。基于此，本文在分析现有TDCP方法的基础上，提出基于历元差分原理的BDS测速模型，并用实测的数据进行测速性能分析。

1 历元差分模型 1.1 TDCP测速算法

 $\begin{array}{*{20}{c}} {\lambda \mathit{\Phi }_{r\left( {ti} \right)}^s = \rho _{r\left( {ti} \right)}^s - {{\left( {\delta {t_r} - \delta {t_s}} \right)}_{\left( {ti} \right)}}c - }\\ {\lambda N_{\left( {ti} \right)}^s - {\delta _{{\rm{ion}}\left( {ti} \right)}} + {\delta _{{\rm{trop}}\left( {ti} \right)}}} \end{array}$ (1)

 $\begin{array}{*{20}{c}} {\Delta \lambda \mathit{\Phi }_{r\left( {t1,2} \right)}^s = \Delta \rho _{r\left( {t1,2} \right)}^s - \Delta \delta {t_{r\left( {t1,2} \right)}}c + }\\ {\Delta \delta {t_{s\left( {t1,2} \right)}}c - \Delta {\delta _{{\rm{ion}}\left( {t1,2} \right)}} + {\delta _{{\rm{trop}}\left( {t1,2} \right)}}} \end{array}$ (2)

 $\rho _{r\left( {ti} \right)}^s = \left( {\mathit{\boldsymbol{e}}_{\left( {ti} \right)}^{\left( {ti} \right)},{\mathit{\boldsymbol{R}}_{sr\left( {ti} \right)}} - {\mathit{\boldsymbol{r}}_{\left( {ti} \right)}}} \right)$ (3)

 $\begin{array}{l} \Delta \rho _{r\left( {t1,2} \right)}^s = \left( {\mathit{\boldsymbol{e}}_{t2}^{t2},{\mathit{\boldsymbol{R}}_{sr\left( {t2} \right)}} - {\mathit{\boldsymbol{r}}_{\left( {t2} \right)}}} \right) - \left( {\mathit{\boldsymbol{e}}_{t1}^{t1},{\mathit{\boldsymbol{R}}_{sr\left( {t1} \right)}} - {\mathit{\boldsymbol{r}}_{\left( {t1} \right)}}} \right) = \\ \left( {\mathit{\boldsymbol{e}}_{t2}^{t2},{\mathit{\boldsymbol{R}}_{sr\left( {t2} \right)}}} \right) - \left( {\mathit{\boldsymbol{e}}_{t1}^{t1},{\mathit{\boldsymbol{R}}_{sr\left( {t1} \right)}}} \right) - \left( {\mathit{\boldsymbol{e}}_{t2}^{t2},{\mathit{\boldsymbol{r}}_{\left( {t2} \right)}}} \right) + \left( {\mathit{\boldsymbol{e}}_{t1}^{t1},{\mathit{\boldsymbol{r}}_{\left( {t1} \right)}}} \right) \end{array}$ (4)

 $\begin{array}{l} \Delta \rho _{r\left( {t1,2} \right)}^s = - \left( {\mathit{\boldsymbol{e}}_{t2}^{t2},\Delta \mathit{\boldsymbol{r}}} \right) + \left( {{\mathit{\boldsymbol{e}}_{\left( {t2} \right)}},{\mathit{\boldsymbol{R}}_{sr\left( {t2} \right)}}} \right) - \\ \left( {\mathit{\boldsymbol{e}}_{t1}^{t1},{\mathit{\boldsymbol{R}}_{sr\left( {t1} \right)}}} \right) - \left( {\mathit{\boldsymbol{e}}_{t2}^{t2},{\mathit{\boldsymbol{r}}_{\left( {t1} \right)}}} \right) + \left( {\mathit{\boldsymbol{e}}_{t1}^{t1},{\mathit{\boldsymbol{r}}_{\left( {t1} \right)}}} \right) = - \left( {\mathit{\boldsymbol{e}}_{t2}^{t2},} \right.\\ \left. {\Delta \mathit{\boldsymbol{r}}} \right) + \left( {\mathit{\boldsymbol{e}}_{t2}^{t2},{\mathit{\boldsymbol{R}}_{sr\left( {t2} \right)}} - {\mathit{\boldsymbol{r}}_{\left( {t1} \right)}}} \right) - \left( {\mathit{\boldsymbol{e}}_{t1}^{t1},{\mathit{\boldsymbol{R}}_{sr\left( {t1} \right)}} - {\mathit{\boldsymbol{r}}_{\left( {t1} \right)}}} \right) \end{array}$ (5)

1.2 改进的历元差分测速算法

r(ti)=r0(ti)ri，其中r0(ti)表示ti历元接收机的近似坐标，Δri表示ti历元接收机近似坐标的误差，则式(4)可以表示为：

 $\begin{array}{*{20}{c}} {\Delta \rho _{r\left( {t1,2} \right)}^s = - \left( {\mathit{\boldsymbol{e}}_{t2}^{t2},\Delta \mathit{\boldsymbol{r}}} \right) + \left( {\mathit{\boldsymbol{e}}_{t2}^{t2},{\mathit{\boldsymbol{R}}_{sr\left( {t2} \right)}} - {\mathit{\boldsymbol{r}}_{0\left( {t1} \right)}} - \Delta {\mathit{\boldsymbol{r}}_1}} \right) - }\\ {\left( {\mathit{\boldsymbol{e}}_{t1}^{t1},{\mathit{\boldsymbol{R}}_{sr\left( {t1} \right)}} - {\mathit{\boldsymbol{r}}_{0\left( {t1} \right)}} - \Delta {\mathit{\boldsymbol{r}}_1}} \right) = - \left( {\mathit{\boldsymbol{e}}_{t2}^{t2},\Delta \mathit{\boldsymbol{r}}} \right) + }\\ {\left( {\mathit{\boldsymbol{e}}_{t2}^{t2},{\mathit{\boldsymbol{R}}_{sr\left( {t2} \right)}} - {\mathit{\boldsymbol{r}}_{0\left( {t1} \right)}}} \right) - \left( {\mathit{\boldsymbol{e}}_{t1}^{t1},{\mathit{\boldsymbol{R}}_{sr\left( {t1} \right)}} - {\mathit{\boldsymbol{r}}_{0\left( {t1} \right)}}} \right) + }\\ {\left( {\mathit{\boldsymbol{e}}_{t1}^{t1} - \mathit{\boldsymbol{e}}_{t2}^{t2},\Delta {\mathit{\boldsymbol{r}}_1}} \right)} \end{array}$ (6)

r0(t2)=r0(t1)，即用上一历元的接收机坐标作为这一历元的接收机坐标近似值[7]，则式(6)表示为：

 $\begin{array}{*{20}{c}} {\Delta \rho _{r\left( {t1,2} \right)}^s = - \left( {\mathit{\boldsymbol{e}}_{t1}^{t2},\Delta \mathit{\boldsymbol{r}}} \right) + \left( {\mathit{\boldsymbol{e}}_{t2}^{t2},{\mathit{\boldsymbol{R}}_{sr\left( {t2} \right)}} - {\mathit{\boldsymbol{r}}_{0\left( {t2} \right)}}} \right) - }\\ {\left( {\mathit{\boldsymbol{e}}_{t1}^{t1},{\mathit{\boldsymbol{R}}_{sr\left( {t1} \right)}} - {\mathit{\boldsymbol{r}}_{0\left( {t1} \right)}}} \right) + \left( {\mathit{\boldsymbol{e}}_{t1}^{t1} - \mathit{\boldsymbol{e}}_{t2}^{t2},\Delta {\mathit{\boldsymbol{r}}_1}} \right)} \end{array}$ (7)

 $\begin{array}{*{20}{c}} {\Delta \rho _{r\left( {t1,2} \right)}^s = - \left( {\mathit{\boldsymbol{e}}_{t1}^{t2},\Delta \mathit{\boldsymbol{r}}} \right) + \left( {\mathit{\boldsymbol{e}}_{t2}^{t2},{\mathit{\boldsymbol{R}}_{sr\left( {t2} \right)}} - {\mathit{\boldsymbol{r}}_{0\left( {t2} \right)}}} \right) - }\\ {\left( {\mathit{\boldsymbol{e}}_{t1}^{t1},{\mathit{\boldsymbol{R}}_{sr\left( {t1} \right)}} - {\mathit{\boldsymbol{r}}_{0\left( {t1} \right)}}} \right) = - \left( {\mathit{\boldsymbol{e}}_{t1}^{t2},\Delta \mathit{\boldsymbol{r}}} \right) + \rho _{r0\left( {t2} \right)}^s - \rho _{r\left( {t1} \right)}^s} \end{array}$ (8)

 $\begin{array}{*{20}{c}} {\Delta \lambda \mathit{\Phi }_{r\left( {t1,2} \right)}^s = - \left( {\mathit{\boldsymbol{e}}_{t1}^{t2},\Delta \mathit{\boldsymbol{r}}} \right) - \Delta \delta {t_{r\left( {t1,2} \right)}}c + \Delta {\delta _{{\rm{trop}}\left( {t1,2} \right)}} + }\\ {\rho _{r\left( {t2} \right)}^s - \rho _{r\left( {t1} \right)}^s + \Delta \delta {t_{s\left( {t1,2} \right)}}c - \Delta {\delta _{{\rm{ion}}\left( {t1,2} \right)}}} \end{array}$ (9)

 $\begin{array}{*{20}{c}} {\Delta R_{r\left( {t1,2} \right)}^s = - \left( {\mathit{\boldsymbol{e}}_{t1}^{t2},\Delta \mathit{\boldsymbol{r}}} \right) - \Delta \delta {t_{r\left( {t1,2} \right)}}c + \Delta {\delta _{{\rm{trop}}\left( {t1,2} \right)}} + }\\ {\rho _{r\left( {t2} \right)}^s - \rho _{r\left( {t1} \right)}^s + \Delta \delta {t_{s\left( {t1,2} \right)}}c - \Delta {\delta _{{\rm{ion}}\left( {t1,2} \right)}}} \end{array}$ (10)

2 数据处理 2.1 数据预处理

2.2 误差修正

2.3 参数估计

3 数据测试 3.1 静态数据

3.1.1 精密星历解算

 图 1 BRUN站精密星历BDS历元差分测速结果 Fig. 1 BDS time-differenced velocity estimation results of BRUN station using precise ephemeris

3.1.2 广播星历解算

 图 2 BRUN站广播星历BDS历元差分测速结果 Fig. 2 BDS time-differenced velocity estimation results of BRUN station using broadcast ephemeris
3.2 动态数据

 图 3 载体运动轨迹 Fig. 3 Movement track
3.2.1 精密星历解算

 图 4 动态数据BDS历元差分测速结果 Fig. 4 BDS time-differenced velocity estimation results of dynamic data

 图 5 第1时段BDS TDCP-IE速度差值、BDS-IE速度差值以及GPS-IE速度差值 Fig. 5 BDS-IE TDCP velocity difference and BDS-IE velocity difference and GPS-IE velocity difference of first period

 图 6 第2时段BDS TDCP-IE速度差值、BDS-IE速度差值以及GPS-IE速度差值 Fig. 6 BDS-IE TDCP velocity difference and BDS-IE velocity difference and GPS-IE velocity difference of second period

 图 7 2个时段BDS-IE速度差值与PDOP值以及卫星数目的关系 Fig. 7 Relation between BDS-IE velocity difference and PDOP values and satellite numbers of two periods

3.2.2 广播星历解算

 图 8 2个时段BDS广播星历和精密星历测速差值与PDOP值以及卫星数目的关系 Fig. 8 Relation between BDS broadcast-precise ephemeris velocity difference and PDOP values and satellite numbers of two periods

4 结语

 [1] 闫勇伟, 叶世榕, 夏敬潮. BDS载波相位历元间差分测速方法研究[J]. 测绘科学, 2016, 41(7): 193-196 (Yan Yongwei, Ye Shirong, Xia Jingchao. Research of BDS Velocity Estimation with Time Differenced Carrier Phase Method[J]. Science of Surveying and Mapping, 2016, 41(7): 193-196) (0) [2] 刘洋.基于载波相位时间差分测速的GPS/INS组合导航研究[D].北京: 中国矿业大学, 2016 (Liu Yang. Research on GPS/INS Integrated Navigation Based on the Time Differenced Carrier Phase Velocity Estimation Approach[D]. Beijing: China University of Mining and Technology, 2016) (0) [3] Freda P, Angrisano A, Gaglione S, et al. Time-Differenced Carrier Phases Technique for Precise GNSS Velocity Estimation[J]. GPS Solutions, 2015, 19(2): 335-341 DOI:10.1007/s10291-014-0425-1 (0) [4] Graas F V, Soloviev A. Precise Velocity Estimation Using a Stand-alone GPS Receiver[J]. Navigation, 2004, 51(4): 283-292 DOI:10.1002/navi.2004.51.issue-4 (0) [5] Soon B K H, Scheding S, Lee H K, et al. An Approach to Aid INS Using Time-Differenced GPS Carrier Phase (TDCP) Measurements[J]. GPS Solutions, 2008, 12(4): 261-271 DOI:10.1007/s10291-007-0083-7 (0) [6] 刘志强, 王解先, 王虎. 基于相位单差精密测速的动态精密单点定位算法[J]. 宇航学报, 2012, 33(3): 405-410 (Liu Zhiqiang, Wang Jiexian, Wang Hu. An Approach for Kinematic Precise Point Positioning Based on Precise Velocity Estimation[J]. Journal of Astronautics, 2012, 33(3): 405-410 DOI:10.3873/j.issn.1000-1328.2012.03.019) (0) [7] Ding W D, Wang J L. Precise Velocity Estimation with a Stand-Alone GPS Receiver[J]. Journal of Navigation, 2011, 64(2): 311-325 DOI:10.1017/S0373463310000482 (0) [8] 范士杰, 牟春霖, 刘焱雄, 等. 历元间差分精密单点定位的精度分析[J]. 测绘科学, 2016, 41(1): 122-126 (Fan Shijie, Mu Chunlin, Liu Yanxiong, et al. Precision Analysis of Precise Point Positioning Based on the Epoch-Difference Model[J]. Science of Surveying and Mapping, 2016, 41(1): 122-126) (0) [9] 李浩军, 王解先, 胡丛玮, 等. 基于历元间差分技术的精密单点定位研究[J]. 宇航学报, 2010, 31(3): 748-752 (Li Haojun, Wang Jiexian, Hu Congwei, et al. The Research on Precise Point Positioning Based on the Epoch-Difference[J]. Journal of Astronautics, 2010, 31(3): 748-752 DOI:10.3873/j.issn.1000-1328.2010.03.020) (0) [10] 周命端, 郭际明, 孟祥广. GPS对流层延迟改正UNB3模型及其精度分析[J]. 测绘信息与工程, 2008, 33(4): 3-5 (Zhou Mingduan, Guo Jiming, Meng Xiangguang. GPS Tropspheric Delay Model UNB3 and Its Accuracy Analysis[J]. Journal of Geomatics, 2008, 33(4): 3-5 DOI:10.3969/j.issn.1007-3817.2008.04.002) (0)
BDS Velocity Estimation and Performance Analysis Based on Time-Difference Model
WANG Xingxing1,2     TU Rui1,2     HONG Ju1,2     LIU Chongjin1,2     LIU Jinhai1,2
1. National Time Service Center, CAS, 3 East-Shuyuan Road, Xi'an 710600, China;
2. University of Chinese Academy of Sciences, A19 Yuquan Road, Beijing 100049, China
Abstract: We build a new time-difference model for velocity estimation based on the existing time-differenced carrier phase technique. In the new model, time-differenced pseudorange observations are included. The static and kinematic data of Beidou navigation satellite system (BDS) is used to verify and analyze the improved method. The results show that the precision of the new time-differenced method could reach mm/s level in static conditions, equal to the GPS precision, and the accuracy of horizontal is better than the vertical. Furthermore, while in dynamic conditions, the mean square statistics of the velocity discrepancies between BDS time-differenced method and IE (inertial explorer) accord with cm/s, and the accuracy of the horizontal is better than the vertical.
Key words: Beidou navigation satellite system; time-difference; velocity estimation; carrier phase; pseudorange