﻿ 陆地导航中GNSS单天线姿态测量的误差及精度分析
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 大地测量与地球动力学  2021, Vol. 41 Issue (10): 1014-1017, 1050  DOI: 10.14075/j.jgg.2021.10.005

### 引用本文

WEI Yongseng, HE Kaifei, QIU Lijie, et al. Error and Accuracy Analysis of GNSS Single-Antenna Attitude Determination for Land Navigation[J]. Journal of Geodesy and Geodynamics, 2021, 41(10): 1014-1017, 1050.

### Foundation support

National Natural Science Foundation of China, No. 41604027; Natural Science Foundation of Shandong Province, No. ZR2016DQ01; Open Fund of Qingdao National Laboratory for Marine Science and Technology, No. QNLM2016ORP0401.

### Corresponding author

HE Kaifei, PhD, associate professor, majors in GNSS integrated marine navigation and positioning, E-mail: kfhe@upc.edu.cn.

### 第一作者简介

WEI Yongseng, postgraduate, majors in GNSS attitude determination and data processing, E-mail: wys_upc@163.com.

### 文章历史

1. 中国石油大学(华东)海洋与空间信息学院, 青岛市长江西路66号, 266580

1 单天线测姿基本原理

 $\lambda D = \dot \rho + c{{\dot t}_{\rm{r}}} - c{{\dot t}^{\rm{j}}} + \dot T - \dot I + \dot \varepsilon$ (1)

 \begin{aligned} &y=\left\{\begin{array}{l} \arctan \left(v_{E} / v_{N}\right), v_{E}>0, v_{N}>0 \\ \pi+\arctan \left(v_{E} / v_{N}\right), v_{N}<0 \\ 2 \pi+\arctan \left(v_{E} / v_{N}\right), v_{E}<0, v_{N}>0 \end{array}\right. \end{aligned} (2)
 $p=\arctan \left(v_{U} / \sqrt{\left(v_{E}\right)^{2}+\left(v_{N}\right)^{2}}\right)$ (3)

 $r = {\rm{arcsin}}\left[ {\left( {l \times p} \right)/\left( {\left| l \right| \times |p|} \right)} \right]$ (4)

2 GNSS单天线测姿误差分析

2.1 速度相关误差

 ${\delta _y} = \frac{{{v_N}{\delta _{{V_E}}} - {v_E}{\delta _{{V_N}}}}}{{v_E^2 + v_N^2}}$ (5)

 $\sigma_{y}=\frac{\sqrt{v_{N}^{2} \sigma_{v_{E}}^{2}+v_{E}^{2} \sigma_{v_{N}}^{2}}}{v_{E}^{2}+v_{N}^{2}} \approx \frac{\sigma_{v_{H}}}{v_{H}}$ (6)

 $\sigma_{p}=\frac{\sqrt{\left(v_{E}^{2}+v_{N}^{2}\right)^{2} \sigma_{v_{U}}^{2}+v_{E}^{2} v_{U}^{2} \sigma_{v_{E}}^{2}+v_{N}^{2} v_{U}^{2} \sigma_{v_{N}}^{2}}}{\left(v_{E}^{2}+v_{N}^{2}+v_{U}^{2}\right) \sqrt{v_{E}^{2}+v_{N}^{2}}}$ (7)

 ${\sigma _p} \approx \frac{{\sqrt {v_H^2\sigma _{{v_U}}^2 + v_U^2\sigma _{{v_H}}^2} }}{{v_{ENU}^2}}$ (8)

2.2 天线相关误差

 $\alpha \approx {\rm{arctan}}\left( {l/R} \right)$ (9)
 图 1 天线位置偏差引起的速度误差 Fig. 1 Velocity error caused by antenna position deviation

2.3 运动环境引起的误差

3 实验测试及结果分析

3.1 速度测量误差影响

 图 2 航向角变化 Fig. 2 Changes of heading angle

 图 3 俯仰角变化 Fig. 3 Changes of pitch angle

 图 4 航向角残差序列 Fig. 4 The residual sequence of heading angle

 图 5 俯仰角残差序列 Fig. 5 The residual sequence of pitch angle

3.2 天线位置偏差影响

 图 6 不同运动状态下航向角的误差比对 Fig. 6 The error of heading angle under different motion states

4 结语

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Error and Accuracy Analysis of GNSS Single-Antenna Attitude Determination for Land Navigation
WEI Yongseng1     HE Kaifei1     QIU Lijie1     LIU Duxue1
1. College of Oceanography and Space Informatics, China University of Petroleum, 66 West-Changjiang Road, Qingdao 266580, China
Abstract: In this paper, the GNSS raw Doppler observation and the carrier phase derived Doppler observation are used to verify the performance of single antenna attitude determination in a kinematic environment, and we compare the accuracy of the attitude determination for the kinematic platform in different motion states. The experimental results show that when the kinematic platform is moving at a lower speed, the RMS values of the heading angle calculated by the carrier phase derived Doppler observation, the raw Doppler observation are both within 0.35°, and the RMS value of the pitch angle is within 0.15°. The attitude result calculated by the carrier phase derived Doppler observation is more stable than the raw Doppler observation. The heading accuracy calculated by using the carrier phase derived Doppler observation when going straight and turning are within 0.15° and 0.81° respectively, and the accuracy of the calculated attitude results when the carrier is going straight is higher than when turning.
Key words: GNSS; single-antenna; low-dynamic; attitude determination; error analysis