| Citation: |
LI Jingsen, XUE Shuqiang, XIAO Zhen, WANG Kaiming. Uncertainty Evaluation on Arm Length Correction of GNSS/A Combined Observation[J]. Geomatics and Information Science of Wuhan University, 2025, 50(3): 535-544. DOI: 10.13203/j.whugis20220673
|
When global navigation satellite system/acoustic（GNSS/A） technology is applied in seafloor geodesy, GNSS antenna coordinates are converted to transducer position by arm length parameters and platform attitude observations. The conversion involves not only the error propagation of GNSS positioning error, but also the propagation of arm length error and attitude measurement error, which is a typical nonlinear error propagation problem.
In this paper, both the guide to the expression of uncertainty in measurement (GUM) based on linearized error propagation and Monte Carlo method (MCM) based on nonlinear error propagation are used to evaluate the uncertainty of transducer location.
The results show that GUM and MCM have a good consistency on the whole process, but with the increase of nonlinear strength and measurement uncertainty, these two methods have a significant difference. The uncertainty of transducer increases with the increase of arm length, and increases with the decreas of the accuracies of attitude measurement and arm length measurement. It means that the longer the arm length of GNSS/A combined observation, the higher the requirement for attitude measurement accuracy. Attitude measurement uncertainty has the least influence on the uncertainty of transducer location, GNSS positioning uncertainty has the most, and arm length parameter has the secondary.
| [1] |
乔学军, 王伟, 林牧, 等. 海底地壳形变监测现状与启示[J]. 地球物理学报, 2021, 64（12）： 4355-4363.
QIAO Xuejun, WANG Wei, LIN Mu, et al. Current Situation and Enlightenment of Seafloor Crustal Deformation Monitoring[J]. Chinese Journal of Geophysics, 2021, 64（12）： 4355-4363.
|
| [2] |
杨元喜, 刘焱雄, 孙大军, 等. 海底大地基准网建设及其关键技术[J]. 中国科学： 地球科学, 2020, 50（7）： 936-945.
YANGYuanxi,LIU Yanxiong,SUN Dajun,et al.Seafloor Geodetic Network EStablishment and Key Technologies[J].Scientia Sinica（Terrae）,2020,50（7）： 936-945.
|
| [3] |
胡圣武, 陶本藻. 非线性模型的误差传播及其在GIS中的应用[J]. 武汉大学学报（信息科学版）, 1997, 22（2）： 129-131.
HU Shengwu, TAO Benzao. Nonlinear Error Pro-pagation and Its Application in GIS[J]. Geomatics and Information Science of Wuhan University, 1997, 22（2）： 129-131.
|
| [4] |
杨元喜. 卫星导航的不确定性、不确定度与精度若干注记[J]. 测绘学报, 2012, 41（5）： 646-650.
YANG Yuanxi. Some Notes on Uncertainty, Uncertainty Measure and Accuracy in Satellite Navigation[J]. Acta Geodaetica et Cartographica Sinica, 2012, 41（5）： 646-650.
|
| [5] |
GB/T 27418⁃2017. 测量不确定度评定和表示[S].北京： 中国国家标准化管理委员会, 2017.
GB/T 27418⁃2017. Guide to The Evaluation and Expression of Uncertainty in Measurement[S].Beijing： Standardization Administration of China, 2017.
|
| [6] |
Uncertainty of Measurement-Part 3： Guide To the Expression of Uncertainty in Measurement （GUM： 1995）： ISO/IEC Guide 98-3[S]. Geneva, Switzerland： ISO, 1995.
|
| [7] |
JJF 1059.1⁃2012. 测量不确定度评定与表示[S].北京： 国家质量监督检验检疫总局, 2012.
JJF 1059.1⁃2012. Evaluation and Expression of Uncertainty in Measurement[S]. Beijing： General Administration of Quality Supervision, Inspection and Quarantine of China, 2012.
|
| [8] |
JJF 1059.2-2012. 用蒙特卡洛法评定测量不确定度[S].北京： 国家质量监督检验检疫总局, 2012.
JJF 1059.2-2012. Monte Carlo Method for Evaluation of Measurement Uncertainty[S]. Beijing： General Administration of Quality Supervision, Inspection and Quarantine of China, 2012.
|
| [9] |
杨元喜. 关于“新的点位误差度量” 的讨论[J]. 测绘学报, 2009, 38（3）： 280-282.
YANG Yuanxi. Discussion on “a New Measure of Positional Error”[J]. Acta Geodaetica et Cartographica Sinica, 2009, 38（3）： 280-282.
|
| [10] |
邢永丽, 陈建春. 泰勒级数在近似计算中的应用[J]. 湘潭师范学院学报（自然科学版）, 2004, 26（1）： 5-8.
XING Yongli, CHEN Jianchun. The Application of Taloy Series in Approximation Calculation[J]. Journal of Xiangtan Normal University （Natural Science Edition）, 2004, 26（1）： 5-8.
|
| [11] |
XUE S Q, YANG Y X. Unbiased Nonlinear Least Squares Estimations of Short-Distance Equations[J]. Journal of Navigation, 2017, 70（4）： 810-828.
|
| [12] |
薛树强. 大地测量观测优化理论与方法研究[D]. 西安： 长安大学, 2018.
XUE Shuqiang. Research on Geodetic Observation Optimization Theory and Methods[D]. Xi'an： Chang'an University, 2018.
|
| [13] |
马宏伟, 李赫. 温升法测量压气机等熵效率的不确定度[J]. 航空动力学报, 2022, 37（10）： 2242-2252.
MA Hongwei, LI He. Uncertainty of Measuring Isentropic Efficiency of Compressor by Temperature Rise Method[J]. Journal of Aerospace Power, 2022, 37（10）： 2242-2252.
|
| [14] |
陶本藻, 蓝悦明. GIS叠置位置不确定度的统计估计方法[J]. 武汉大学学报（信息科学版）, 2001, 26（2）： 101-104.
TAO Benzao, LAN Yueming. The Statistical Estimation Method of GIS Overlay Uncertainty[J].Geomatics and Information Science of Wuhan University, 2001, 26（2）： 101-104.
|
| [15] |
邹永刚, 翟京生, 刘雁春, 等. 利用不确定度的海底数字高程模型构建[J]. 武汉大学学报（信息科学版）, 2011, 36（8）： 964-968.
ZOU Yonggang, ZHAI Jingsheng, LIU Yanchun, et al. Seabed DEM Construction Based on Uncertainty[J]. Geomatics and Information Science of Wuhan University, 2011, 36（8）： 964-968.
|
| [16] |
刘智敏, 杨安秀, 陈景涛, 等. 基于消声水池的多波束测深不确定度检测方法[J]. 武汉大学学报（信息科学版）, 2018, 43（6）： 908-914.
LIU Zhimin, YANG Anxiu, CHEN Jingtao, et al. Detecting Method of Uncertainty in Multi-beam Echosounding Based on the Anechoic Tank[J]. Geomatics and Information Science of Wuhan University, 2018, 43（6）： 908-914.
|
| [17] |
梁冠辉, 陶常飞, 周兴华, 等. GNSS海洋浮标海面高程动态不确定度研究[J]. 海洋科学进展, 2020, 38（3）： 532-540.
LIANG Guanhui, TAO Changfei, ZHOU Xinghua, et al. Study on Dynamic Uncertainty of Sea-Level Elevation Measured by GNSS Ocean Buoy[J]. Advances in Marine Science, 2020, 38（3）： 532-540.
|
| [18] |
吴燕雄, 滕云田, 吴琼, 等. 船载绝对重力仪测量系统的误差修正模型及不确定度分析[J]. 武汉大学学报（信息科学版）, 2022, 47（4）： 492-500.
WU Yanxiong, TENG Yuntian, WU Qiong, et al. Error Correction Model and Uncertainty Analysis of the Shipborne Absolute Gravity Measurement System[J]. Geomatics and Information Science of Wuhan University, 2022, 47（4）： 492-500.
|
| [19] |
刘园园, 杨健, 赵希勇, 等. GUM法和MCM法评定测量不确定度对比分析[J]. 计量学报, 2018, 39（1）： 135-139.
LIU Yuanyuan, YANG Jian, ZHAO Xiyong, et al. Comparative Analysis of Uncertainty Measurement Evaluation with GUM and MCM[J]. Acta Metrologica Sinica, 2018, 39（1）： 135-139.
|
| [20] |
ÁNGELES HERRADOR M, GONZÁLEZ A G. Evaluation of Measurement Uncertainty in Analytical Assays by Means of Monte-Carlo Simulation[J]. Talanta, 2004, 64（2）： 415-422.
|
| [21] |
曹芸, 陈怀艳, 韩洁. 采用MCM对GUM法测量不确定度评定的验证方法研究[J]. 宇航计测技术, 2012, 32（2）： 75-78.
CAO Yun, CHEN Huaiyan, HAN Jie. Research About Validating GUM Uncertainty Evaluation Using MCM[J]. Journal of Astronautic Metrology and Measurement, 2012, 32（2）： 75-78.
|
| [22] |
WATANABE S I, ISHIKAWA T, YOKOTA Y, et al. GARPOS： Analysis Software for the GNSS-A Seafloor Positioning with Simultaneous Estimation of Sound Speed Structure[J]. Frontiers in Earth Science, 2020, 8： 508.
|
| [23] |
魏明明. 蒙特卡洛法与GUM评定测量不确定度对比分析[J]. 电子测量与仪器学报, 2018, 32（11）： 17-25.
WEI Mingming. Comparative Analysis of Measurement Uncertainty Evaluation with Monte Carlo Method and GUM[J]. Journal of Electronic Measurement and Instrumentation, 2018, 32（11）： 17-25.
|
| [1] | GAO Yang, SHA Hai, CHU Henglin, WANG Mengli. Non-ideality Characteristic Analysis and Receiver Design Constraints Recommendation for BDS B1C and B2a Signals[J]. Geomatics and Information Science of Wuhan University, 2023, 48(4): 587-592. DOI: 10.13203/j.whugis20200568 |
| [2] | LI Jianan, LI Yu, ZHAO Quanhua, JIANG Haonan, HONG Yong. SAR Image Absolute Radiometric Calibration Based on RCS Modeling of Communication Tower[J]. Geomatics and Information Science of Wuhan University, 2021, 46(11): 1746-1755. DOI: 10.13203/j.whugis20210052 |
| [3] | XIE Ping, ZHANG Shuangxi, WANG Haihong, WU Tengfei, CAI Jianfeng. Cross Wavelet Analysis on the Influence of the Three Gorges Dam Impounding on the Reservoir Precipitation[J]. Geomatics and Information Science of Wuhan University, 2019, 44(6): 821-829, 907. DOI: 10.13203/j.whugis20180410 |
| [4] | YANG Jie, CHANG Yonglei, LI Pingxiang, ZHAO Lingli, SHI Lei. Distributed Targets Extraction for SAR Polarimetric Calibration Using Helix Scattering[J]. Geomatics and Information Science of Wuhan University, 2018, 43(12): 2023-2029. DOI: 10.13203/j.whugis20180180 |
| [5] | XU Xiyu, WANG Zhenzhan, XU Ke. Application of Laser Tracking Technology to Absolute Calibration of Space-borne Radar Altimeters[J]. Geomatics and Information Science of Wuhan University, 2017, 42(1): 103-108. DOI: 10.13203/j.whugis20140542 |
| [6] | WENG Yinkan, LI Song, YANG Jinling, YI Hong, WANG Hong, MA Yue. Fast Solution to the RCS of Corner Reflector for the SAR Radiometric Calibration[J]. Geomatics and Information Science of Wuhan University, 2015, 40(11): 1551-1556. DOI: 10.13203/j.whugis20130613 |
| [7] | LIAO Lu, LI Pingxiang, YANG Jie, CHANG Hong. An Improved Method to SAR Polarimetric Calibration Based on Reciprocity Judgement Using Distributed Target[J]. Geomatics and Information Science of Wuhan University, 2015, 40(8): 1042-1047. DOI: 10.13203/j.whugis20140096 |
| [8] | JIN Taoyong, HU Minzhang, JIANG Tao, ZHANG Shoujian. Cross-Calibration and Errors Analysis of Ionosphere Correction in Satellite Altimetry[J]. Geomatics and Information Science of Wuhan University, 2012, 37(6): 658-661. |
| [9] | WEN Xingping, HU Guangdao, YANG Xiaofeng. Cross Calibration of CBERS-02 CCD Image Based on the Pseudo-invariant Reflectance Targets[J]. Geomatics and Information Science of Wuhan University, 2009, 34(4): 409-413. |
| [10] | SUN Zhongmiao, XIA Zheren, LI Yingchun. Cross-Coupling Correction for LaCoste&Romberg Airborne Gravimeter[J]. Geomatics and Information Science of Wuhan University, 2006, 31(10): 883-886. |
| 1. |
严颂华，梅捷，陈永谦，陈璨. 地基GNSS-R公路边坡形变监测实验及误差分析. 武汉大学学报(信息科学版). 2024(01): 100-108 .
| |
| 2. |
邓垦，周佩元，杜兰，蔡巍. 多系统单频紧组合GNSS-R测高方法. 武汉大学学报(信息科学版). 2024(01): 146-155 .
| |
| 3. |
侯金华，贺凯飞，高凡，储倜，吴宇. 岸基BDS-R海面测高及其观测值加权方法. 北京航空航天大学学报. 2024(03): 1015-1026 .
| |
| 4. |
张云，赵乐久，孟婉婷，秦瑾，盛志超，杨树瑚. 北斗卫星反射信号岸基海面高度反演精度的评估. 北京航空航天大学学报. 2023(05): 999-1008 .
| |
| 5. |
桑文刚，刘迎春，何秀凤，王昭然. 库区GNSS-R精细化反演水面高度及其验证研究. 全球定位系统. 2022(01): 43-48 .
| |
| 6. |
邢进，刘思琦，王峰，张国栋，俞永庆，王林峰. 岸基GNSS-R海洋遥感系统设计与实现. 无线电工程. 2021(10): 1104-1109 .
|
Supported by: Beijing Renhe Information Technology Co., Ltd. 
DownLoad: