GNSS伪三角高程测量方法

doi:10.11947/j.AGCS.2025.20250020

测绘学报 ›› 2025, Vol. 54 ›› Issue (7): 1170-1177.doi: 10.11947/j.AGCS.2025.20250020

GNSS伪三角高程测量方法

李建章¹^,²^,³(), 闫浩文¹^,²^,³(), 杨维芳¹^,²^,³, 苏小宁¹^,²^,³

^1.兰州交通大学测绘与地理信息学院，甘肃　兰州　730070
^2.地理国情监测技术应用国家地方联合工程研究中心，甘肃　兰州　730070
^3.甘肃省测绘科学与技术重点实验室，甘肃　兰州　730070

收稿日期:2025-01-14 修回日期:2025-06-26 出版日期:2025-08-18 发布日期:2025-08-18
通讯作者: 闫浩文 E-mail:lijianzhang@mail.lzjtu.cn;haowen2010@gmail.com
作者简介:李建章（1974—），男，博士，副教授，研究方向为高速铁路控制网数据处理。E-mail：lijianzhang@mail.lzjtu.cn
基金资助:
国家自然科学基金(42361073)

GNSS pseudo trigonometric leveling method

Jianzhang LI¹^,²^,³(), Haowen YAN¹^,²^,³(), Weifang YANG¹^,²^,³, Xiaoning SU¹^,²^,³

^1.Faculty of Geomatics, Lanzhou Jiaotong University, Lanzhou 730070, China
^2.National-Local Joint Engineering Research Center of Technologies and Applications for National Geographic State Monitoring, Lanzhou 730070, China
^3.Key Laboratory of Science and Technology in Surveying & Mapping, Gansu Province, Lanzhou 730070, China

Received:2025-01-14 Revised:2025-06-26 Online:2025-08-18 Published:2025-08-18
Contact: Haowen YAN E-mail:lijianzhang@mail.lzjtu.cn;haowen2010@gmail.com
About author:LI Jianzhang (1974—), male, PhD, associate professor, majors in data processing of high speed railway control network. E-mail: lijianzhang@mail.lzjtu.cn
Supported by:
The National Natural Science Foundation of China(42361073)

摘要/Abstract

摘要：

针对传统全站仪三角高程测量精度低的问题，提出了一种GNSS伪三角高程测量方法。本文方法要求在测站周围布设一定数量的辅助点，利用精密水准仪与GNSS接收机建立测站天顶方向（铅垂线反方向）基线向量，并以GNSS基线向量代替传统的全站仪视线，通过向量点积公式获得目标点的天顶距，进而获得两点间三角高程测量值。GNSS伪三角高程测量不要求两点通视，没有大气折光的影响，特别适合跨越障碍物（江河、湖海、山谷等）的长距离高程传递。在长为3.8 km的水准路线上采用精密水准测量和GNSS伪三角高程往返测量进行了对比试验。试验结果表明，两种方法测量结果差异小于二等水准检测限差11.7 mm。

关键词: 伪三角高程测量, GNSS静态测量, 水准测量, 大气垂直折光

Abstract:

A GNSS pseudo trigonometric leveling method is proposed to address the issue of low accuracy in traditional total station trigonometric leveling. This method requires the deployment of a certain number of auxiliary points around the measurement station, the establishment of a zenith direction (opposite direction of vertical line) baseline vector using a precision level and GNSS receiver, and the replacement of the traditional total station line of sight with the GNSS baseline vector. The zenith distance of the target point is obtained through the vector dot product formula, and then the trigonometric leveling measurement value between two points is obtained. GNSS pseudo trigonometric leveling does not require two-point visibility and is not affected by atmospheric refraction, making it particularly suitable for long-distance elevation transmission across obstacles such as rivers, lakes, and valleys. A comparative experiment was conducted on a 3.8 km leveling route using precision leveling measurement and GNSS pseudo trigonometric leveling round-trip measurement. The experimental results showed that the difference between the two methods was less than the second-order leveling detection limit of 11.7 mm.

Key words: pseudo trigonometric leveling, GNSS static measurement, leveling, atmospheric vertical refraction

中图分类号:

P216

李建章, 闫浩文, 杨维芳, 苏小宁. GNSS伪三角高程测量方法[J]. 测绘学报, 2025, 54(7): 1170-1177.

Jianzhang LI, Haowen YAN, Weifang YANG, Xiaoning SU. GNSS pseudo trigonometric leveling method[J]. Acta Geodaetica et Cartographica Sinica, 2025, 54(7): 1170-1177.

图/表 7

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参考文献 26

[1]	蒋利龙. 精密EDM三角高程测量中的折光改正实用方法[J]. 测绘科学, 2006, 31(6): 129-130, 132, 8-9.
	JIANG Lilong. A practicable method of correction for atmospheric refraction in precise EDM trigonometric leveling[J]. Science of Surveying and Mapping, 2006, 31(6): 129-130, 132, 8-9.
[2]	杨立华, 高平和. 三角高程测量中“两差”改正系数C的确定方法[J]. 长春工程学院学报(自然科学版), 2009, 10(3): 83-85.
	YANG Lihua, GAO Pinghe. Method for determine double-difference correction coefficient C in triangle leveling[J]. Journal of Changchun Institute of Technology (Natural Sciences Edition), 2009, 10(3): 83-85.
[3]	刘念, 盛新蒲. 三角高程测量中大气折光影响的分析[J]. 测绘科学, 2012, 37(6): 26-28, 36.
	LIU Nian, SHENG Xinpu. Influence of atmospheric refraction in trigonometric leveling[J]. Science of Surveying and Mapping, 2012, 37(6): 26-28, 36.
[4]	刘新峰. 大气竖直折光对三角高程测量影响因素的研究[J]. 东华理工大学学报(自然科学版), 2016, 39(): 166-168.
	LIU Xinfeng. Study on the influence factors of atmospheric vertical refraction on trigonometric leveling[J]. Journal of East China University of Technology (Natural Science), 2016, 39(): 166-168.
[5]	王欢, 刘成龙, 杨雪峰, 等. 大气折光系数测定及在悬索桥基准索股线形测量中的应用[J]. 测绘通报, 2019(5): 129-133.
	WANG Huan, LIU Chenglong, YANG Xuefeng, et al. Surveying and calculating single-refraction coefficient and using in surveying the linear of datum strand of suspension bridge[J]. Bulletin of Surveying and Mapping, 2019(5): 129-133.
[6]	张正禄, 邓勇, 罗长林, 等. 精密三角高程代替一等水准测量的研究[J]. 武汉大学学报(信息科学版), 2006, 31(1): 5-8.
	ZHANG Zhenglu, DENG Yong, LUO Changlin, et al. Research on precise triangulated height surveying in place of first order leveling[J]. Geomatics and Information Science of Wuhan University, 2006, 31(1): 5-8.
[7]	白少云, 杨琦. 基于MS05AX测量机器人的精密三角高程误差来源与精度分析[J]. 测绘通报, 2015(2): 58-63.
	BAI Shaoyun, YANG Qi. Analysis of errors and precision for precise triangulated height based on MS05AX measuring robots[J]. Bulletin of Surveying and Mapping, 2015(2): 58-63.
[8]	郑德华. 精密测距三角高程精度分析及高程混合网定权[J]. 同济大学学报(自然科学版), 2004, 32(4): 507-512.
	ZHENG Dehua. Accuracy analysis of subtend trigonometric leveling and determination of weight matrix for adjustment of elevation mixed network[J]. Journal of Tongji University (Natural Science), 2004, 32(4): 507-512.
[9]	施一民. 现代大地控制测量[M]. 2版. 北京: 测绘出版社, 2008.
	SHI Yimin. Contemporary geodetic control survey[M]. 2nd ed. Beijing: Surveying and Mapping Press, 2008.
[10]	徐亚明, 施斌, 王代雄, 等. 改进的三角高程法在跨海高程传递中的应用[J]. 测绘通报, 2014(4): 65-67, 78.
	XU Yaming, SHI Bin, WANG Daixiong, et al. An improved trigonometric leveling method for cross-sea elevation transfer[J]. Bulletin of Surveying and Mapping, 2014(4): 65-67, 78.
[11]	吴迪军, 李剑坤, 何广源. 三角高程法超长距离跨海高程传递实验研究[J]. 测绘科学, 2017, 42(12): 195-200.
	WU Dijun, LI Jiankun, HE Guangyuan. Study of extra-long distance sea-crossing elevation transference based on trigonometric levelling[J]. Science of Surveying and Mapping, 2017, 42(12): 195-200.
[12]	王文利, 王斌, 马新莹, 等. 2020年珠峰三角高程测量数据处理与结果分析[J]. 测绘科学, 2022, 47(10): 96-104, 131.
	WANG Wenli, WANG Bin, MA Xinying, et al. 2020 Mount Qomolangma triangle elevation survey data processing and result analysis[J]. Science of Surveying and Mapping, 2022, 47(10): 96-104, 131.
[13]	李志伟, 李克昭, 赵磊杰. 精密三角高程测量在港珠澳青州航道桥中的应用[J]. 测绘工程, 2016, 25(9): 35-39.
	LI Zhiwei, LI Kezhao, ZHAO Leijie. Application of precise trigonometric leveling measurement to the Hong Kong-Zhuhai-Macao bridge Qingzhou channel bridge[J]. Engineering of Surveying and Mapping, 2016, 25(9): 35-39.
[14]	LI J, YAN H. Parameter method data processing for CPⅢ precise trigonometric leveling network[J]. Journal of Geodesy and Geoinformation Science, 2020, 3(3): 67-75.
[15]	张恒, 胡波, 袁长征. 精密三角高程代替二等水准实现跨河水准测量的研究与应用[J]. 测绘通报, 2019(11): 121-125.
	ZHANG Heng, HU Bo, YUAN Changzheng. Research and application of precise trigonometric leveling to replace second-class leveling achieving river-crossing leveling[J]. Bulletin of Surveying and Mapping, 2019(11): 121-125.
[16]	郝旦, 王芬. 自动照准全站仪精密三角高程测量在跨河水准测量中的应用[J]. 测绘通报, 2019(3): 159-162.
	HAO Dan, WANG Fen. Application of precision trigonometric elevation measurement in river-crossing leveling based on autocollimation total station[J]. Bulletin of Surveying and Mapping, 2019(3): 159-162.
[17]	赖鸿斌, 马德英, 梅熙, 等. 山区二等三角高程测量方法的应用研究[J]. 铁道工程学报, 2012, 29(6): 15-19, 23.
	LAI Hongbin, MA Deying, MEI Xi, et al. Application research on the second trigonometric leveling method in mountain area[J]. Journal of Railway Engineering Society, 2012, 29(6): 15-19, 23.
[18]	韩昀, 程新文, 刘成, 等. 精密三角高程代替二等水准测量在山区铁路勘测中的运用[J]. 测绘科学, 2011, 36(4): 106-107.
	HAN Yun, CHENG Xinwen, LIU Cheng, et al. Application of precision triangle elevation instead of second-order leveling in the use of railway survey in the mountains area[J]. Science of Surveying and Mapping, 2011, 36(4): 106-107.
[19]	邹进贵, 朱勇超, 童魁. 精密三角高程测量技术在高海拔山区的应用[J]. 测绘地理信息, 2013, 38(6): 6-9.
	ZOU Jingui, ZHU Yongchao, TONG Kui. Application of precise trigonometric leveling technology at high altitude[J]. Journal of Geomatics, 2013, 38(6): 6-9.
[20]	邹进贵, 徐亚明, 潘正风, 等. 基于TCRP1201全站仪的高程自动测量系统开发与应用研究[J]. 测绘通报, 2007(12): 30-33.
	ZOU Jingui, XU Yaming, PAN Zhengfeng, et al. The research on the development and application of auto-height surveying system based on TCRP1201 total station[J]. Bulletin of Surveying and Mapping, 2007(12): 30-33.
[21]	刘成龙, 杨雪峰, 张阅川. 基于测量机器人的二等高程控制测量新方法[J]. 西南交通大学学报, 2013, 48(1): 69-74.
	LIU Chenglong, YANG Xuefeng, ZHANG Yuechuan. New method of second-order height control surveying based on georobot[J]. Journal of Southwest Jiaotong University, 2013, 48(1): 69-74.
[22]	肖根旺, 许提多, 周文健, 等. 高精度三角高程测量的严密公式[J]. 测绘通报, 2004(10): 15-17, 45.
	XIAO Genwang, XU Tiduo, ZHOU Wenjian, et al. The strict formula of high precise trigonometric leveling[J]. Bulletin of Surveying and Mapping, 2004(10): 15-17, 45.
[23]	程效军, 鲍峰, 顾孝烈. 测量学[M]. 5版. 上海: 同济大学出版社, 2016.
	CHENG Xiaojun, BAO Feng, GU Xiaolie. Elementary surveying[M]. 5th ed. Shanghai: Tongji University Press, 2016.
[24]	潘正风, 程效军, 成枢, 等. 数字地形测量学[M]. 武汉: 武汉大学出版社, 2015.
	PAN Zhengfeng, CHENG Xiaojun, CHENG Shu, et al. Digital topographic survey[M]. Wuhan: Wuhan University Press, 2015.
[25]	张正禄. 工程测量学[M]. 2版. 武汉: 武汉大学出版社, 2013.
	ZHANG Zhenglu. Engineering surveying[M]. 2nd ed. Wuhan: Wuhan University Press, 2013.
[26]	国家质量监督检验检疫总局, 中国国家标准化管理委员会. 国家一、二等水准测量规范：GB/T 12897—2006E[S]. 北京: 中国标准出版社, 2006.
	General Administration of Quality Supervision, Inspection and Quarantine of the People's Republic of China, Standardization Administration of the People's Republic of China. Specifications for the first and second order leveling: GB/T 12897—2006E[S]. Beijing: Standards Press of China, 2006.

点号	纬度	经度	大地高/m
E	36°07′44.359 04″N	103°43′34.945 72″E	16 59.894 90
K0D1	36°07′46.008 40″N	103°43′32.565 63″E	1 659.999 00
K0D2	36°07′45.503 66″N	103°43′35.870 95″E	1 660.485 90
K0D3	36°07′43.282 04″N	103°43′38.833 00″E	1 660.631 00
K0D4	36°07′41.589 45″N	103°43′36.472 20″E	1 659.497 90
K0D5	36°07′42.348 62″N	103°43′32.256 22″E	1 658.404 20
F	36°09′31.171 04″N	103°43′11.497 58″E	1 754.421 20
K0H1	36°09′30.509 53″N	103°43′08.706 11″E	1 753.236 89
K0H2	36°09′32.485 81″N	103°43′09.251 00″E	1 754.929 80
K0H3	36°09′35.220 34″N	103°43′12.667 73″E	1 757.545 80
K0H4	36°09′33.847 61″N	103°43′15.185 55″E	1 757.535 67
K0H5	36°09′30.131 09″N	103°43′13.794 09″E	1 754.902 51

测段号	高差	测段号	高差
E-K0D1	0.105 10	F-K0H1	－1.183 10
E-K0D2	0.590 20	F-K0H2	0.509 60
E-K0D3	0.732 30	F-K0H3	3.123 90
E-K0D4	－0.397 70	F-K0H4	3.112 00
E-K0D5	－1.488 90	F-K0H5	0.479 50

基线名	ΔX	ΔY	ΔZ
E-K0D1	64.943 30	－15.013 16	41.087 32
E-K0D2	－17.435 90	－25.590 33	28.388 39
E-K0D3	－98.931 02	－3.952 88	－26.891 12
E-K0D4	－48.879 61	39.894 30	－68.977 13
E-K0D5	56.689 40	51.457 18	－50.053 20
F-K0H1	64.947 50	28.242 25	－16.467 29
F-K0H2	60.239 00	－9.913 80	32.727 79
F-K0H3	－10.950 47	－78.497 92	100.798 64
F-K0H4	－78.027 48	－69.167 95	66.629 02
F-K0H5	－60.266 59	4.761 39	－25.885 99

序号	水准线路长/km	GNSS伪三角高程测量高差/m				精密水准测量高差/m	较差/mm	二等水准测量限差/mm
序号	水准线路长/km	往测	反测	平均	中误差	精密水准测量高差/m	较差/mm	二等水准测量限差/mm
1	2.5	65.935 3	－66.819 6	66.377 5	0.004 2	66.381 0	－3.5	9.4
2	2.5	65.933 1	－66.817 4	66.375 3	0.003 6	66.381 0	－5.7	9.4
3	3.8	95.329 1	－97.082 9	96.206 0	0.004 1	96.210 6	－4.6	11.7
4	3.8	95.335 0	－97.089 0	96.212 0	0.003 9	96.210 6	1.4	11.7

GNSS伪三角高程测量方法

GNSS pseudo trigonometric leveling method

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