﻿ 高程系统定义分析与高精度GNSS代替水准算法
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The Analysis of Height System Definition and the High Precision GNSS Replacing Leveling Method
ZHANG Chuanyin, JIANG Tao, KE Baogui, WANG Wei
Chinese Academy of Surveying and Mapping, Beijing 100830, China
Foundation support: The National Natural Science Foundation of China (Nos. 41374081;41674024)
First author: ZHANG Chuanyin(1968—), male, PhD, researcher, majors in geodesy. E-mail: zhangchy@casm.ac.cn
Corresponding author: JIANG Tao, E-mail: jiangtao@casm.ac.cn
Abstract: Based on the definition of height system, the gravitational equipotential property of height datum surface is discussed in this paper, differences of the heights at ground points that defined in different height systems are tested and analyzed as well. A new method for replacing leveling using GNSS is proposed to ensure the consistency between GNSS replacing leveling and spirit leveling at mm accuracy level. The main conclusions include:① For determining normal height at centimeter accuracy level, the datum surface of normal height should be the geoid. The 1985 national height datum of China adopts normal height system, its datum surface is the geoid passing the Qingdao zero point.② The surface of equi-orthometric height in the near earth space is parallel to the geoid. The combination of GNSS precise positioning and geoid model can be directly used for orthometric height determination. However, the normal height system is more advantageous for describing the terrain and relief.③ Based on the proposed method of GNSS replacing leveling, the errors in geodetic height affect more on normal height result than the errors of geoid model, the former is about 1.5 times of the latter.
Key words: GNSS replacing leveling     height system     height datum surface
1 若干定义 1.1 正(常)高的力学定义

(1)

(2)

(3)

1.2 解析正高与Molodensky正常高

1.2.1 解析正高

(4)

(5)

1.2.2 Molodensky正常高

 图 1 Molodensky正常高的几何意义 Fig. 1 Geometric interpretation for Molodensky normal height

U0=W0，由Molodensky基本条件U0-UQ=W0-W

(6)

(7)

(8)

2 高程基准面的重力等位性质

2.1 由高程系统定义分析高程基准面的等位性质

2.2 非地面点的高程异常及其正常高起算面

(9)

A点不在地面上，如在地面下方或低空高度上，Δζ的绝对值还会进一步增大。因此，将似大地水准面作为正常高的起算面是不严密的。

3 不同类型高程系统地面点高程之间的差别测试分析 3.1 地面点正常高h*与Molodensky正常高hγ的差别

(10)

ζ=-50 m，h*=6000 m，则h*-hγ=-0.308 6×10-6×50×6000 m≈-0.09 m。Molodensky正常高hγ与正常高h*的差异在中国大陆东部地区约为0~3 cm，中部2~5 cm，西部4~10 cm。

 图 2 地面点Molodensky正常高hγ与正常高h*之差 Fig. 2 Differences between Molodensky normal height hγ and normal height h* at ground points

(11)

3.2 解析正高h′与H-N的差别测试分析

 图 3 GNSS直接代替水准测定的正高h与解析正高h′的差别 Fig. 3 Differences between orthometric height h determined by GNSS replacing leveling and actual orthometric height h′

3.3 Molodensky正常高hγH-N的差别测试分析

(12)

 图 4 Molodensky正常高hγ与(H-N)的差别 Fig. 4 Differences between Molodensky normal height hγ and (H-N)

(13)
4 不同类型高程的水准面不平行性 4.1 GNSS代替水准中水准面不平行改正的通用形式

(14)

(15)

G=g′时，hG=c/G=c/g′=h′为解析正高，此时∈=c/g′-H+N=h′-H+N=0。因此在GNSS代替水准中，解析正高h′的水准面不平行改正恒等于零。

G=gHγ*γG时，∈≠0。因此在GNSS代替水准中，Helmert正高hH、正常高h*、Molodensky正常高hγ和力高hd(力高中G为常量，力高系统可看成是与重力位数系统等价的一种特殊类型正常高系统)，都需要增加水准面不平行改正∈。

(16)
4.2 地面点正高与正常高力学性质的差异

 图 5 重力位对比图 Fig. 5 Gravitational potential contrast

5 GNSS代替水准测定正常高的新算法 5.1 GNSS代替水准测定近地点正常高的统一算法

(17)

(18)

5.2 高精度GNSS代替水准测定正常高的误差分析

(19)

(20)

(21)

(22)

≈0.308 6×10-5s-2ζ=-70 m，γ-≈9.8 m2/s2，则，因此式(22) 右边第2项可以忽略，即

(23)

(24)
6 小结

(1) 当精度要求达到厘米级水平时，正常高的基准面也应是大地水准面。中国国家1985高程基准采用正常高系统，其高程基准面是过青岛零点的大地水准面。

(2) 近地空间中等解析正高面与大地水准面平行，GNSS代替水准能直接测定地面点的解析正高，但正常高系统更有利于描述地势和地形起伏。

(3) 本文给出的GNSS代替水准测定近地点正常高算法，大地高误差对正常高结果的影响比大地水准面误差大，前者影响约为后者的1.5倍。

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http://dx.doi.org/10.11947/j.AGCS.2017.20170058

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#### 文章信息

ZHANG Chuanyin, JIANG Tao, KE Baogui, WANG Wei

The Analysis of Height System Definition and the High Precision GNSS Replacing Leveling Method

Acta Geodaetica et Cartographica Sinica, 2017, 46(8): 945-951
http://dx.doi.org/10.11947/j.AGCS.2017.20170058