Methodology for local correction of the heights of global geoid models to improve the accuracy of GNSS leveling

At present,one of the methods used to determine the height of points on the Earth’s surface is Global Navigation Satellite System(GNSS)leveling.It is possible to determine the orthometric or normal height by this method only if there is a geoid or quasi-geoid height model available.This paper proposes the methodology for local correction of the heights of high-order global geoid models such as EGM08,EIGEN-6C4,GECO,and XGM2019e_2159.This methodology was tested in different areas of the research field,covering various relief forms.The dependence of the change in corrected height accuracy on the input data was analyzed,and the correction was also conducted for model heights in three tidal systems:"tide free","mean tide",and"zero tide".The results show that the heights of EIGEN-6C4 model can be corrected with an accuracy of up to 1 cm for flat and foothill terrains with the dimensionality of 1°×1°,2°×2°,and 3°×3°.The EGM08 model presents an almost identical result.The EIGEN-6C4 model is best suited for mountainous relief and provides an accuracy of 1.5 cm on the 1°×1°area.The height correction accuracy of GECO and XGM2019e_2159 models is slightly poor,which has fuzziness in terms of numerical fluctuation.

Refining geoid and vertical gradient of gravity anomaly

We have derived and tested several relations between geoid （N） and quasi-geoid （~） with model validation. The elevation correction consists of the first-term （Bouguer anomaly） and second-term （vertical gradient of gravity anomaly）. The vertical gradient was obtained from direct measurement and terrain calcula- tion. The test results demonstrated that the precision of geoid can reach centimeter-level in mountains less than 5000 meters high.

Review of the Research Progress on Static Earth Gravity Field and Vertical Datum in China during 2019—2023

The contribution presents the representative research progress on global static gravity field modeling,regional geoid/quasigeoid determination,vertical datum study,as well as the theory,algorithm and software for gravity field study in China from 2019 to 2023,which are the highlights of the chapter 6“Progress in Earth Gravity Model and Vertical Datum”in the“2019—2023 China National Report on Geodesy”that submitted to the International Association of Geodesy(IAG).In addition,suggestions are proposed to promote the research in the fields of earth gravity field,geoid/quasigeoid and vertical datumin China according to trends of international geodesy and related disciplines.

Calculation of geoid undulations and gravity anomaliesin the Northwest Pacific by using the Topex/Poseidonand Geosat altimeter data

The geoid undulations in the Northwest Pacific were calculated by usingtheTopex/Poseidon and Geosataltimeter data. Firstly the bias between two types of the altimeter data was removed and the geoid undulations in theNorthwest Pacific were acquired by a long wave bias diminishing model with a resolution of 30 km and precision of 14cm. Then an algorithm of inversion of gravity anomalies was derived , and the gravity anomalies in the East China Seawere calculated by using the algorithm and the geoid undulations. The rms of difference between the in situ measure-ments the gravity anomalies from altimeter data was 3 .8× 10-5 m/s2. A method to colculate the gravity anomaliesin a larger area was developed which combined gravity anomalies in four subregions overlapping each other into one data set in a larger region. The error analysys shaws that the model and result of the inversion of gravity anomalies were reliable.

Determination of Antarctic geoid by using global gravity field

With Chinese latest global gravity field model WDM94, the authors provide the geoid height and mean free air gravity anomaly of Antarctica (The range of latitude is from -60° to -90°). In order to conclude and analyze the characters of Antarctic geoid roundly, the authors collect the latest oversea global gravity field model OSU91 (to degree and order 360) and JGMOSU (to degree and order 360), get the corresponding geoid height and mean free air gravity anomaly. The results are compared with the results got from WDM94, thus we get the difference. The standard deviation of geoid height between WDM94 and OSU91 is ±1.90 m;the deviation of geoid between WDM94 and JGMOSU is ±2.09 m. The standard deviation of mean gravity anomaly are ±8.97 mGal and ±9.32 mGal respectively. [WT9.HZ]

Analysis of the merged quasi-geoid of neighbouring areas

Employing the merged quasi-geoid, we analyses the causes of systematic errors in modelling of quasigeoid of neighbouring areas in the paper, and the efficient method is introduced to improve the accuracy of quasi-geoid. First, the systematic error is weakened with the moving window method applied to established quasi-geoids in two adjacent regions, and the accuracy of the merged quasi-geoid in the stitching region is checked using the measured GPS benchmark data; Second, the whole quasi-geoid is recomputed with data obtained from two adjacent regions if the accuracy of the quasi-geoid obtained from the first step in the stitching region is low; Finally, the quasi-geoids in two adjacent regions are recomputed respectively using GPS benchmark data of own region and adjacent region with the same solution if the accuracy of whole quasi-geoid obtained from the second step also is low. Actual data sets from Sichuan Province and Chongqing City are employed to test the moving window method. It is shown that the quasi-geoid models with high resolution and accuracy were obtained.

Direct regional quasi-geoid determination using EGM2008 and DEM:A case study for China's Mainland and its vicinity areas

Earth＇s gravity model（EGM） helps people better determine the figure of Earth, which is generally represented by a global geoid. For a considerable amount of practical applications, people use quasi-geoid to approximate the geoid, thus the quasi-geoid is also treated as an important height datum. In this study we revisit the method to directly determine regional quasi-geoid using EGM and digital elevation model（DEM）, on the basis of Molodensky theory. According to the method we obtain a 50 50quasi-geoid for China's Mainland and its vicinity areas, based on the EGM2008 gravitational potential model and the Shuttle Radar Topography Mission（SRTM） DEM model. By comparing height anomalies derived from EGM2008 with observations at 70 GPS/leveling points in areas including northwest,mid-west, mid-east and southeast of China, we find that the 50 50EGM2008 quasi-geoid well fits the GPS/leveling results, with average deviations less than 10 cm for the selected areas in east China（with mainly plain topography） and ~20 cm for the selected areas in west China（highland or mountainous areas）. We also discuss a few technical issues for directly determining height anomalies based on EGM and DEM, under the frame of Molodensky theory.

基于准零刚度机构与间接力控制的恒拉力系统设计与分析

现有的悬吊式微低重力模拟恒拉力系统常采用力传感器数值作为反馈直接控制系统,但实际情况下力作为反馈信号常会产生突变,影响系统控制精度。为了改进刚性控制策略下系统稳定性差与大冲击条件下力误差大的状况,文中设计了包含准零刚度机构的恒拉力系统,通过控制准零刚度机构长度间接对恒拉力系统输出拉力进行控制。对准零刚度机构进行受力分析,明确影响准零刚度机构性能的关键指标和准零刚度机构的工作行程区间,建立恒拉力系统动力学模型,设计控制系统。为了验证系统控制精度与系统抗干扰性能,进行了动力学联合仿真对设计进行验证,仿真结果表明:该恒拉力系统拉力的控制误差可控制在2%以内,且具有较好的鲁棒性。

湖南省似大地水准面模型对比研究

正常高系统是以似大地水准面为基准的高程系统,也是中国目前采用的高程系统。随着GNSS定位技术的广泛应用,已能在10-7~10-9的精度量级上获得测量点的平面位置,但是却一直未能以相应的精度求解点的高程值。因此,通过建立高精度、高分辨率的区域似大地水准面模型提升高程测量的精度,成为重要的技术手段。该文通过对湖南省2007似大地水准面模型后期各似大地水准面模型的对比研究,找到模型的差异,并对差异较大的地区进行特征分析,查找形成差异的原因,可为全省二、三等水准网测量和大地水准面再精化工作提供参考。

EGM2008模型计算重力扰动位及相关量的方法研究

地球重力场模型EGM2008提供了计算全球高分辨率和高精度重力场相关参量的可能。本文采用球谐综合的方法,对重力扰动位、重力异常、大地水准面高等物理量的计算步骤和方法进行了研究和分析,并编制了相应的计算程序基于EGM2008无潮模型和零潮模型对以上参量进行了计算,同NGA发布的计算程序计算的结果进行了比对,验证了计算的方法正确性和可靠性。

喀斯特地貌地区GNSS高精度静态测量方案

喀斯特地貌地区控制点的高精度测量对区域地形调绘和水文测验均有重要意义。在喀斯特地貌地区传统测量困难,CORS站点稀疏,静态测量多路径效应严重,单点GNSS静态测量无法满足精度要求。为此,针对布设的237个GNSS E级控制点,设计出相应的GNSS静态测量方案以提高测量精度。该方案在测区中间添加1个全天候观测的固定基准站,测量时再添加1个移动基准站,与其它N个流动站进行同步测量,然后结合6个连续运行的CORS站点进行解算。最终静态测量的结果符合测量标准要求,其中控制检核点X坐标平均中误差为0.007 m,Y坐标平均中误差为0.018 m。测量的大地高结合广西似大地水准面精化模型进行精化后,控制点高程测量结果与测出的水准高程进行对比,较差中误差为0.024 m,且所有点较差都低于限差。“1+1+N”静态测量模式显著提高了喀斯特地貌地区测量精度,通过似大地水准面精化模型精化后的结果符合四等水准测量高程的要求。

2020年珠峰高程测量与确定流程解析

着重解析2020年珠峰高程测量数据处理流程。首先详细介绍用于计算珠峰峰顶海拔高的2个重要数值的计算过程,然后给出中尼联合发布的基于国际高程参考系统(international height reference system,IHRS)的珠峰高程成果(8 848.86 m),最后总结本次珠峰高程测量成果特点,阐述其精度与可靠性。

长距离跨海高程基准传递方法研究及广西北部湾工程验证

针对陆海基准高程传递过程中传统方法的测量精度受海岛与陆地距离、陆海环境等因素的影响,对海域内的多个不连续岛屿进行测量时过程较为复杂的问题,本文提出了利用高精度似大地水准面进行高程传递的方法,研究了误差积累因素,给出了高程传递的理论模型及具体的技术流程。在北部湾海域,利用该方法将1985国家高程基准由陆地传递到距离北海市40 km的涠洲岛和斜阳岛上,传递后GNSS水准点间的高程差与涠洲岛二等水准测量成果的独立高程差均优于±4.1 cm,为全国范围离岛高程传递工程提供了实践参考。

GNSS观测值类型对短基线大地高差精度的影响分析

基于某市C级网的观测数据,分析了采用不同原始观测值和无电离层组合等四种不同基线解算策略对短基线大地高差精度的影响,结果发现,仅通过基线较差分析难以评估不同解算策略的基线处理精度.为此,联合二等水准测量和似大地水准面模型对基线结果进行了外部检核,发现采用无电离层组合的结果中大地高差存在约2.2 cm的系统差,而使用原始双频观测值的结果精度最高,是短基线处理的最佳策略.

惠州市国产北斗化平台实时定位精度测试分析

惠州市连续运行卫星定位服务系统(HZCORS)在2022年完成了国产北斗化升级改造工作,实现了基准站接收机全面支持北斗三号卫星导航系统即北斗三号(BDS-3)数据,且新的国产北斗化平台(简称“新平台”)具备支持北斗三号数据兼容其他卫星系统数据的处理能力,并支持实时播发1985国家高程(简称“85高”)。作为惠州市现代测绘基准体系的重要支撑,新平台投入使用前的测试显得尤为重要。测试结果表明:①新平台平面和高程的实时定位精度较以往有所提高。②新平台分别使用惠州市似大地水准面模型和广东省似大地水准面模型采集得到的高程成果,契合度均较好。③新平台的平均时间可用性为96.48%,优于规范指标的95%。

陆海交界处基于重力场模型解算的大地水准面精度分析--以山东省为例

大地水准面作为高程基准和深度基准相互转换的中间基准面,其精度对基准转换效果至关重要。以山东省为例,本文分别使用目前较优的三种超高阶重力场模型EGM2008、EIGEN-6C4和SSG-UGM-2解算陆海交接处的大地水准面,分析其在山东省内的分布特征。利用收集到的GNSS水准点数据对三种重力场模型解算结果进行精度分析。研究发现,基于EIGEN-6C4模型的解算结果是三种模型中最符合实际情况的,同时使用85高程基准面重力位解算结果精度更高。

广东省高程异常坡度坡向分析

为了确定高程异常的空间变化情况,更好地指导全球导航卫星系统高程测量、数字高程基准维持等生产实践,提出利用数字高程模型(digital elevation model,DEM)理论研究似大地水准面的坡度、坡向等形态特征方法,建立高程异常与水平距离和方位之间的联系。对广东省DEM,以及不同精度、分辨率的似大地水准面提取坡度、坡向后进行了重分类和统计分析比较。结果表明,广东省似大地水准面坡度、坡向上都存在一个主要数值,不同于普通DEM特征;整体上以坡度0.0020°,沿坡向297°逐渐下降;该方向上高程异常值变化率约3.49 cm/km;似大地水准面的坡度、坡向与其分辨率和精度都密切相关;坡度值受分辨率的影响更大,受精度的影响较小;分辨率的粗略化会降低其坡度值。

似大地水准面与大地水准面转换分析

传统的似大地水准面与大地水准面近似转换在地形复杂的山区难以满足精度需求。本文基于似大地水准面与大地水准面严密转换方法,计算珠峰地区转换改正数值大小,分析似大地水准面与大地水准面转换的空间变化。结果表明,严密方法计算的转换值变化范围为-3.270~-0.119 m,其中地形位差改正极值达到1.272 m,重力梯度改正极值达到-0.138 m,这两项改正影响幅度较大,在山区需顾及;严密方法计算和近似计算结果都与地形高度具有一定的相关性,但前者结果相较于后者更为平滑,在布格重力异常与地形变化的共同影响下,严密方法局部特征与地形高度负相关。

特大型跨海桥梁工程似大地水准面精化实践与分析

特大型跨海桥梁工程似大地水准面精化应用实践极少。为解决风浪大、长距离等复杂海况下海上施工的高精度定位和放样等难题,本文对某特大型跨海桥梁工程进行高精度似大地水准面精化,基于地形、重力数据等基础数据和先进的理论模型,采用应用广泛的第二类Helmert聚集法计算得到似大地水准面模型。经实践验证,该似大地水准面模型精度达±0.008 m,应用实测平均精度为±0.0118 m,成果满足设计精度要求;同时,通过将格网模型植入该桥梁建设所建立的工程用连续运行基准站(CORS)系统内,方便大桥日常建设中采用网络实时动态定位(RTK)实现高精度的施工放样,提高工作效率,为大桥顺利建设提供重要的基础技术支持和保障。

似大地水准面精化工程标准化探讨

我国开展区域似大地水准面精化工程已经超过20年,目前多个省市都开展了高精度似大地水准精化工作,但在标准化工作上只有《区域似大地水准面精化基本技术规定》一个国家标准规定了工程实施的技术要求,而在成果检验、成果服务应用等方面还没有出台相应标准,对应用影响较大。本文结合各省市开展此类工作实际,对应用方面存在的问题进行分析,并提出相关标准建设的基本思路。