Transformation of coordinates between two horizontal geodetic datums

The following topics are discussed in this paper: the geocentric coordinate system and its different realizations used in geodetic practice; the definition of a horizontal geodetic datum (reference ellipsoid) and its positioning and orientation with respect to the geocentric coordinate system; positions on a horizontal datum and errors inherent in the process of positioning; and distortions of geodetic networks referred to a horizontal datum. The problem of determining transformation parameters between a horizontal datum and the geocentric coordinate system from known positions is then analysed. It is often found necessary to transform positions from one horizontal datum to another. These transformations are normally accomplished through the geocentric coordinate system and they include the transformation parameters of the two datums as well as the representation of the respective network distortions. Problems encountered in putting these transformations together are pointed out.     

The parallel sum of matrices and its application in geodetic adjustments

Summary . It is well known that for the comparison and combination of geodetic networks their heterogeneous datum definitions are well to be considered. Various algorithms have been developed for this purpose. As an alternative concept to deal with hybrid datum problems, the operator parallel sum of matrices is introduced in this paper. To begin with, a definition is given and some basic properties are explained. To demonstrate the usefulness of the operator, two practical applications are given. The first deals with the estimation of parameters describing the deformation of two networks which are to be compared to each other. The second one treats the estimation of parameters representing the heterogeneous datum definitions of two networks which are to be merged into a hybrid network. It will be shown that – regardless of the datum definitions of the preadjusted individual networks – the parallel sum of matrices can be used to simplify the algorithms applied for the estimation of those parameters. Received 15 December 1995; Accepted 24 September 1996     

Robust estimation of geodetic datum transformation

The robust estimation of geodetic datum transformation is discussed. The basic principle of robust estimation is introduced. The error influence functions of the robust estimators, together with those of least-squares estimators, are given. Particular attention is given to the robust initial estimates of the transformation parameters, which should have a high breakdown point in order to provide reliable residuals for the following estimation. The median method is applied to solve for robust initial estimates of transformation parameters since it has the highest breakdown point. A smooth weight function is then used to improve the efficiency of the parameter estimates in successive iterative computations. A numerical example is given on a datum transformation between a global positioning system network and the corresponding geodetic network in China. The results show that when the coordinates are contaminated by outliers, the proposed method can still give reasonable results. Received: 25 September 1997 / Accepted: 1 March 1999     

Generalized inner constraints for geodetic network densification problems

The estimated coordinates from a minimum-constrained (MC) network adjustment are generally influenced by two different error sources, that is the data noise from the available measurements and the so-called datum noise due to random errors in the fiducial coordinates that are used for the datum definition with regard to an external reference frame. Although the latter source does not affect the estimable characteristics of a MC solution, it still contributes a datum-related noise to the estimated positions which reflects the uncertainty of the coordinate system itself for the adjusted network. The aim of this paper is to develop a new type of MCs which minimizes both of the aforementioned effects in the final coordinates of an adjusted network. This particular problem has not been treated in the geodetic literature and the solution which is presented herein offers an elegant unification of the classic inner constraints into a more general framework for the datum choice problem of network optimization theory. Furthermore, the findings of our study provide a useful and rigorous tool for frame densification problems by means of an optimal MC adjustment in geodetic networks.     

On rotation of frames and physical vectors: an exercise based on plate tectonics theory

The mathematical interaction between the simultaneous rotation of both a coordinate frame and a set of physical vectors in that frame is covered and theoretically and empirically explained. A practical example related to the secular motion of the pole determined using recent GPS results is addressed. A least-squares adjustment is introduced to determine a possible displacement of the geodetic north pole of the frame caused by plausible changes in the coordinates of the observing stations defining the frame due to the rotation of the plates on which these stations are located. Two examples of GPS networks are investigated both referred to the latest definition of the IGS08 geodetic frame. The positioning and velocities of the points were exclusively obtained using GPS data as published by the International GNSS Service (IGS). The first case comprises the complete GPS/IGS network of global stations; the second one assumes the closest GPS/IGS stations to the now discontinued International Latitude Service network. The results of this exercise hints at the possibility that the secular global rotation of the frame caused by plate rotations should be accounted for in order to rigorously determine the true absolute velocities referred to the IGS frame before the actual velocities of the rotation of the plates using GPS observations are published.     

高程系统定义分析与高精度GNSS代替水准算法

从高程系统定义出发,探讨高程基准面的重力等位性质,测试分析不同类型高程系统地面点高程之间的差异,考察GNSS代替水准与实际水准测量成果的一致性,进而提出新的GNSS代替水准算法。主要结论包括:(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。     

区域与全球高程基准差异的确定

全球高程基准统一是继全球大地测量坐标系及其参考基准统一之后,大地测量学科面临和亟待解决的一个重要问题,也是全球空间信息共享与交换的基础。本文针对区域高程基准与全球高程基准间基准差异确定的理论、方法及实际问题开展研究。利用物理大地测量高程系统的经典理论方法,给出了高程基准差异的定义,并推导了计算基准差异的严密公式,该公式可将高程基准差异确定的现有3种方法统一起来。在此基础上,分析顾及了不同椭球参数对于计算基准差异的影响及量级,同时,高程异常差法还需考虑全球高程基准重力位与模型计算大地水准面位值不一致引起的零阶项改正。利用青岛原点附近152个GPS水准点数据,分别选择GRS80、WGS-84、CGCS2000参考椭球以及EGM2008、EIGEN-6C4、SGG-UGM-1模型,采用位差法和高程异常差法,确定了我国1985高程基准与全球高程基准的差异。其中,EIGEN-6C4模型计算的我国高程基准与WGS-84参考椭球正常重力位U0定义的全球高程基准之间的差异约为-23.1cm。也就是说,我国高程基准低于采用WGS-84参考椭球正常重力位U0定义的全球高程基准,当选取基于平均海面确定的Gauss-Listing大地水准面作为全球高程基准时,我国1985高程基准高于全球基准约21.0cm。从计算结果还可看出,当前重力场模型在青岛周边不同GPS/水准点的精度差别依然较大,这会导致选择不同数据对确定我国85国家高程基准与全球基准之间的差异影响较大,因此,若要实现厘米级精度区域高程基准与全球高程基准的统一,全球重力场模型的精度和可靠性还需要进一步提高。     

江门市高精度GNSS控制网数据处理技术研究

针对华南沿海城市的高精度的CGCS2000大地基准建设要求,分别从基线解算与网平差计算两方面的策略进行探讨分析,建立以江门市为例的高精度大地基准框架。结果表明采用高精度的GAMIT/GLOBK数据处理软件,设置较小的采样间隔和增加一定的观测时长,能为高精度的CGCS2000大地基准建设提供借鉴参考,也为后续的似大地水准面精化提供高精度的大地基准数据基础。     

综合PNT体系及其关键技术

综合定位、导航与授时(PNT)的核心是不过分依赖GNNS,采用一切可以应用的PNT信息源实施全空域目标定位、导航与授时服务。本文分析了综合PNT需求,论述了综合PNT的基本定义和基本概念,分析了综合PNT所涉及的信息源,论述了综合PNT关联的核心技术,包括多源PNT传感器集成技术、多源PNT的数据融合技术。强调指出,综合PNT体系的信息源必须是"基于不同物理原理的多源信息";综合PNT的运控系统应该基于云平台,实现用户志愿者共同测控;用户终端或传感器必须"深度集成、低功耗";PNT服务信息必须是"智能融合或自适应融合"。综合PNT系统应该在统一时空基准下,满足服务的可用性、精确性、可靠性、连续性和稳健性。     

Future global SLR network evolution and its impact on the terrestrial reference frame

Satellite laser ranging (SLR) is an important technique that contributes to the determination of terrestrial geodetic reference frames, especially to the realization of the origin and the scale of global networks. One of the major limiting factors of SLR-derived reference frame realizations is the datum accuracy which significantly suffers from the current global SLR station distribution. In this paper, the impact of a potential future development of the SLR network on the estimated datum parameters is investigated. The current status of the SLR network is compared to a simulated potential future network featuring additional stations improving the global network geometry. In addition, possible technical advancements resulting in a higher amount of observations are taken into account as well. As a result, we find that the network improvement causes a decrease in the scatter of the network translation parameters of up to 24%, and up to 20% for the scale, whereas the technological improvement causes a reduction in the scatter of up to 27% for the translations and up to 49% for the scale. The Earth orientation parameters benefit by up to 15% from both effects.     

Changes of spheroid and of datum

Summary A datum change between two geodetic systems with points in common may be derived in three stages; slight adjustments of coordinates to make the networks of common points geometrically similar in the two systems; a scale factor to make them geometrically congruent; finally, an orthogonal transformation to swing them into coincidence. The geometrical concept is developed of a “datum screw”, not arbitrarily chosen as is the “origin” or “datum point” of a geodetic survey, but intrinsic to the geometry. The conditions under which it degenerates to a simple “datum shift” are discussed. Differential and other formulae for changes of spheroid and of datum are given, together with a set of tables of coefficients.     

Height datum definition,height datum connection and the role of the geodetic boundary value problem

Vertical datum definition is identical with the choice of a potential (or height) value for the fundamental bench mark. Also the connection of two adjacent vertical datums poses no principal problem as long as the potential (or height) value of two bench marks of the two systems is known and they can be connected by levelling. Only the unification of large vertical datums and the connection of vertical datums separated by an ocean remains difficult. Two vertical datums can be connected indirectly by means of a combination of precise geocentric positions of two points, as derived by space techniques, their potential (or height) value in the respective height datum and their geoid height difference. The latter requires the solution of the linear geodetic boundary value problem under the assumption that potential and gravity anomalies refer to a variety of height datums. The unknown off-sets between the various datums appear in the solution inside and outside the Stokes integral and can be estimated in a least squares adjustment, if geocentric positions, levelled heights and adequate gravity material are available for all datum zones. The problem can in principle also be solved involving only two datums, in case a precise global gravity field becomes available purely from satellite methods.     

An evaluation of some systematic error sources affecting terrestrial gravity anomalies

Terrestrial free-air gravity anomalies form a most essential data source in the framework of gravity field determination. Gravity anomalies depend on the datums of the gravity, vertical, and horizontal networks as well as on the definition of a normal gravity field; thus gravity anomaly data are affected in a systematic way by inconsistencies of the local datums with respect to a global datum, by the use of a simplified free-air reduction procedure and of different kinds of height system. These systematic errors in free-air gravity anomaly data cause systematic effects in gravity field related quantities like e.g. absolute and relative geoidal heights or height anomalies calculated from gravity anomaly data. In detail it is shown that the effects of horizontal datum inconsistencies have been underestimated in the past. The corresponding systematic errors in gravity anomalies are maximum in mid-latitudes and can be as large as the errors induced by gravity and vertical datum and height system inconsistencies. As an example the situation in Australia is evaluated in more detail: The deviations between the national Australian horizontal datum and a global datum produce a systematic error in the free-air gravity anomalies of about −0.10 mgal which value is nearly constant over the continent     

我国海洋大地测量基准与海洋导航技术研究进展与展望

领海是国家主权的重要组成部分,国家空间基准和位置服务应该覆盖陆地和海洋。以2000国家大地坐标系和2000国家重力基准为代表,我国已在陆地建成了较为完善的大地测量基准。然而,现有国家空间基准和重力基准未能有效覆盖海洋,海洋大地测量基准和海洋导航技术已严重滞后于国家社会经济发展新形势和国防战略需求。本文主要论述了我国海洋大地测量基准与海洋导航技术的研究现状,梳理了我国海洋大地测量基准所涉及的关键技术,分析了近期及未来我国自主发展海洋大地测量基准与海洋导航技术的主要方向。     

现代大地测量参考系统

概述现代大地测量参考系统的定义及不同参考系统之间的关系.主要讨论我国当代大地测量界常使用的3种用以表示几何位置的参考系统1980年国家大地坐标系、全球大地测量系统 1984 (WGS 84)、国际地球参考系统(ITRS),和一种用以表示物理位置,高程的参考系统1985年国家高程基准.并讨论大地测量中框架和基准的概念.     

全球高程基准研究进展

建立统一的全球高程基准是国际大地测量科学界的核心目标之一,也是全球尺度地球科学研究、跨境工程应用等的必要基础设施。国际大地测量协会（international geodesy association,IAG）2015年发布了国际高程参考系统的定义,并于2019年提出了建立国际高程参考框架的目标。从全球高程参考系统的理论基础和定义出发,对国际高程参考系统与框架的理论、方法和实际问题开展论述与研究,主要包括全球大地水准面重力位$W_{\mathrm{0}}$的确定、基于高阶重力场模型的重力位确定、基于区域重力场建模的重力位确定,并重点论述和分析了IAG组织的科罗拉多大地水准面建模试验和中国2020珠峰高程测量实现国际高程参考系统2项典型案例研究。结果表明,在平坦地区和一般山区,重力大地水准面模型精度能达到1 cm（重力位0.1 m2/s2）,即使在珠穆朗玛峰这样的特大山区,也有望达到2~3 cm精度（重力位0.2~0.3 m2/s2）。综合典型案例研究结果、观测技术、数据资源和区域分布等因素,提出了建立国际高程参考框架的初步策略,包括IHRF参考站布设、重力位确定方法、数据要求、应遵循的标准/约定和预期精度指标等,展望了光学原子钟与相对论大地测量对于全球高程基准统一的潜在贡献。     

On the adjustment of combined GPS/levelling/geoid networks

A detailed treatment of adjustment problems in combined global positioning system (GPS)/levelling/geoid networks is given. The two main types of `unknowns' in this kind of multi-data 1D networks are usually the gravimetric geoid accuracy and a 2D spatial field that describes all the datum/systematic distortions among the available height data sets. An accurate knowledge of the latter becomes especially important when we consider employing GPS techniques for levelling purposes with respect to a local vertical datum. Two modelling alternatives for the correction field are presented, namely a pure deterministic parametric model, and a hybrid deterministic and stochastic model. The concept of variance component estimation is also proposed as an important statistical tool for assessing the actual gravimetric geoid noise level and/or testing a priori determined geoid error models. Finally, conclusions are drawn and recommendations for further study are suggested. Received: 9 September 1998 / Accepted: 8 June 1999     

On the meaning of geodetic orientation

After deriving models for changes of coordinates and azimuths due to rotations, the investigation considers methods for modeling terrestrial orientation in adjustments of geodetic networks. If a misorientation of a geodetic network exists, this can be due to systematic errors in astronomic longitude or in astronomic azimuth, or in both. A separation of these two effects is not possible in practice. The initial azimuth at the datum origin contributes to the orientation only as much as any other azimuth of the same weight.     

A geodetic approach for the recovery of global kinematic plate parameters

Modern techniques of precise geodetic positioning are capable of monitoring global tectonic movements. We can avoid the tremendous effort of observing those point motions at every place on the earth, if we accept the model of rigid tectonic plates, which allows us to extrapolate from discrete point observations to the appertaining plates. The target of describing plate kinematics is the determination of its kinematic parameters, which are the coordinates of the rotation pole and the rotational velocity of each tectonic plate. A mathematical model is presented, which is capable of including geodetic observations (point coordinate shifts, distance changes) as well as geophysical quantities (sea floor spreading rates, earthquake slip vectors). The parameter estimation procedure is derived and demonstrated in simulated examples. Finally a global geodetic network for space techniques is designed, which provides an optimum parameter estimation.     

通导遥一体化深远海PNT基准及服务网络构想

从海底控制网设计、布设、测量、数据处理和海洋声速场构建几个方面介绍了海底控制网建设的现状。结合国家海洋战略需求和海洋大地测量技术发展,分析了现阶段海底控制网建设面临的问题:认为目前的海底网规模小,缺乏信息共享,功能单一;设计与布设原则未与控制网等级关联,多为定性描述,缺乏操作性;声速场精度和分辨率偏低;测量和数据处理仅考虑了海底控制点的定位问题,难以满足大区域、高精度海洋PNT（positioning, navigation, and timing）基准网建设需求。据此,利用海洋声道的远程通讯和测距定位能力,提出了建设联合北斗/GNSS（global navigation satellite system）定位和通信导航功能的通导遥一体化深远海PNT基准及服务网络的构想,针对该网络的功能和布放设计、高精度、高分辨率海洋声速场模型的构建、各类PNT基准点的测量和整体网平差处理、海底PNT基准点的自校准和自维护、覆盖水域的位置增强服务、目标和环境的遥测和感知服务等几个关键技术问题,提出了实施方法和设想,以期解决当前海洋控制网大区域建设面临的缺乏通讯、布网原则和测量方法不完善、功能单一等问题,为新一代高性能海洋大地测量及PNT导航定位服务网络的建设提供支撑。认为随着长距离布网优化设计、增强位置服务、精确授时和时间同步、远程通讯及网络功能的拓展和应用服务等难题的突破,所构想的网络体系必将引起海洋PNT建设的一次变革。