Reference frame stability and nonlinear distortion in minimum-constrained network adjustment

The aim of this paper is to investigate the influence of the minimum constraints (MCs) on the reference frame parameters in a free-net solution. The non-estimable part of these parameters (which is not reduced by the available data) is analysed in terms of its stability under a numerical perturbation of the constrained datum functionals. In practice, such a perturbation can be ascribed either to hidden errors in the known coordinates/velocities that participate in the MCs or to a simple change of their a priori values due to a datum switch on a different fiducial dataset. In addition, a perturbation of this type may cause a nonlinear variation to the estimable part of the reference frame parameters, since it theoretically affects the adjusted observations that are implied by the network’s nonlinear observational model. The aforementioned effects have an impact on the quality of a terrestrial reference frame (TRF) that is established via a minimum-constrained adjustment, and our study shows that they are both controlled through a characteristic matrix which is inherently linked to the MC system (the so-called TRF stability matrix). The structure of this matrix depends on the network’s spatial configuration and the ‘geometry’ of the datum constraints, while its main role is the filtering of any MC-related errors into the least-squares adjustment results. A number of examples with different types of geodetic networks are also presented to demonstrate the theoretical findings of our study.     

Extended free net adjustment constraints

The contribution of geodetic measurements to the establishment of a control network can be partitioned into global and local (individual) components. The global component epitomized in a number of geometrically meaningful parameters can be estimated together with the individual point coordinates. The additional rank defect created by the extension of the parameter list is corrected by free net adjustment constraints which are extended beyond those needed for a solution of the network datum problem. Two applications of extended free net adjustment are outlined and illustrated by elementary numerical examples. A non-Cartesian (skew) reference system discussed in the Appendix provides an exotic interpretation of the estimated global and individual parameters. Prepared during a grant period (September 1984 through February 1985) while serving as a Visiting Senior Scientist in Geodesy, National Research Council, National Academy of Sciences, Washington, D.C.     

STABILITY OF SOLUTION FOR DYNAMIC GEODETIC NETWORK ADJUSTMENT

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Stability of solution for dynamic geodetic network adjustment

This paper discusses theoretically the stability of solutions for dynamic geodetic network adjustment, Kalman filtering and sequence adjustment, and two examples are given. The solution for dynamic geodetic network adjustment is stable if the dynamic geodetic network is a classical network. There is not rank deficit in datum, or else the solution is not stable, which will depend on the initial value.     

基于JSCORS的江苏省现代大地坐标框架的建设与维护

本文结合江苏省现代大地坐标框架的建设和JSCORS的运行维护,通过对江苏省原大地坐标框架的情况分析,介绍了江苏大地坐标框架的建设方案.结合区域稳定基点组的确定、框架维护和复测机制的建立、框架维护系统的建设等内容,提出江苏省大地坐标框架维护的解决方案.     

坐标基准维持与动态监测网数据处理

坐标基准的维持不仅要求有高精度的连续大地测量观测或定期复测,还要求采用合理的数据处理原则与方法。分析了不同平差方法对基准的影响,其中包括经典整体平差、序贯平差和自适应序贯平差。利用GPS监测网数据进行了计算与分析,结果表明,当个别点位发生异常移动或变形时,序贯平差会使坐标基准产生实际的扭曲,而自适应序贯平差则能有效控制异常点位对平差基准的影响,保证了坐标基准的可靠性和现势性。     

Possibilities of GPS Kinematic Measurements for Geological Survey in East Slovakia

This paper deals with transformation procedures for observed GPS data from the world geodetic system WGS-84 into the national geodetic grid datum S-UTCN(system of united trigonometric cadaster network) and Baa(the Baltic Sea after adjustment).Transformation from WGS-84 into SUTCN is performed most frequently by means of the 7-element Helmert transformation with three identical points.Geodetic network was adjusted by two ways.     

Possibilities of GPS kinematic measurements for geological survey in East Slovakia

This paper deals with transformation procedures for observed GPS data from the world geodetic system WGS-84 into the national geodetic grid datum S-UTCN (system of united trigonometric cadaster network) and Baa (the Baltic Sea after adjustment). Transformation from WGS-84 into SUTCN is performed most frequently by means of the 7-element Helmert transformation with three identical points. Geodetic network was adjusted by two ways.     

Local datum definition and geodetic network positioning using global navigation satellite systems

The problem of datum definition as applied to local-area geodetic networks is investigated using data collected from global navigation satellite systems (GNSS). It is shown that the process of double differencing makes the model more sensitive to computational errors that reduce the ability of the satellites alone to control the translation component of the datum definition, and as a result additional regularization is required. Traditionally, datum definition has been accomplished by constraining one station to set coordinates. Alternative regularization strategies are analysed in terms of their effects on positioning and ambiguity resolution. In doing so, processing strategies are developed which can improve the quality of global positioning system (GPS)-based position solutions in geodetic network applications of limited spatial extent, such as high-precision engineering and deformation monitoring networks.     

Convex optimization under inequality constraints in rank-deficient systems

Many geodetic applications require the minimization of a convex objective function subject to some linear equality and/or inequality constraints. If a system is singular (e.g., a geodetic network without a defined datum) this results in a manifold of solutions. Most state-of-the-art algorithms for inequality constrained optimization (e.g., the Active-Set-Method or primal-dual Interior-Point-Methods) are either not able to deal with a rank-deficient objective function or yield only one of an infinite number of particular solutions. In this contribution, we develop a framework for the rigorous computation of a general solution of a rank-deficient problem with inequality constraints. We aim for the computation of a unique particular solution which fulfills predefined optimality criteria as well as for an adequate representation of the homogeneous solution including the constraints. Our theoretical findings are applied in a case study to determine optimal repetition numbers for a geodetic network to demonstrate the potential of the proposed framework.     

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。     

Effect of the selection of reference radio sources on geodetic estimates from VLBI observations

This paper evaluates the effect of the accuracy of reference radio sources on the daily estimates of station positions, nutation angle offsets, and the estimated site coordinates determined by very long baseline interferometry (VLBI), which are used for the realization of the international terrestrial reference frame (ITRF). Five global VLBI solutions, based on VLBI data collected between 1979 and 2006, are compared. The reference solution comprises all observed radio sources, which are treated as global parameters. Four other solutions, comprising different sub-sets of radio sources, were computed. The daily station positions for all VLBI sites and the corrections to the nutation offset angles were estimated for these five solutions. The solution statistics are mainly affected by the positional instabilities of reference radio sources, whereas the instabilities of geodetic and astrometric time-series are caused by an insufficient number of observed reference radio sources. A mean offset of the three positional components (Up, North, East) between any two solutions was calculated for each VLBI site. From a comparison of the geodetic results, no significant discrepancies between the respective geodetic solutions for all VLBI sites in the Northern Hemisphere were found. In contrast, the Southern Hemisphere sites were more sensitive to the selected set of reference radio sources. The largest estimated mean offset of the vertical component between two solutions for the Australian VLBI site at Hobart was 4 mm. In the worst case (if a weak VLBI network observed a limited number of reference radio sources) the daily offsets of the estimated height component at Hobart exceeded 100 mm. The exclusion of the extended radio sources from the list of reference sources improved the solution statistics and made the geodetic and astrometric time-series more consistent. The problem with the large Hobart height component offset is magnified by a comparatively small number of observations due to the low slewing rate of the VLBI dish (1°/ s). Unless a minimum of 200 scans are performed per 24-h VLBI experiment, the daily vertical positions at Hobart do not achieve 10 mm accuracy. Improving the slew rate at Hobart and/or having an increased number of new sites in the Southern Hemisphere is essential for further improvement of geodetic VLBI results for Southern Hemisphere sites.     

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.     

简便实用的GPS网平差模型

采用数值微商求偏导数的方法，从而使ＧＰＳ网平差的计算模型非常简洁。选用平面坐标和大地高作为平差参数，可以方便地简化为平面网或高程网，加入地面归心数据和常规观测数据也变得十分容易。对旋转角大的地方独立坐标系，提出了处理办法。经对实测数据的处理，证明了模型的正确性     

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.     

关于改善和更新国家大地测量基准的思考

大地测量基准是地理信息系统和测图的基础框架,其建立,维护,改善和更新是国家测绘行政主管部门的重要职责。大地测量基准中的重力基准和坐本身由于自然和人为原因,破损严重,因此顺应科技进步,国家建设和社会发展的需要。     

全国天文大地网与空间大地网联合平差

天文大地网与空间大地网联合平差,对于检核、控制与加强天文大地网以及建立与扩展地心坐标系,都具有重要意义,全国天文大地网与全国ＧＰＳ大地网联合平差（Ｉ期）于１９９８年初完成,本文报告平差采用的原则和模型,并提出平差结果,通过联合平差,消除了天文大地网尺度的系统偏差,减弱了它的局部变形,改善了它的整体精度,更重要的是建立了由近５万个大地点坐标体现的地心参考系,其地心坐标的水平分量精度好于０．５ｍ。     

中国现代大地基准——中国大地坐标系2000(CGCS 2000)及其框架

简要介绍2008年7月1日启用的中国地心坐标系统2000 (CGCS 2000)的定义及其采用的大地测量基本常数,并对CGCS 2000的坐标框架进行了评述:它应该是高精度,涵盖全部陆海国土,动态,具有方便用户的密度和分布,它由全球导航卫星系统国家级连续运行站网和国家高精度大地控制网这两部分组成.目前的框架由2000国家GPS大地网和它与全国天文大地网联合平差的成果构成,可以满足近期的需求.采用CGCS 2000后将引起中国境内地面奌的大地经纬度值、高斯平面坐标值、地图上点间的方向和长度值等的变动,本文给出了相应的变动值和应对的基本思路.     

株洲市2000国家大地坐标联测及控制网的改造升级

株洲市基于CGCS2000的城市控制网升级改造,获取了株洲市2000国家大地坐标系的大地基准和原有城市控制点及升级改造后控制点的2000国家大地坐标,并通过了检测验收;改造升级了的株洲城市控制网,更新了株洲市控制网的1954坐标,建立了与2000国家大地坐标系、1980坐标的转换关系,实现了基于CZTCORS网络RTK技术的似大地水准面成果的应用.     

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.