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.     

利用大地边值问题方法统一全球高程基准

为解决世界各国高程基准差异的问题,提出联合卫星重力场模型、地面重力数据、GNSS大地高、局部高程基准的正高或正常高,按大地边值问题法确定局部高程基准重力位差的方法。首先推导了利用传统地面"有偏"重力异常确定高程基准重力位差的方法;接着利用改化Stokes核函数削弱"有偏"重力异常的影响,并联合卫星重力场模型和地面"有偏"重力数据,得到独立于任何局部高程基准的重力水准面,以此来确定局部高程基准重力位差;最后利用GNSS+水准数据和重力大地水准面确定了美国高程基准与全球高程基准W₀的重力位差为-4.82±0.05 m²s^-2。     

Separation between reference surfaces of selected vertical datums

This paper discusses the separation between the reference surface of several vertical datums and the geoid. The data used includes a set of Doppler positioned stations, transformation parameters to convert the Doppler positions to ITRF90, and a potential coefficient model composed of the JGM-2 (NASA model) from degree 2 to 70 plus the OSU91A model from degree 71 to 360. The basic method of analysis is the comparison of a geometric geoid undulation derived from an ellipsoidal height and an orthometric height with the undulation computed from the potential coefficient model The mean difference can imply a bias of the datum reference surface with respect to the geoid. Vertical datums in the following countries were considered: England, Germany, United States, and Australia. The following numbers represent the bias values of each datum after adopting an equatorial radius of 6378136.3m: England (-87 cm), Germany (4 cm), United States (NGVD29 (-26 cm)), NAVD88 (-72 cm), Australia AHD (mainland, -68 cm); AHD (Tasmania, -98 cm). A negative sign indicates the datum reference surface is below the geoid. The 91 cm difference between the datums in England and Germany has been independently estimated as 80 cm. The 30 cm difference between AHD (mainland) and AHD (Tasmania) has been independently estimated as 40 cm. These bias values have been estimated from data where the geometric/ gravimetric geoid undulation difference standard deviation, at one station, is typically ±100 cm, although the mean difference is determined more accurately.The results of this paper can be improved and expanded with more accurate geocentric station positions, more accurate and consistent heights with respect to the local vertical datum, and a more accurate gravity field for the Earth. The ideas developed here provide insight on the determination of a world height system.     

A bias-free geodetic boundary value problem approach to height datum unification

A geodetic boundary value problem (GBVP) approach has been formulated which can be used for solving the problem of height datum unification. The developed technique is applied to a test area in Southwest Finland with approximate size of 1.5° × 3° and the bias of the corresponding local height datum (local geoid) with respect to the geoid is computed. For this purpose the bias-free potential difference and gravity difference observations of the test area are used and the offset (bias) of the height datum, i.e., Finnish Height Datum 2000 (N2000) fixed to Normaal Amsterdams Peil (NAP) as origin point, with respect to the geoid is computed. The results of this computation show that potential of the origin point of N2000, i.e., NAP, is (62636857.68 ± 0.5) (m²/s²) and as such is (0.191 ± 0.003) (m) under the geoid defined by W ₀ = 62636855.8 (m²/s²). As the validity test of our methodology, the test area is divided into two parts and the corresponding potential difference and gravity difference observations are introduced into our GBVP separately and the bias of height datums of the two parts are computed with respect to the geoid. Obtaining approximately the same bias values for the height datums of the two parts being part of one height datum with one origin point proves the validity of our approach. Besides, the latter test shows the capability of our methodology for patch-wise application.     

格尔木市高精度数字高程基准模型研究

大地水准面(数字高程基准)为国家高程基准的建立与维持提供了全新的思路。然而,受限于地形、重力数据等原因,高原地区高精度数字高程基准模型的建立一直是大地测量领域的难题。本文以格尔木地区为例,探讨了高原地区高精度数字高程基准模型的建立方法。首先,基于重力和地形数据,由第二类Helmert凝集法计算了格尔木重力似大地水准面。在计算中,考虑到高原地形对大地水准面模型的影响,采用了7.5″×7.5″分辨率和高精度的地形数据来恢复大地水准面短波部分的方法,以提高似大地水准面的精度。然后,利用球冠谐调和分析方法将GNSS水准与重力似大地水准面联合,建立了格尔木高精度数字高程基准模型。与实测的67个高精度GNSS水准资料比较,重力似大地水准面的外符合精度为3.0 cm,数字高程基准模型的内符合精度为2.0 cm。     

应用最佳回归方法确定局部区域GPS网的正常高

针对常用的几种几何方法在实用中的局限性，提出了一种经过改进的多元回归方法。试验结果表明，应用该方法，可使正常高求解精度明显改善。     

推求网格点高程异常的方法

本文给出了推求网格点高程异常的方法,用它可以加密我国的高程异常数据,从而得到高分辨率的高程异常图。     

基于Kriging估计的GPS高程转换

随着GPS测量精度的不断提高,其平面测量已经在多种领域得到应用,成为测量工作的一个全新的手段与工具,但在GPS测高方面需要改善和研究。Kriging方法是地统计学的基本方法,其理论核心是变异函数,它是一种最好的线性无偏估计法,在地理学、生态学、环境科学等领域都得到了广泛的应用,取得了很好效果。本文在详细介绍kriging法的基础上,建立了Kriging法的GPS高程拟合模型,利用该模型对两个实例的GPS高程数据拟合,得到了正常高,结果表明Kriging法在GPS高程拟合中的应用精度达到厘米级,且得出了一些有益的结论,为以后GPS高程的应用提供一些参考。     

局部无缝垂直参考基准面的建立方法研究

为在局域建立一个无缝垂直参考基准面，提出了两步转换的思想和方法，即从大地高到正高然后到海图高。利用该方法。构造了Saint John河高程转换模型，并在该河段建立了无缝垂直参考基准面，且得到了实际验证。     

1985国家高程基准与全球似大地水准面之间的系统差及其分布规律

将由大地高和正常高导出的几何高程异常与由位系数模型计算得到的物理高程异常进行比较,求出1985国家高程基准与全球似大地水准面之间的系统差,并分析其分布特性.为抵制异常值的影响,引入"抗差等价权".利用分布全国大陆范围的GPS网949个点的GPS/水准数据和地球重力场模型EGM96、DQM99A,求出1985国家高程基准点与WGS84定义的似大地水准面之间有35.7 cm的垂直偏差,1985国家高程基准面的系统差自东向西、自南向北明显增大,给出相应的数学模型.     

基于坐标转换法的GPS-RTK高程测量及成果检核

GPS-RTK高程测量的主要方法是坐标转换和高程拟合。本文主要结合某线路介绍了坐标转换方法以及如何对其测量成果进行检核。常规的高程检核方法是比较联测水准点高程和GPS-RTK测量高程,而本文结合线路作业的特点提出了利用直线或平面拟合方法对线路基于坐标转换法获得的GPS-RTK高程测量成果进行检核,结果表明本文的方法是可行的。     

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     

时序PSInSAR研究建筑物高度信息提取

基于干涉相位的统计分析,给出一种利用高分辨率时间序列永久散射体雷达干涉技术（PSI）提取人工建/构筑物高度的方法。利用给出的测高模型,借助27景高分辨率TerraSAR-X影像获取天津市北辰区典型建筑高度信息,并通过实测值进行验证。结果表明该方法提取的建筑物高度与实测值相互吻合,说明了该方法的可行性与有效性。     

GPS高程转换中不同高程异常基准对正常高高差的影响

为了解决不同坐标系统下高程异常对正常高高差转换的影响，通过模拟计算得出了对正常高高差影响的定量结论，对于大地水准面的精化和应用似大地水准面确定GPS正常高具有一定的参考价值。     

论相对点位精度的合理评定

按现行方法求得的相对点位精度由于未顾及起始数据误差的影响 ,且非实际所需评定的相对点位精度 ,因此并不客观、可靠。本文所提出的协方差基准的概念 ,用来定义相对点位精度和绝对点位精度有其客观性和实用性 ,协方差基准作为控制网点精度的参考基准 ,并不重合于网点坐标的参考基准—坐标基准 ,而可按应用的需要 ,方便地进行协方差基准转换。本文提出了合理评定相对点位精度的新方法 ,并用高精度工程控制网的实测数据进行了分析验证     

基于移除-恢复法的GPS水准高差拟合方法研究

讨论了将GPS测得的大地高差转换为正常高差的基本原理和算法,研究了移除-恢复算法在GPS高差转换中的应用。利用该算法对某一线路GPS大地高差观测数据进行了处理,结果表明基于移除-恢复法的GPS高差转换方法能改善高差转换精度,具有很好的实用价值。     

应用GPS水准与重力数据联合解算大地水准面

GPS水准大地水准面与重力大地水准面之差不仅由基准不同引起,而且也包含重力与GPS水准观测值的误差。建立了这两个水准面之差与基准转换参数、重力和GPS水准观测值的残差之间的关系,并基于最小二乘准则解算了基准转换参数和重力与GPS水准观测值的残差,即计算转换参数及重力与GPS观测值的改正。尤其当GPS水准精度远高于重力水准面时,联合解算模型可固定GPS水准大地水准面,只对重力观测值进行改正。     

Global height datum unification: a new approach in gravity potential space

The problem of “global height datum unification” is solved in the gravity potential space based on: (1) high-resolution local gravity field modeling, (2) geocentric coordinates of the reference benchmark, and (3) a known value of the geoid’s potential. The high-resolution local gravity field model is derived based on a solution of the fixed-free two-boundary-value problem of the Earth’s gravity field using (a) potential difference values (from precise leveling), (b) modulus of the gravity vector (from gravimetry), (c) astronomical longitude and latitude (from geodetic astronomy and/or combination of (GNSS) Global Navigation Satellite System observations with total station measurements), (d) and satellite altimetry. Knowing the height of the reference benchmark in the national height system and its geocentric GNSS coordinates, and using the derived high-resolution local gravity field model, the gravity potential value of the zero point of the height system is computed. The difference between the derived gravity potential value of the zero point of the height system and the geoid’s potential value is computed. This potential difference gives the offset of the zero point of the height system from geoid in the “potential space”, which is transferred into “geometry space” using the transformation formula derived in this paper. The method was applied to the computation of the offset of the zero point of the Iranian height datum from the geoid’s potential value W ₀=62636855.8 m²/s². According to the geometry space computations, the height datum of Iran is 0.09 m below the geoid.     

对流层延迟对GPS大地高的影响

分析了对流层延迟的基本特性及常用的处理措施,通过实例表明了不同对流层的处理方法对大地高精度有较大影响:当基线两端高差较大时,即使基线较短,其气象条件也有所差异,仅仅通过差分或模型改正仍不能消除对流层延迟的影响,残余的对流层延迟仍然影响大地高的解算精度,通过对残余对流层延迟进行估计能够明显改善大地高的精度。