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21.
Béla Paláncz Piroska Zaletnyik Joseph L. Awange Erik W. Grafarend 《Journal of Geodesy》2008,82(8):505-511
The Dixon resultant is proposed as an alternative to Gröbner basis or multipolynomial resultant approaches for solving systems of polynomial equations inherent in geodesy. Its smallness in size, high density (ratio on the number of nonzero elements to the number of all elements), speed, and robustness (insensitive to combinatorial sequence and monomial order, e.g., Gröbner basis) makes it extremely attractive compared to its competitors. Using 3D-intersection and conformal C 7 datum transformation problems, we compare its performance to those of the Sturmfels’s resultant and Gröbner basis. For the 3D-intersection problem, Sturmfels’s resultant needed 0.578 s to solve a 6 × 6 resultant matrix whose density was 0.639, the Dixon resultant on the other hand took 0.266 s to solve a 4 × 4 resultant matrix whose density was 0.870. For the conformal C 7 datum transformation problem, the Dixon resultant took 2.25 s to compute a quartic polynomial in scale parameter whereas the computaton of the Gröbner basis fails. Using relative coordinates to compute the quartic polynomial in scale parameter, the Gröbner basis needed 0.484 s, while the Dixon resultant took 0.016 s. This highlights the robustness of the Dixon resultant (i.e., the capability to use both absolute and relative coordinates with any order of variables) as opposed to Gröbner basis, which only worked well with relative coordinates, and was sensitive to the combinatorial sequence and order of variables. Geodetic users uncomfortable with lengthy expressions of Gröbner basis or multipolynomial resultants, and who aspire to optimize on the attractive features of Dixon resultant, may find it useful. 相似文献
22.
The sea surface cannot be used as reference for Major Vertical Datum definition because its deviations from the ideal equipotential surface are very large compared to rms in the observed quantities. The quasigeoid is not quite suitable as the surface representing the most accurate Earth's model without some additional conditions, because it depends on the reference field. The normal Earth's model represented by the rotational level ellipsoid can be defined by the geocentric gravitational constant, the difference in the principal Earth's inertia moments, by the angular velocity of the Earth's rotation and by the semimajor axis or by the potential (U
0
) on the surface of the level ellipsoid. After determining the geopotential at the gauge stations defining Vertical Datums, gravity anomalies and heights should be transformed into the unique vertical system (Major Vertical Datum). This makes it possible to apply Brovar's (1995) idea of determining the reference ellipsoid by minimizing the integral, introduced by Riemann as the Dirichlet principle, to reach a minimum rms anomalous gravity field. Since the semimajor axis depends on tidal effects, potential U
0
should be adopted as the fourth primary fundamental geodetic constant. The equipotential surface, the actual geopotential of which is equal to U
0
, can be adopted as reference for realizing the Major Vertical Datum. 相似文献
23.
Robust estimation of geodetic datum transformation 总被引：18，自引：1，他引：17
Y. Yang 《Journal of Geodesy》1999,73(5):268-274
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 相似文献
24.
On symmetrical three-dimensional datum conversion 总被引：2，自引：0，他引：2
A 3-D similarity transformation is frequently used to convert GPS-WGS84-based coordinates to those in a local datum using
a set of control points with coordinate values in both systems. In this application, the Gauss-Markov (GM) model is often
employed to represent the problem, and a least-squares approach is used to compute the parameters within the mathematical
model. However, the Gauss–Markov model considers the source coordinates in the data matrix (A) as fixed or error-free; this is an imprecise assumption since these coordinates are also measured quantities and include
random errors. The errors-in-variables (EIV) model assumes that all the variables in the mathematical model are contaminated
by random errors. This model may be solved using the relatively new total least-squares (TLS) estimation technique, introduced
in 1980 by Golub and Van Loan. In this paper, the similarity transformation problem is analyzed with respect to the EIV model,
and a novel algorithm is described to obtain the transformation parameters. It is proved that even with the EIV model, a closed
form Procrustes approach can be employed to obtain the rotation matrix and translation parameters. The transformation scale
may be calculated by solving the proper quadratic equation. A numerical example and a practical case study are presented to
test this new algorithm and compare the EIV and the GM models. 相似文献
25.
为了给防雷工程设计、雷电损害风险评估和建筑物站址选择提供更加科学准确的年平均雷暴日资料,引入主成分典型相关分析(PC-CCA)方法,建立了月雷暴日资料延长模式,用多年人工观测雷暴日资料,对江西省区域内闪电定位网探测的月雷暴日数场序列进行订正延长试验。试验结果表明,模式中提取5个主分量的总体效果最好,PC-CCA方法用于月雷暴日资料的延长是可行的;在此基础上,进行各月累加平均求取年平均雷暴日资料也是可行的。 相似文献
26.
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. 相似文献
27.
1985国家高程基准相对于大地水准面的垂直偏差 总被引：12，自引：1，他引：12
局部高程基准通常由一个 (或多个 )验潮站所测的当地平均海面确定。由于海面地形的客观存在 ,人们已经认识到当地平均海面与大地水准面的差异可能达 2m之多。为了获得这一垂直偏差 ,很有必要确定当地平均海面和全球大地水准面上的重力位值。提出了利用全球重力场模型和GPS/水准资料计算局部高程基准相对全球大地水准面垂直偏差的 2种不同方法。我国目前采用的 1 985国家高程基准 ,由青岛验潮站所处黄海平均海面 1 95 2～ 1 979年的验潮记录计算得到。利用全球重力场模型和分布全国大陆范围的GPS/水准数据 ,计算了 1 985高程基准与大地水准面的垂直偏差。结果表明 1 985国家高程基准点的重力位值为( 62 63685 3.40± 0 .1 3)m2 s- 2 ,这比重力位W0 =( 62 63685 6.0± 0 .5 )m2 s- 2 隐含的大地水准面高 ( 0 .2 6± 0 .0 5 )m。 相似文献
28.
针对PSInSAR技术监测大空间尺度地表垂直形变场的不足,提出通过基准转换与数据拼接、融合不同轨道多个独立片区(Frame)获取大空间尺度地表垂直形变场方法.由于不同轨道主影像选取的参考基准不一致、不同轨道垂直基线不同、不同片区相位解缠的参考PS不同等因素影响,使得PSInSAR获得的不同轨道地表垂直形变场的空间基准存在差异,提取的地表形变信息不具有可比性.利用两个相邻片区重叠区域的PS点集,根据迭代最近点算法提取两片区公共区域内同名点,并兼顾同名点距离的权,精确计算两片区的配准参数,实现两片区的"无缝"连接,最后使各独立片区拼接成一个连续的大空间尺度地表垂直形变场.本文推导了多轨PSInSAR技术获得的不同片区形变场基准转换与数据拼接的数学模型,并以华北平原(115.32°E—118.79°E, 36.81°N—40.58°N)为实验区,解析了3个不同轨道共12个片区PS目标,获取了研究区2006—2010年地表垂直形变速度场.分析表明:(1)研究区大范围处于下沉状态,形成以北京、廊坊、天津、沧州、泊头—德州等城市为中心向外扩展的地表沉降发展态势,几个沉降中心的平均沉降速率分别达到-34.7 mm/a、-26.3 mm/a、-64.2 mm/a、-34.6 mm/a和-37.7 mm/a;(2)地表沉降的空间分布特征表明,城市工业生产和生活抽取地下水是地表沉降的主要诱因,农业灌溉和油气开采是导致华北平原大范围地表沉降的另一个重要因素;(3)研究区最大沉降带沿北北东向展布,与区内断裂分布一致,表明沉降的空间分布受到断裂带控制;(4)利用地表同期一等水准测量成果检验了本研究结果,精度达到4.72 mm,表明本文提出的数据处理策略能够满足大时空尺度地表形变监测的需求. 相似文献
29.
区域性高程基准的统一 总被引：2，自引：2，他引：0
全球或区域性高程基准面的统一始终是大地测量学研究的主要内容之一 ,对于构建“数字区域”和“数字地球”及研究全球或区域性环境变化具有重要的科学意义和现实意义。本文利用全球重力场模型EGM 96和WDM94及GPS水准数据 ,确定了香港主要高程基准面与我国 195 6黄海高程基准面的重力位差。计算结果表明 ,这两个基准面的重力位差为 (8 36 6± 0 76 5 )m2 s-2 ,表明香港主要高程基准面平均低于我国 195 6黄海高程基准面 (0 85 5± 0 0 78)m2 s-2 。本文的计算结果有助于本地区高程基准面的统一 相似文献
30.
Prediction of china’s submerged coastal areas by sea level rise due to climate change 总被引：2，自引：0，他引：2
Based on the simulation with the Ocean-Atmosphere Coupled Model CCSM and Ocean Model POP under the greenhouse gas emission scenario of the IPCC SRES A2 (IPCC, 2001), and on the earth crust subsidence and glacier melting data, the relative sea level change is obtained along the coast of China in the 21st century. Using the SRTM elevation data the submergence of coastal low land is calculated under the extreme water level with a 100-year return period. The total flooding areas are 98.3×103 and 104.9×103 km2 for 2050 and 2080, respectively. For the three regions most vulnerable to extreme sea level rise, i.e., the coast of Bohai Bay, the Yangtze River Delta together with neighboring Jiangsu Province and northern Zhejiang Province, and the Pearl River Delta, the flooded areas are 5.0×103, 64.1×103 and 15.3×103 km2 in 2050 and 5.2×103, 67.8×103 and 17.2×103 km2 in 2080, respectively. 相似文献