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1.
2.
海岸带是影响人类活动的重要地带,海岸带专题地图能够详细表示出海岸带的特性。随着海洋经济的发展,海岸图的需求日益增加。从地图的数学要素出发,提出目前海岸图绘制存在的问题,并从地图学、海洋学、遥感地学的角度,对地图投影的选择、坐标系转换、比例尺对海岸图编绘的影响及控制点的确定等问题进行了综合分析。 相似文献
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A data-driven approach to local gravity field modelling using spherical radial basis functions 总被引:3,自引:0,他引:3
We propose a methodology for local gravity field modelling from gravity data using spherical radial basis functions. The methodology
comprises two steps: in step 1, gravity data (gravity anomalies and/or gravity disturbances) are used to estimate the disturbing
potential using least-squares techniques. The latter is represented as a linear combination of spherical radial basis functions
(SRBFs). A data-adaptive strategy is used to select the optimal number, location, and depths of the SRBFs using generalized
cross validation. Variance component estimation is used to determine the optimal regularization parameter and to properly
weight the different data sets. In the second step, the gravimetric height anomalies are combined with observed differences
between global positioning system (GPS) ellipsoidal heights and normal heights. The data combination is written as the solution
of a Cauchy boundary-value problem for the Laplace equation. This allows removal of the non-uniqueness of the problem of local
gravity field modelling from terrestrial gravity data. At the same time, existing systematic distortions in the gravimetric
and geometric height anomalies are also absorbed into the combination. The approach is used to compute a height reference
surface for the Netherlands. The solution is compared with NLGEO2004, the official Dutch height reference surface, which has
been computed using the same data but a Stokes-based approach with kernel modification and a geometric six-parameter “corrector
surface” to fit the gravimetric solution to the GPS-levelling points. A direct comparison of both height reference surfaces
shows an RMS difference of 0.6 cm; the maximum difference is 2.1 cm. A test at independent GPS-levelling control points, confirms
that our solution is in no way inferior to NLGEO2004. 相似文献
6.
On the multivariate total least-squares approach to empirical coordinate transformations. Three algorithms 总被引:2,自引:1,他引:1
The multivariate total least-squares (MTLS) approach aims at estimating a matrix of parameters, Ξ, from a linear model (Y−E
Y
= (X−E
X
) · Ξ) that includes an observation matrix, Y, another observation matrix, X, and matrices of randomly distributed errors, E
Y
and E
X
. Two special cases of the MTLS approach include the standard multivariate least-squares approach where only the observation
matrix, Y, is perturbed by random errors and, on the other hand, the data least-squares approach where only the coefficient matrix
X is affected by random errors. In a previous contribution, the authors derived an iterative algorithm to solve the MTLS problem
by using the nonlinear Euler–Lagrange conditions. In this contribution, new lemmas are developed to analyze the iterative
algorithm, modify it, and compare it with a new ‘closed form’ solution that is based on the singular-value decomposition.
For an application, the total least-squares approach is used to estimate the affine transformation parameters that convert
cadastral data from the old to the new Israeli datum. Technical aspects of this approach, such as scaling the data and fixing
the columns in the coefficient matrix are investigated. This case study illuminates the issue of “symmetry” in the treatment
of two sets of coordinates for identical point fields, a topic that had already been emphasized by Teunissen (1989, Festschrift
to Torben Krarup, Geodetic Institute Bull no. 58, Copenhagen, Denmark, pp 335–342). The differences between the standard least-squares
and the TLS approach are analyzed in terms of the estimated variance component and a first-order approximation of the dispersion
matrix of the estimated parameters. 相似文献
7.
基于最小二乘配置的三维空间坐标转换 总被引:1,自引:0,他引:1
在求解未知转换参数时,鉴于公共点坐标本身的误差,提出利用最小二乘配置法进行空间坐标转换,即将公共点本身坐标作为随机参数,把转换参数作为非随机参数进行处理,最后通过实验对比分析表明,该方法明显优于一般坐标转换方法。 相似文献
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9.
Patterns of crystallographic preferred orientation are referred to as texture. The specific subject of texture analysis is
the experimental determination and interpretation of the statistical distribution of orientations of crystals within a specimen
of polycrystalline material, which could be metals or rocks. The objective is to relate an observed pattern of preferred orientation
to its generating processes and vice versa. In geosciences, texture of minerals in rocks is used to infer constraints on their
tectono-metamorphic history. Since most physical properties of crystals, such as elastic moduli, the coefficients of thermal
expansion, or chemical resistance to etching depends on crystal symmetry and orientation, the presence of texture imparts
directional properties to the polycrystalline material.
A major issue of mathematical texture analysis is the resolution of the inverse problem to determine a reasonable orientation
density function on SO(3) from measured pole intensities on
, which relates to the inverse of the totally geodesic Radon transform. This communication introduces a wavelet approach into
mathematical texture analysis. Wavelets on the two-dimensional sphere
and on the rotational group SO(3) are discussed, and an algorithms for a wavelet decomposition on both domains following the
ideas of Ta-Hsin Li is given. The relationship of these wavelets on both domains with respect to the totally geodesic Radon
transform is investigated. In particular, it is shown that the Radon transform of these wavelets on SO(3) are again wavelets
on
. A novel algorithm for the inversion of experimental pole intensities to an orientation density function based on this relationship
is developed. 相似文献
10.
随着数字高程模型(DEM)在电力行业的广泛应用,电力地图需求部门对数字高程模型的要求越来越高。针对在数字高程模型生产中,电力业主方提供的立体模型高程基准不统一的问题,本文提出了基于特征数据的DEM基础转换方法。该方法在进行DEM制作过程中采用先采集特征数据,后转换特征数据高程基准的方式,实现了DEM成果的高程基准的转换,并进行了实验验证。结果表明,通过对比转换前后的DEM成果位置精度,验证了该方法的正确性。 相似文献