顾及框架点坐标误差的三维基准转换严密模型

框架点坐标是由观测数据通过平差得到的,不可避免地受到观测误差的影响。针对原框架和目标框架坐标均存在误差、非公共点与公共点间存在相关性,以及转换系数矩阵中仅部分元素存在误差的实际情况,提出了同时考虑框架内误差以及转换点间相关性的基准转换严密模型,该模型将公共点和非公共点联合处理,同时计算坐标转换参数和所有点的坐标转换值,推导出了新的严格坐标转换公式,该公式为传统坐标转换公式基础上增加一改正量的形式;进一步,推导了原框架和目标框架坐标的方差不一致情况下的坐标转换模型的自适应解法;最后,利用"陆态网络工程"2000个区域站的实测坐标进行坐标转换验证,结果表明,这种严密模型较传统坐标转换模型具有更高的坐标转换精度。     

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.     

基于六参数仿射变换的控制点选取及坐标校正分析

以经纬度坐标转换到深圳坐标为例,利用卫星遥感影像,通过全局搜寻算法选择控制点对求解仿射变换六参数值,在不同约束目标下对坐标距离偏差程度进行筛选分析,确定适合深圳坐标下能有效提高校正精度的控制点对组合及校正坐标公式。     

三维坐标转换公共点最优权值的单纯形搜索算法

为提高三维坐标转换参数的求解质量,本文基于最优化算法提出了一种稳健的公共点加权坐标转换方法。以坐标转换后公共点的点位残差加权平方和最小为目标函数,利用Nelder-Mead单纯形直接搜索算法,寻找公共点坐标分量在解算坐标转换参数时的最优权重组合。以粒子加速器磁铁的准直安装为应用场景,利用模拟数据和实测数据对本文方法进行验证。结果表明:本文方法能够有效降低粗差观测值及质量不佳观测值的权重。与最小二乘、抗差估计等方法相比,本文方法解算结果的点位残差加权平方和更小,坐标转换参数质量更优。本文方法能提高三维坐标转换参数的求解质量,尤其适用于验前精度未知、观测数据质量不佳的情况。     

Development of a Coordinate Transformation method for direct georeferencing in map projection frames

This paper develops a novel Coordinate Transformation method (CT-method), with which the orientation angles (roll, pitch, heading) of the local tangent frame of the GPS/INS system are transformed into those (omega, phi, kappa) of the map projection frame for direct georeferencing (DG). Especially, the orientation angles in the map projection frame were derived from a sequence of coordinate transformations. The effectiveness of orientation angles transformation was verified through comparing with DG results obtained from conventional methods (Legat method¹ and POSPac method²) using empirical data. Moreover, the CT-method was also validated with simulated data. One advantage of the proposed method is that the orientation angles can be acquired simultaneously while calculating position elements of exterior orientation (EO) parameters and auxiliary points coordinates by coordinate transformation.These three methods were demonstrated and compared using empirical data. Empirical results show that the CT-method is both as sound and effective as Legat method. Compared with POSPac method, the CT-method is more suitable for calculating EO parameters for DG in map projection frames. DG accuracy of the CT-method and Legat method are at the same level. DG results of all these three methods have systematic errors in height due to inconsistent length projection distortion in the vertical and horizontal components, and these errors can be significantly reduced using the EO height correction technique in Legat’s approach. Similar to the results obtained with empirical data, the effectiveness of the CT-method was also proved with simulated data.     

基于Delaunay三角网的大范围GPS坐标转换研究

针对土地监管中大范围区域GPS坐标转换的问题,提出一种基于Delaunay三角网的大范围GPS坐标转换方法.根据土地监管区域的已知控制点构建Delaunay三角网,然后确定待转换点属于哪一个三角形,结合三角形的3个控制点,利用九参数坐标转换模型求解转换参数并转换待转换点.以整个天津市为研究对象,通过BURSA-WOLF...     

关于重心基准的坐标转换方法研究

基准统一与转换是测量工程中的重要问题,文中通过数值计算表明,为了克服坐标转换模型中参数之间的强相关问题,采用坐标重心化策略,得到的结果与四参数方法基本相同,重心化方法减小了参与计算的坐标数值,增强数值计算的可靠性,随着现代计算技术(计算设备)的广泛应用,两者的差异并不明显。各种坐标转换算法的可靠性依赖于公共点的精度与公共点的分布形式,在极坐标方法中尤其要避免边长悬殊的短边参与参数解算。      

浅谈常用坐标系统的关系及坐标转换的原理

GPS观测成果是WGS-84中的地心空间直接坐标,现实测绘中,我们通常需要的是国家平面坐标。如何有效地转换该坐标成果,一直是工作中的难题。在介绍几种常用坐标系统的基础上,简单分析了坐标转换的基本原理,结合转换模型取得的精度,得出了一些有益的结论。     

一种实现西安80坐标系地形图向北京54坐标系快速转换的简易方法

本文针对GIS应用中经常遇到的西安80和北京54坐标之间的转换问题,提出了实现两种坐标系地形图相互转换的简易方法。首先利用MAPGIS软件自动生成西安80矢量标准图框,根据坐标改正参数,将西安80坐标系图框转换到北京54坐标系,再以它为参照基准,对地形图进行逐格网纠正,实现西安80坐标系地形图向北京54坐标系的转换。该方法操作简单,易于实现,非常适合于非测绘人员使用。     

The geodetic boundary value problem and the coordinate choice problem

Summary The geodetic boundary value problem (g.b.v.p.) is a free boundary value problem for the Laplace operator: however, under suitable change of coordinates, it can be transformed into a fixed boundary one. Thus a general coordinate choice problem arises: two particular cases are more closely analyzed, namely the gravity space approach and the intrinsic coordinates (Marussi) approach.     

广州平面坐标到1980西安坐标的转换方法研究与实现

根据我国多种坐标系统共存的现实,结合生产实际需求,研究了一种利用不同坐标系公共点确定广州坐标系到1980西安坐标转换的实用方法。这种实用方法的特点是充分考虑广州坐标系统的独特性,提出了广州平面坐标到西安80坐标转换的坐标转换技术方案。同时,开发了实用方便的计算软件。通过算例证明了该方法的可行性和可靠性。     

坐标参数加权平差法在线路补测中的应用

在线路施工的补充测量控制中,对先期控制点老坐标的如何使用,关系到新坐标的网形精度和与老坐标的差异程度.介绍了对先期控制点坐标进行赋权参加平差的方法,并给出评定结果的指标.用实例分析验证了这种方法的有效性.     

On symmetrical three-dimensional datum conversion

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.     

A coordinate-invariant model for deforming geodetic networks: understanding rank deficiencies,non-estimability of parameters,and the effect of the choice of minimal constraints

By considering a deformable geodetic network, deforming in a linear-in-time mode, according to a coordinate-invariant model, it becomes possible to get an insight into the rank deficiency of the stacking procedure, which is the standard method for estimating initial station coordinates and constant velocities, from coordinate time series. Comparing any two out of the infinitely many least squares estimates of stacking unknowns (initial station coordinates, velocity components and transformation parameters for the reference system in each data epoch), it is proven that the two solutions differ only by a linear-in-time trend in the transformation parameters. These pass over to the initial coordinates (the constant term) and to the velocity estimates (the time coefficient part). While the difference in initial coordinates is equivalent to a change of the reference system at the initial epoch, the differences in velocity components do not comply with those predicted by the same change of reference system for all epochs. Consequently, the different velocity component estimates, obtained by introducing different sets of minimal constraints, correspond to physically different station velocities, which are therefore non-estimable quantities. The theoretical findings are numerically verified for a global, a regional and a local network, by obtaining solutions based on four different types of minimal constraints, three usual algebraic ones (inner or partial inner) and the lately introduced kinematic constraints. Finally, by resorting to the basic ideas of Felix Tisserand, it is explained why the station velocities are non-estimable quantities in a very natural way. The problem of the optimal choice of minimal constraints and, hence, of the corresponding spatio-temporal reference system is shortly discussed.     

基于RANSAC的坐标系转换抗差算法研究

空间坐标转换在大地测量、工程测量等领域应用广泛.在利用公共点求解坐标转换参数时,针对公共点中混有多粗差点的情形,给出了基于罗德里格矩阵的坐标系转换模型,并在此基础上提出了基于随机抽样一致性(RANSAC)算法粗差剔除的坐标系转换抗差估计.最后利用仿真数据对该算法进行了验证,同时将该抗差算法与基于IGG3方案的最小二乘抗差估计算法进行了比较.算例结果表明,在20个仿真公共点数据中(仿真多组数据),当粗差点个数超过公共点总数的3/10时,基于IGG3方案的最小二乘抗差算法失效,而基于RANSAC的抗差算法在粗差点个数达到公共点总数的1/2时,依然能保证坐标转换的精度.该抗差算法将RANSAC算法的思想应用到坐标系转换上,有效地剔除了公共点中混有的大量粗差点.     

Transforming ellipsoidal heights and geoid undulations between different geodetic reference frames

Transforming height information that refers to an ellipsoidal Earth reference model, such as the geometric heights determined from GPS measurements or the geoid undulations obtained by a gravimetric geoid solution, from one geodetic reference frame (GRF) to another is an important task whose proper implementation is crucial for many geodetic, surveying and mapping applications. This paper presents the required methodology to deal with the above problem when we are given the Helmert transformation parameters that link the underlying Cartesian coordinate systems to which an Earth reference ellipsoid is attached. The main emphasis is on the effect of GRF spatial scale differences in coordinate transformations involving reference ellipsoids, for the particular case of heights. Since every three-dimensional Cartesian coordinate system ‘gauges’ an attached ellipsoid according to its own accessible scale, there will exist a supplementary contribution from the scale variation between the involved GRFs on the relative size of their attached reference ellipsoids. Neglecting such a scale-induced indirect effect corrupts the values for the curvilinear geodetic coordinates obtained from a similarity transformation model, and meter-level apparent offsets can be introduced in the transformed heights. The paper explains the above issues in detail and presents the necessary mathematical framework for their treatment. An erratum to this article can be found at     

一种遥感图像的坐标转换方法

在遥感应用中,要将遥感影像的空间信息转换到其他坐标系中,一般通过几何校正来实现。这种方法工作量大而且不可避免会引入新的误差。本文从坐标转换的角度出发,通过事先计算两个坐标系之间的转换参数,结合遥感影像中储存空间信息的方式,推导出遥感图像坐标转换的计算公式,并由此推导出根据坐标转换参数计算重采样像元坐标变换函数。根据本文提出方法,可以很方便地实现遥感图像的坐标转换,将遥感图像的空间信息转换到不同坐标系下。     

Assessment of second- and third-order ionospheric effects on regional networks: case study in China with longer CMONOC GPS coordinate time series

Higher-order ionospheric (HOI) delays are one of the principal technique-specific error sources in precise global positioning system analysis and have been proposed to become a standard part of precise GPS data processing. In this research, we apply HOI delay corrections to the Crustal Movement Observation Network of China’s (CMONOC) data processing (from January 2000 to December 2013) and furnish quantitative results for the effects of HOI on CMONOC coordinate time series. The results for both a regional reference frame and global reference frame are analyzed and compared to clarify the HOI effects on the CMONOC network. We find that HOI corrections can effectively reduce the semi-annual signals in the northern and vertical components. For sites with lower semi-annual amplitudes, the average decrease in magnitude can reach 30 and 10 % for the northern and vertical components, respectively. The noise amplitudes with HOI corrections and those without HOI corrections are not significantly different. Generally, the HOI effects on CMONOC networks in a global reference frame are less obvious than the results in the regional reference frame, probably because the HOI-induced errors are smaller in comparison to the higher noise levels seen when using a global reference frame. Furthermore, we investigate the combined contributions of environmental loading and HOI effects on the CMONOC stations. The largest loading effects on the vertical displacement are found in the mid- to high-latitude areas. The weighted root mean square differences between the corrected and original weekly GPS height time series of the loading model indicate that the mass loading adequately reduced the scatter on the CMONOC height time series, whereas the results in the global reference frame showed better agreements between the GPS coordinate time series and the environmental loading. When combining the effects of environmental loading and HOI corrections, the results with the HOI corrections reduced the scatter on the observed GPS height coordinates better than the height when estimated without HOI corrections, and the combined solutions in the regional reference frame indicate more preferred improvements. Therefore, regional reference frames are recommended to investigate the HOI effects on regional networks.     

已知平面与高程点不同时的严密三维基准变换

由于常规控制网的平面与高程网分开布设,当求解常规控制网与GNSS三维控制网的基准变换参数时,需要分别利用其平面坐标和高程的已知成果。传统控制网与三维GNSS控制网都存在误差,文中在解算变换参数时,同时对两套坐标引入改正数,并顾及公共点与转换点观测误差的相关性,利用公共点的改正数推估转换点的改正数,实现两套坐标的基准变换。模拟数据的分析结果表明,文中方法能够在常规平面与高程控制网分开布设时,实现与GNSS三维控制网的基准变换。     

综合不同时期的GPS数据求解转换参数的方法

提出了综合利用不同时期的GPS数据解算三维坐标转换参数的一种方法 ,并结合上海地区 1999年和 2 0 0 2年施测的两个GPS控制网数据 ,验证了给出的模型和方法。结果表明 ,利用本方法是合理而有效的