共查询到20条相似文献，搜索用时 15 毫秒
1.
Approximating covariance matrices estimated in multivariate models by estimated auto- and cross-covariances 总被引：1，自引：1，他引：0
Quantities like tropospheric zenith delays or station coordinates are repeatedly measured at permanent VLBI or GPS stations
so that time series for the quantities at each station are obtained. The covariances of these quantities can be estimated
in a multivariate linear model. The covariances are needed for computing uncertainties of results derived from these quantities.
The covariance matrix for many permanent stations becomes large, the need for simplifying it may therefore arise under the
condition that the uncertainties of derived results still agree. This is accomplished by assuming that the different time
series of a quantity like the station height for each permanent station can be combined to obtain one time series. The covariance
matrix then follows from the estimates of the auto- and cross-covariance functions of the combined time series. A further
approximation is found, if compactly supported covariance functions are fitted to an estimated autocovariance function in
order to obtain a covariance matrix which is representative of different kinds of measurements. The simplification of a covariance
matrix estimated in a multivariate model is investigated here for the coordinates of points of a grid measured repeatedly
by a laserscanner. The approximations are checked by determining the uncertainty of the sum of distances to the points of
the grid. To obtain a realistic value for this uncertainty, the covariances of the measured coordinates have to be considered.
Three different setups of measurements are analyzed and a covariance matrix is found which is representative for all three
setups. Covariance matrices for the measurements of laserscanners can therefore be determined in advance without estimating
them for each application. 相似文献
2.
The 3D similarity coordinate transformation with the Gauss–Helmert error model is investigated. The first-order error analysis of an analytical least-squares solution to this problem is developed in detail. While additive errors are assumed in the translation and scale estimates, a 3 × 1 multiplicative error vector is defined to effectively parameterize the rotation matrix estimation error. The propagation of the errors in the coordinate measurements to the errors in the estimated transformation parameters is derived step-by-step, and the formulae for calculating the variance–covariance matrix of the estimated parameters are presented. 相似文献
3.
顾及框架点坐标误差的三维基准转换严密模型 总被引：1，自引：1，他引：0
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。 相似文献
4.
三维坐标转换参数求解的一种直接搜索法 总被引：1，自引：0，他引：1
采取了两步措施简化三维坐标转换非线性模型:①旋转矩阵的3个旋转角用一个反对称矩阵的3个独立元素代替,将旋转矩阵由反对称矩阵构成Lodrigues矩阵;②将坐标转换7参数模型变换成基线向量模型,消去平移3参数.然后,采用遗传算法与模式搜索法相结合的一种直接搜索法求解参数.算例表明,该算法是可行的.最后,从坐标转换精度的角度时基线向量模型原点与公共点的选取进行了分析,结论是原点选取的点的精度相对较高时坐标转换精度相对较高,公共点的选取以3～5个精度高的点为宜. 相似文献
5.
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。 相似文献
6.
Estimability analysis of variance and covariance components 总被引：1，自引：1，他引：1
Although variance and covariance components have been extensively investigated and a number of elegant formulae to compute
them have been derived, nothing is known, without any ambiguity, about their estimability in the case of a fully unknown variance–covariance
matrix. We prove that variance and covariance components in this case are not estimable, thus clarifying the ambiguity of
the literature on the topic and correcting some erroneous statements in the literature. We also give a new theorem on the
estimability of a linear function of variance and covariance components. Then we propose a new method to estimate the variance–covariance
matrix with special structure, which can presumably be represented by, at most, r(r + 1)/2 independent parameters to guarantee its estimability in such a subspace, by directly implementing the positive definiteness
of the matrix as constraint to the restricted maximum likelihood method, where r is the number of redundant measurements. Therefore, our estimates of the variance and covariance components always reconstruct
a positive definite matrix and are always physically meaningful. 相似文献
7.
在利用函数映射计算模型间对应关系时,提出了一种校准三维几何模型之间基矩阵的新方法,将模型间对应关系的构建转化为由模型特征函数构建的基矩阵之间的校准运算。首先计算三维模型的Laplace算子,获得模型的特征值和特征向量,并利用所得到的特征向量构建基矩阵;其次,提出了协方差的最小值校准算法,以计算模型基矩阵之间的校准矩阵 S ,并用矩阵 S 对两个模型的函数基进行校准;最后,计算校准模型所有点的高斯曲率来采样源模型尖端特征点,并在校准后的目标模型上遍历所有点,以寻求最优对应点来构建等距变换（或近似等距变换）的三维模型间的对应关系。通过计算采样点与最优对应点的测地错误,以衡量所提算法的匹配准确率。实验结果表明,与已有算法相比,本算法可以较为准确地构建两个或多个模型间的对应关系,同时也克服了模型自身对称性影响对应关系计算的问题。 相似文献
8.
Yehuda Bock 《Journal of Geodesy》1983,57(1-4):294-311
The estimation of crustal deformations from repeated baseline measurements is a singular problem in the absence of prior information. One often applied solution is a free adjustment in which the singular normal matrix is augmented with a set of inner constraints. These constraints impose no net translation nor rotation for the estimated deformations X which may not be physically meaningful for a particular problem. The introduction of an available geophysical model from which an expected deformation vector \(\bar X\) and its covariance matrix \(\sum _{\bar X} \) can be computed will direct X to a physically more meaningful solution. Three possible estimators are investigated for estimating deformations from a combination of baseline measurements and geophysical models. 相似文献
9.
A new method through Gauss–Helmert model of adjustment is presented for the solution of the similarity transformations, either 3D or 2D, in the frame of errors-in-variables (EIV) model. EIV model assumes that all the variables in the mathematical model are contaminated by random errors. Total least squares estimation technique may be used to solve the EIV model. Accounting for the heteroscedastic uncertainty both in the target and the source coordinates, that is the more common and general case in practice, leads to a more realistic estimation of the transformation parameters. The presented algorithm can handle the heteroscedastic transformation problems, i.e., positions of the both target and the source points may have full covariance matrices. Therefore, there is no limitation such as the isotropic or the homogenous accuracy for the reference point coordinates. The developed algorithm takes the advantage of the quaternion definition which uniquely represents a 3D rotation matrix. The transformation parameters: scale, translations, and the quaternion (so that the rotation matrix) along with their covariances, are iteratively estimated with rapid convergence. Moreover, prior least squares (LS) estimation of the unknown transformation parameters is not required to start the iterations. We also show that the developed method can also be used to estimate the 2D similarity transformation parameters by simply treating the problem as a 3D transformation problem with zero (0) values assigned for the z-components of both target and source points. The efficiency of the new algorithm is presented with the numerical examples and comparisons with the results of the previous studies which use the same data set. Simulation experiments for the evaluation and comparison of the proposed and the conventional weighted LS (WLS) method is also presented. 相似文献
10.
为了合理地求定按附合网平差的网点坐标的实际精度,本文推广了半动态法,籍此可在首级网的基准下,统一求定顾及各级控制网测量误差影响精度的全部网点坐标的方差—协方差阵。本文所提出的方法适用于种种情况下的精度估计:等级数不受限制的平面、高程或三维网,本级网平差中的固定数据以及待估计的平差值函数可以包含不同级的网点,从而克服了半动态法原有的局限性。 相似文献
11.
Fast GNSS ambiguity resolution as an ill-posed problem 总被引：4，自引：0，他引：4
A linear observational equation system for real-time GNSS carrier phase ambiguity resolution (AR) is often severely ill-posed
in the case of poor satellite geometry. An ill-posed system may result in unreliable or unsuccessful AR if no care is taken
to mitigate this situation. In this paper, the GNSS AR model as an ill-posed problem is solved by regularizing its baseline
and ambiguity parameters, respectively, with the threefold contributions: (i) The regularization parameter is reliably determined
in context of minimizing mean square error of regularized solution where the covariance matrix of initial values of unknowns
is used as an approximate smoothness term instead of the quadratic matrix of the true values of unknowns; (ii) The different
models for computing initial values of unknowns are systematically discussed in order to address the potential schemes in
real world applications; (iii) The superior performance of the regularized AR are demonstrated through the numerically random
simulations as well as the real GPS experiments. The results show that the proposed regularization strategies can effectively
mitigate the model’s ill-condition and improve the success AR probability of the observational system with a severely ill-posed
problem. 相似文献
12.
Large-scale least squares problems require tailored numerical techniques to overcome the computational burden. For these types
of problems, iterative strategies are suitable because of their flexibility and effectiveness. The only shortcoming of iterative
strategies in least squares estimation is that the inverse of the normal equation matrix as the carrier of the covariance
information is either unavailable or very expensive to compute. This paper presents algorithms based on Monte Carlo integration,
which can be incorporated very efficiently into iterative solvers and which are demonstrated to close the aforementioned gap.
Tailored strategies for different types of solution techniques with respect to normal equations, observation equations, and
combined models are treated. Finally, the paper presents new criteria to define confidence regions for the estimated covariance
matrix of the parameters, as well as for all additional derived quantities. In a case study these techniques are applied to
simulated GOCE data, where satellite gravity gradiometry and satellite-to-satellite tracking information are combined for
reconstructing the gravity field. The problem of deriving the covariance matrix of gravity fields with high spatial resolution
by combined iterative estimation processes, unsolved until now, is treated. 相似文献
13.
Summary Using a data set of 260 000 gravity anomalies it is shown that common characteristics for a local covariance function exist
in an area as large as Canada excluding the Rocky Mountains. After eliminating global features by referencing the data to
the GEM-10 satellite solution, the shape of the covariance function is remarkably consistent from one sample area to the next.
The determination of the essential parameters and the fitting of the covariance function are discussed in detail.
To test the reliability of the derived function, deflections of the vertical are estimated at about 230 stations where astrogeodetic
data are available. Results show that the standard error obtained from the discrepancies is about1″ for each component and that the error covariance matrix of least-squares collocation reflects this accuracy remarkably well. 相似文献
14.
Klaus-Peter Schwarz 《Journal of Geodesy》1974,48(2):171-186
When combining satellite and terrestrial networks, covariance matrices are used which have been estimated from previous data.
It can be shown that the least-squares estimator of the unknown parameters using such an estimated covariance matrix is not
necessarily the best. There are a number of cases where a more efficient estimator can be obtained in a different way. The
problem occurs frequently in geodesy, since in least-squares adjustment of correlated observations estimated covariance matrices
are often used.
If the general structure of the covariance matrix is known, results can often be improved by a method called covariance adjustment.
The statistical model used in least-squares collocation leads to a type of covariance matrix which fits into this framework.
It is shown in which way improvements can be made using a modified approach of principal component analysis.
As a numerical example the combination of a satellite and a terrestrial network has been computed with varying assumptions
on the covariance matrix. It is shown which types of matrices are critical and where the usual least-squares approach can
be applied without hesitation. Finally, a simplified representation of covariances for spatial networks by means of a suitable
covariance function is suggested.
Paper presented at the International Symposium on Computational Methods in Geometrical Geodesy-Oxford, 2–8 September, 1973. 相似文献
15.
时平面控制网的相对点位精度评定问题做了一些理论分析,探讨了在不同基准条件下协因数阵的转换关系,及依据转换后的协因数阵来评定相对点位精度的问题.在有关数学模型推导的基础上,利用MATLAB语言编制了控制网平差及相对点位精度的评定程序,并结合具体的工程进行了算例分析. 相似文献
16.
H. Wolf 《Journal of Geodesy》1980,54(1):45-53
Summary In a combined Doppler and terrestrial net adjustment not only the known systematic discrepancies in scale and orientation
between the Doppler measurements and the terrestrial results must be modelled, but also all available informations about the
accuracy of these systematic differences are to be taken into account. Using the Helmert-block method for the combination
procedure, no covariance matrices for the terrestrially determined coordinates must be computed, their numerical evaluation
being a computational detour. The proposed procedure as applied to real nets, includes all different kinds of geometric or
physical models, whereby their specific parameters are eliminated at this level. Two solutions are discussed, a three-dimensional
and a two-dimensional one, but “two-dimensional” is not equivalent to “non-spatial” in this context. 相似文献
17.
18.
为方便三维点云数据的统一管理和工程应用,需要为其提供统一的坐标基准。在数据采集阶段,对于在控制点可通视的测区内,可利用后视定向的方法完成点云扫描测量工作。针对控制点无法通视的测区,本文提出基于全站仪三维自由设站控制测量的方法,建立间接设站点平差模型并进行平差,进而解算标靶点坐标,利用标靶将扫描点转换到绝对坐标系中。试验结果表明:标靶坐标的测量精度和点云拼接的精度符合要求。在测区观测条件不好的情况下,自由设站法的应用为点云拼接提供了一种可行的方法。 相似文献
19.
GNSS模糊度降相关算法及其评价指标研究 总被引：4，自引：0，他引：4
针对Gauss、LDL和LLL算法构造整数阵存在的实数阵元素计算、实数至整数阵转换的排序问题,分别研究了相应的元素升序降相关算法和整逆型(先求逆后取整)降相关算法。分析了谱条件数、降相关系数和平均相关系数等降相关算法评价指标的优缺点,提出了等效相关系数评价指标。研究结果表明,等效相关系数较其他3种指标能更有效地评价不同维数方差阵,尤其是高维情况的降相关算法效果;逆整型优于整逆型降相关算法,升序(逆整型)降相关算法更佳,且优劣顺序为升序LDL、升序Gauss和升序LLL算法。 相似文献
20.
On weighted total least-squares adjustment for linear regression 总被引：16，自引：5，他引：11
The weighted total least-squares solution (WTLSS) is presented for an errors-in-variables model with fairly general variance–covariance
matrices. In particular, the observations can be heteroscedastic and correlated, but the variance–covariance matrix of the
dependent variables needs to have a certain block structure. An algorithm for the computation of the WTLSS is presented and
applied to a straight-line fit problem where the data have been observed with different precision, and to a multiple regression
problem from recently published climate change research. 相似文献