共查询到19条相似文献，搜索用时 671 毫秒
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论测量平差中的权和权阵 总被引：1，自引：0，他引：1
平差教材中关于权和权阵的论述分散在第三、四两章中,不利于教学和学生复习。先给出观测向量的方差阵,由方差阵定义协因数阵、协因数,再由协因数阵定义权阵,将更宜于教学和学习。 相似文献
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空间直角坐标的协因数阵转换到高斯平面上的计算公式 总被引：5，自引：0，他引：5
导出了由空间直角坐标的协因数阵向大地坐标的协因数阵；由大地坐标的协因数阵向高斯平面直角坐标的协因数阵转换的计算公式。在此基础上，导出了直接由空间角坐标的协因数阵计算高斯平面直角坐标的因数阵的简便公式。 相似文献
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马凌会 《测绘与空间地理信息》2009,32(3):205-207
提出了利用普通间接平差和相关间接平差两种平差方法相结合,进行以坐标差作为观测值进行导线网相关平差的方法.在该平差方法中,利用普通的简介平差原理推求出坐标差观测值的相关协因数阵,并以此作为已知数据进行以坐标差观测值作为观测值的导线网的相关平差. 相似文献
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闫伟新 《测绘与空间地理信息》2019,42(11)
针对目前隧道洞外GPS控制网横向贯通误差严密计算方法在理论上的不足,本文基于坐标转换模型和协因数传播定律推导了隧道独立坐标协因数阵的计算公式,研究了基于验后单位权中误差和隧道独立坐标协因数阵的隧道洞外GPS网引起的横向贯通误差严密计算方法。之后,以某特长铁路隧道工程洞外GPS控制网实测数据作为研究对象,阐述了横向贯通误差严密计算的技术流程。研究成果为控制隧道工程准确贯通提供了参考。 相似文献
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本文提出了一种钭地心笛卡尔坐标系中一地面投影到旋转椭球面的快速迭代解法。并由此点的地心笛片尔坐标协因数阵导出此点及其到椭球面投影响的坐标全向量协因数阵，用以计算椭球高及相关方差。 相似文献
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非线性观测值函数的协方差和协因数传播及其权倒数 总被引：10，自引：1，他引：10
将非线性观测值函数在其近似值处泰勒级数展开，取至二次项，得到线性－二次项形式。利用线性空间［Ｌ，Ｑ］＾Ｎ的概念和性质，将它表示成［α，β］的向量形式。定义广义协方差算子和广义协因数算子，导出了线性－二次项的非线性观测值函数的广义协方差和广义协因数传播律。在此基础上，给出了非线性平差值函数和未知数函数的权倒数公式。 相似文献
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当观测向量和系数矩阵不等精度时,利用系数矩阵元素和观测向量之间的映射关系,通过误差传播定律推导了系数矩阵的协因数阵,算例结果表明,改进的加权总体最小二乘法能够得到正确、合理的参数,且本文方法简单、实用。 相似文献
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加权整体最小二乘方法是一种能同时顾及EIV（errors-in-variables）模型中系数矩阵和观测向量误差的参数估计方法。根据不同的应用场景，EIV模型则表现出不同的结构特征。"加权整体最小二乘EIO模型与算法"一文采用EIO模型处理EIV模型中的结构化问题*。为了将其与现有方法进行对比，本文罗列出4种处理EIV模型结构特征的方法，并归纳了8种参数估计公式。同时从精度评定的角度讨论了整体最小二乘解的一阶及更高阶精度近似评定方法。需要强调的是，针对EIV模型及其参数估计理论可以从函数模型、随机模型和参数估计方法3个方面展开研究，但各方法殊途同归。 相似文献
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基于加权整体最小二乘的牛顿-高斯迭代算法,提出了一种抗差加权整体最小二乘模型。利用标准化残差构造权因子函数,并采用中位数法获得具有抗差性的单位权中误差估值,能同时实现观测空间和结构空间抗差。为获得标准化残差,利用线性近似的协因数传播律推导了加权整体最小二乘残差协因数阵的表达式,并给出模型的迭代计算方法。试验结果表明:对于加权整体最小二乘的粗差处理问题,本文提出的方法具有良好的抗差性能,参数估值与不含粗差时加权整体最小二乘的结果没有显著的差异,性能优于直接由残差构造的稳健加权整体最小二乘模型。 相似文献
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P. J. G. Teunissen 《Journal of Geodesy》1997,71(9):541-551
In this contribution we analyse in a qualitative sense for the geometry-free model the dependency of the location, the size
and the shape of the ambiguity search space on different factors of the stochastic model. For this purpose a rather general
stochastic model is used. It includes time-correlation, cross-correlation, satellite elevation dependency and the use of an
a priori weighted ionospheric model, having the ionosphere-fixed model and the ionosphere-float model as special cases. It
is shown that the location is invariant for changes in the cofactor matrix of the phase observables. This also holds true
for the cofactor matrix of the code observables in the ionosphere-float case. As for time-correlation and satellite elevation
dependency, it is shown that they only affect the size of the search space, but not its shape and orientation. It is also
shown that the least-squares ambiguities, their variance matrix and its determinant, for, respectively, the ionosphere-fixed
model, the ionosphere-float model and the ionosphere-weighted model, are all related through the same scalar weighted mean,
the weight of which is governed by the variance ratio of the ionospheric delays and the code observables. A closed-form expression
is given for the area of the search space in which all contributing factors are easily recognized. From it one can infer by
how much the area gets blown up when the ionospheric spatial decorrelation increases. This multiplication factor is largest
when one switches from the ionosphere-fixed model to the ionosphere-float model, in which case it is approximately equal to
the ratio of the standard deviation of phase with that of code. The area gives an indication of the number of grid points
inside the search space.
Received: 11 November 1996 / Accepted: 21 March 1997 相似文献
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根据GPS相对定位数据处理的一般模型,导出了GPS基线向量的协因数阵,结合GPS桥梁控制网的模拟算例,采用GPS控制网整体平差理论,通过计算机编程实现了模拟网的点位精度估算. 相似文献
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回归预测模型是对传统回归模型的进一步扩展,不仅涉及回归模型的固定参数估计,而且将模型预测纳入平差的部分内容,更加符合实际解算需求。针对在回归模型预测中经常出现待预测非公共点(自变量)含有观测误差和随机模型不准确的问题,基于EIV(errors-in-variables)模型提出了一种同时顾及所有变量观测误差的整体解法。同时,将方差-协方差分量估计方法引入回归预测模型解算中,以修正随机模型与待预测非公共点的先验协因数阵,并推导了相关计算公式和迭代算法。算例试验表明,该方法能够有效估计各类观测数据的方差分量,为获取更合理的参数估计与更高的模型预测精度提供了可行手段。另外,通过设计多种对比方案可知,该方法的预测效果较好,尤其是针对观测数据与系数矩阵中随机元素之间存在一定相关性的情况。 相似文献
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Xing Fang 《Journal of Geodesy》2014,88(8):805-816
Observation systems known as errors-in-variables (EIV) models with model parameters estimated by total least squares (TLS) have been discussed for more than a century, though the terms EIV and TLS were coined much more recently. So far, it has only been shown that the inequality-constrained TLS (ICTLS) solution can be obtained by the combinatorial methods, assuming that the weight matrices of observations involved in the data vector and the data matrix are identity matrices. Although the previous works test all combinations of active sets or solution schemes in a clear way, some aspects have received little or no attention such as admissible weights, solution characteristics and numerical efficiency. Therefore, the aim of this study was to adjust the EIV model, subject to linear inequality constraints. In particular, (1) This work deals with a symmetrical positive-definite cofactor matrix that could otherwise be quite arbitrary. It also considers cross-correlations between cofactor matrices for the random coefficient matrix and the random observation vector. (2) From a theoretical perspective, we present first-order Karush–Kuhn–Tucker (KKT) necessary conditions and the second-order sufficient conditions of the inequality-constrained weighted TLS (ICWTLS) solution by analytical formulation. (3) From a numerical perspective, an active set method without combinatorial tests as well as a method based on sequential quadratic programming (SQP) is established. By way of applications, computational costs of the proposed algorithms are shown to be significantly lower than the currently existing ICTLS methods. It is also shown that the proposed methods can treat the ICWTLS problem in the case of more general weight matrices. Finally, we study the ICWTLS solution in terms of non-convex weighted TLS contours from a geometrical perspective. 相似文献
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刘新洪 《测绘与空间地理信息》2012,35(9):167-169
最初给出的灵敏度准则是用来解决监测网中单点移动的情况,本文分析了由此产生的几种处理多点、多块移动方法的不合理性。在此基础上,提出多点、多块移动必须用相应的坐标差协因数子矩阵求最弱检测方向或某给定方向的灵敏度数值,并举例进行论证。 相似文献
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G. Fotopoulos 《Journal of Geodesy》2005,79(1-3):111-123
The well-known statistical tool of variance component estimation (VCE) is implemented in the combined least-squares (LS) adjustment of heterogeneous height data (ellipsoidal, orthometric and geoid), for the purpose of calibrating geoid error models. This general treatment of the stochastic model offers the flexibility of estimating more than one variance and/or covariance component to improve the covariance information. Specifically, the iterative minimum norm quadratic unbiased estimation (I-MINQUE) and the iterative almost unbiased estimation (I-AUE) schemes are implemented in case studies with observed height data from Switzerland and parts of Canada. The effect of correlation among measurements of the same height type and the role of the systematic effects and datum inconsistencies in the combined adjustment of ellipsoidal, geoid and orthometric heights on the estimated variance components are investigated in detail. Results give valuable insight into the usefulness of the VCE approach for calibrating geoid error models and the challenges encountered when implementing such a scheme in practice. In all cases, the estimated variance component corresponding to the geoid height data was less than or equal to 1, indicating an overall downscaling of the initial covariance (CV) matrix was necessary. It was also shown that overly optimistic CV matrices are obtained when diagonal-only cofactor matrices are implemented in the stochastic model for the observations. Finally, the divergence of the VCE solution and/or the computation of negative variance components provide insight into the selected parametric model effectiveness. 相似文献