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具有无限权的平差问题 总被引:1,自引:0,他引:1
研究具有无限权观测值的平差问题,具有理论和实际意义。本文在Linkwitz(1961,1971)解法的基础上,导出了改变部分观测的权对间接平差结果影响的公式,得出了具有无限大权和零权的间接平差法和条件平差法,举例说明了该法可能的实际应用,并对自由网平差的一种解法用无限大权的平差理论作了推导。 相似文献
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将熵权理论引入测量平差中,利用熵权法对观测值进行定权,能更加全面地考虑平差值精度的影响因素,并能根据其影响程度的大小合理地分配不同观测值的权重比例,克服经典测量平差中经验定权法的缺点。通过两个具体实例,分别讨论熵权法在水准网平差和边角同测导线网平差中的具体应用。 相似文献
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在测量平差过程中,权的选取会对平差结果造成一定的影响。定权不合理会导致高差观测值改正数分配不合理,严重时会扭曲三角高程平差值,继而平差结果不能真实反映实际观测。本文在分析连续中间法三角高程测量原理的基础上,依据权的定义及误差理论,推导了中间法三角高程测量平差计算中权的确定公式,得出了权与测站距离平方和成反比的定权方法,该方法能客观地反映中间法三角高程测量高差观测值间的权比,有助于改善三角高程测量的精度。 相似文献
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吴晓清 《武汉大学学报(信息科学版)》1989,(4)
文中阐述了权因子法方差分量估计的原理。利用权因子的概念,对目前方差分量估计存在的几个问题,如负方差问题,作了探讨,并与Helmert法进行比较,得出了一些有益的看法。 算例很好地说明了权因子法方差分量估计的简便和实用性。 相似文献
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《测绘科学技术学报》2020,(1)
由于数据探测法、多维粗差同时定位与定值法、拟准检定法以及部分最小二乘法不能同时解算待估参数和粗差,提出了基于选权拟合的粗差参数化平差模型。首先推导了选权拟合的等价模型;在此基础上提出了参数化粗差的平差模型。由于粗差参数化之后观测系统呈现出不适定性,因此,对非粗差部分采取平方和最小的约束,实际上是构造虚拟观测方程。但是,由于事先并不知道粗差的位置,提出了通过搜索来构造虚拟观测方程系数矩阵的方法。算例表明,这种方法用于GPS单点定位可以有效地消除粗差观测的影响。 相似文献
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当观测数据中存在粗差时,使用经典的最小二乘算法往往不能得到高精度的参数解,此时需要使用具有抗差估计的算法。基于验后方差的选权迭代法,克服了单位权方差未知或者权函数靠经验选取的情况,利用验后方差检验求出方差异常大(即含粗差)的观测值,然后通过不断的迭代,使含粗差的权逐渐趋于一个较小的数,最终实现粗差的探测和改正。结合工程实例,分别比较了不含粗差和含粗差的情况下,利用经典最小二乘法与本文所提的基于验后方差原理的选权迭代法进行平差,结果表明,二者的平差结果相差在1mm以内,解算精度相当。 相似文献
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提出了同伦函数与填充函数相结合进行非线性最小二乘平差的方法。先采用同伦函数求解非线性恰定方程组,得到一个局部最优解,然后以该局部最优解为基础构造填充函数,通过对填充函数求解,得到比当前局部最优解更小的局部极小点,再以该局部极小点为基础重新构造同伦函数和填充函数进行求解,通过有限步的循环迭代,最终找到非线性最小二乘平差的全局最优解。实例验证,该方法能有效地寻找出非线性最小二乘平差的全局最优解。 相似文献
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Compactly supported radial covariance functions 总被引:1,自引:0,他引:1
G. Moreaux 《Journal of Geodesy》2008,82(7):431-443
The Least-squares collocation (LSC) method is commonly used in geodesy, but generally associated with globally supported covariance
functions, i.e. with dense covariance matrices. We consider locally supported radial covariance functions, which yield sparse
covariance matrices. Having many zero entries in the covariance matrice can both greatly reduce computer storage requirements
and the number of floating point operations needed in computation. This paper reviews some of the most well-known compactly
supported radial covariance functions (CSRCFs) that can be easily substituted to the usually used covariance functions. Numerical
experiments reveals that these finite covariance functions can give good approximations of the Gaussian, second- and third-order
Markov models. Then, interpolation of KMS02 free-air gravity anomalies in Azores Islands shows that dense covariance matrices
associated with Gaussian model can be replaced by sparse matrices from CSRCFs resulting in memory savings of one-fortieth
and with 90% of the solution error less than 0.5 mGal.
This article is dedicated to Cerbère. 相似文献
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Standard least-squares collocation (LSC) assumes 2D stationarity and 3D isotropy, and relies on a covariance function to account
for spatial dependence in the observed data. However, the assumption that the spatial dependence is constant throughout the
region of interest may sometimes be violated. Assuming a stationary covariance structure can result in over-smoothing of,
e.g., the gravity field in mountains and under-smoothing in great plains. We introduce the kernel convolution method from
spatial statistics for non-stationary covariance structures, and demonstrate its advantage for dealing with non-stationarity
in geodetic data. We then compared stationary and non- stationary covariance functions in 2D LSC to the empirical example
of gravity anomaly interpolation near the Darling Fault, Western Australia, where the field is anisotropic and non-stationary.
The results with non-stationary covariance functions are better than standard LSC in terms of formal errors and cross-validation
against data not used in the interpolation, demonstrating that the use of non-stationary covariance functions can improve
upon standard (stationary) LSC. 相似文献
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应用抗差最小二乘处理天文测量时间比对数据 总被引:2,自引:0,他引:2
介绍了抗差最小二乘法的原理及其优点,分析了几种常见的权函数;研究了用抗差最小二乘方法(IGG3方案)对天文测量的时间比对数据进行处理方法;最后,用算例说明了抗差最小二乘法对数据处理结果比最小二乘理论+3S法则处理结果精度更高。 相似文献
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ABSTRACTUrban functions are closely related to people’s spatiotemporal activity patterns, transportation needs, and a city’s business distribution and development trends. Studies investigating urban functions have used different data sources, such as remotely sensed imageries, observation, photography, and cognitive maps. However, these data sources usually suffer from low spatial, temporal, and thematic resolution. This article attempts to investigate human activities to understand urban functions through crowdsourcing social media data. In this study, we mined Twitter and Foursquare data to extract and analyze six types of human activities. The spatiotemporal analysis revealed hotspots for different activity intensities at different temporal resolution. We also applied the classified model in a real-time system to extract information of various urban functions. This study demonstrates the significance and usefulness of social sensing in analyzing urban functions. By combining different platforms of social media data and analyzing people’s geo-tagged city experience, this article contributes to leverage voluntary local knowledge to better depict human dynamics, discover spatiotemporal city characteristics, and convey information about cities. 相似文献