共查询到17条相似文献，搜索用时 93 毫秒
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采用不同类数据联合平差时,不仅观测向量含有误差,其对应的系数矩阵也通常受到误差的影响。将加权总体最小二乘方法应用于多类观测数据的联合平差模型,推导相应迭代计算方法,以相对权比权衡各类数据参与联合平差的比重。设计了多种方案,并给出了确定相对权比的判别函数最小化方法。结果表明,验前单位权方差法与总体最小二乘方差分量估计方法具有一定的局限性,当验前信息不准确或者总体最小二乘方差分量估计方法不可估时,判别函数为$\mathop {\mathop \sum \limits_{i = 1} }\limits^{{n_1}} \left| {{{\widehat {\bar e}}_{{1_i}}}} \right| + \mathop {\mathop \sum \limits_{j = 1} }\limits^{{n_2}} \left| {{{\widehat {\bar e}}_{{2_j}}}} \right|$的判别函数最小化法能取得较优的参数估值结果。 相似文献
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针对垂直位移与水平位移的Mogi模型,提出采用总体最小二乘联合（total least squares joint,TLS-J）平差方法进行求解。该方法可同时顾及联合平差函数模型中观测向量与系数矩阵的误差项,且采用3种判别函数最小化法确定相对权比,用以权衡垂直位移与水平位移观测数据在联合求解过程中所占的比重。针对平差过程中出现的病态问题,结合L曲线法确定岭参数。通过实际算例,系统研究了总体最小二乘联合平差方法在长白山天池火山Mogi模型反演中的应用。研究结果表明,以判别函数为$\sum\limits_{i=1}^{n1}{\left| {{{\hat{\bar{e}}}}_{1i}} \right|}+\sum\limits_{j=1}^{n2}{\left| {{{\hat{\bar{e}}}}_{2j}} \right|}$的函数最小化能获得合理的压力源参数估值结果和相对权比大小,具有一定的实际参考价值。 相似文献
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附有相对权比的总体最小二乘平差 总被引：3，自引：1，他引：2
推导了加权情况下附有相对权比的总体最小二乘平差方法,提出了确定相对权比的验前单位权方差法和目标函数最小化法。模拟算例表明,当观测值和系数矩阵的验前单位权方差已知且比较准确时,验前单位权方差法得到的结果与参数真值的差值范数最小;目标函数最小化法的目标函数估值最小,与参数真值的差别比验前单位权方差法的结果稍大。 相似文献
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将顾及观测向量与系数矩阵权比的总体最小二乘法应用于三维坐标转换,阐述了验前单位权方差法和目标函数最小化法确定观测向量与系数矩阵标度的计算步骤,结合算例探讨了两种方法的适用特点,得出了有益的结论。 相似文献
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《武汉大学学报(信息科学版)》2016,(12)
提出了将总体最小二乘方法应用于联合平差的模型,推导了附有相对权比的总体最小二乘联合平差方法。采用了多种方案来确定相对权比的大小。以参数估值与真值的差值范数作为评价指标,分析比较了单一数据总体最小二乘平差和两类数据总体最小二乘联合平差的模拟算例;通过给各类数据加入不同大小的随机噪声,分析了判别函数最小化法中随机噪声大小对确定相对权比的影响。模拟算例表明,平差结果的质量与相对权比的选取有关;当先验信息准确时,验前单位权方差法的结果最好,而当先验信息不准确时,判别函数为∑n_1i=1|V1_i|+∑n_2j=1|V2_j|及∑n_1i=1|V1_i|+∑n_2j=1|V2_j|/(1+X~TX)法均能取得有效的平差的判别函数最小化结果。 相似文献
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非差非组合精密单点定位需要估计电离层延迟参数,采用电离层先验改正模型约束可以辅助电离层参数解算。针对先验电离层改正量与实际观测量之间权比关系难以确定的问题,本文提出一种电离层约束权因子搜索算法,采用权因子对先验电离层改正量的方差进行调整,根据验后残差加权平方和最小原则通过搜索找出较优的权因子,利用验后残差动态调整先验电离层改正量的方差从而达到改善定位结果的目的。采用8个MGEX跟踪站的GPS/BDS观测数据对该算法进行验证。静态结果表明：对比传统约束方法,采用搜索算法后平均三维定位精度由3.96 cm提高到3.40 cm,平均收敛时间由76.3 min缩短为59.9 min。 相似文献
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整体最小二乘法不仅考虑观测向量的误差而且还考虑系数矩阵的误差,平差理论相对更为严密。在研究经典整体最小二乘法的基础之上,对系数矩阵元素是表达式或函数情况的非线性整体最小二乘模型进行了描述,用拉格朗日极值条件式推导了基于牛顿型解法的非线性整体最小二乘平差计算公式,并设计了一种对应的迭代算法。最后设计了两组模拟试验分析在观测向量和系数矩阵的输入向量等精度观测和非等精度观测两种情况下参数和验后方差的估计特点。试验结果表明,非线性整体最小二乘平差法获得的参数估计值比最小二乘平差法获得的估计结果更接近参数的实际值,方差分量(或中误差)估计结果也更接近先验值,本文给出的迭代算法是有效的。 相似文献
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部分变量误差模型(partial EIV model)的加权整体最小二乘(weighted total least-squares,WTLS)估计不具备抵御粗差的能力。鉴于粗差可能同时出现在观测值和系数矩阵中,本文在提出部分变量误差模型WTLS估计的两步迭代解法的基础上,运用抗差M估计的等价权方法,发展了一种整体抗差最小二乘(TRLS)估计方法,并采用一致最大功效统计量确定降权因子。针对WTLS估计两步迭代解法的特点,设计了两个不同的降权方案:第1个方案是在估计系数矩阵元素时,不对观测值降权,仅对系数矩阵降权;第2个方案是在估计系数矩阵元素时,既对系数矩阵降权,同时也对观测值降权。通过对模拟2D仿射变换和线性拟合实例进行计算和分析,结果表明第1方案优于第2方案,并且优于基于残差和验后单位权方差的抗差估计和现有的变量误差模型抗差估计。 相似文献
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顾及像点观测方程的系数矩阵中存在随机误差,提出了基于总体最小二乘的线阵卫星遥感影像光束法平差模型。在假定像点观测误差和系数矩阵误差均为独立、等精度分布的基础上,利用拉格朗日条件极值法推导了包含外方位元素虚拟观测方程和控制点误差方程的总体最小二乘光束法平差算法的具体公式和计算方法。该方法利用方差分量估计确定各类虚拟观测值的方差,可求解包含多类虚拟观测量的平差问题,并可用先验信息或岭迹法确定系数矩阵观测值的权比例系数,从而克服了现有总体最小二乘虚拟观测方法不能处理多类虚拟观测值的不足,确保了光束法平差可正确有效求解。分别利用模拟算例与两组真实影像进行了试验验证。结果表明,相比于常规最小二乘虚拟观测法以及现有总体最小二乘虚拟观测方法,本文方法具有更高的求解精度与适应性。相较于传统线阵卫星遥感影像光束法平差方法,本文方法可以获得更高的平差计算精度。 相似文献
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Torsion balance observations in spherical approximation may be expressed as second-order partial derivatives of the anomalous (gravity) potential,T, $$T_{13} = \frac{{\partial ^2 T}}{{\partial x_1 \partial x_3 }}, T_{23} = \frac{{\partial ^2 T}}{{\partial x_2 \partial x_3 }}, T_{12} = \frac{{\partial ^2 T}}{{\partial x_1 \partial x_2 }}, T_\Delta = \frac{{\partial ^2 T}}{{\partial x_1^2 }} - \frac{{\partial ^2 T}}{{\partial x_1^2 }},$$ wherex 1 ,x 2 andx 3 are local coordinates withx 1 “east”,x 2 “north” andx 3 “up.” Auto- and cross-covariances for these quantities derived from an isotropic covariance function for the anomalous potential will depend on the directions between the observation points. However, the expressions for the covariances may be derived in a simple manner from isotropic covariance functions of torsion balance measurements. These functions are obtained by transforming the torsion balance observations in the points to local (orthogonal) horizontal coordinate systems with first axes in the direction to the other observation point. If the azimuth of the direction from one point to the other point is a, then the result of this transformation may be obtained by rotating the vectors $$\left\{ \begin{gathered} T_{13} \hfill \\ T_{23} \hfill \\ \end{gathered} \right\}and\left\{ \begin{gathered} T_\Delta \hfill \\ 2T_{12} \hfill \\ \end{gathered} \right\}$$ the angles a?90° and 2 (a?90°) respectively. The reverse rotations applied on the 2×2 matrices of covariances of these quantities will produce all the direction dependent covariances of the original quantities. 相似文献
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GPS Solutions - We propose a filter and a piecewise smoother based on the matrix Lie group of double direct isometries ( $${\mathrm{SE}}_{2}(3)$$ ) to improve the accuracy of the Global Navigation... 相似文献
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This research represents a continuation of the investigation carried out in the paper of Petrovskaya and Vershkov (J Geod 84(3):165–178, 2010) where conventional spherical harmonic series are constructed for arbitrary order derivatives of the Earth gravitational potential in the terrestrial reference frame. The problem of converting the potential derivatives of the first and second orders into geopotential models is studied. Two kinds of basic equations for solving this problem are derived. The equations of the first kind represent new non-singular non-orthogonal series for the geopotential derivatives, which are constructed by means of transforming the intermediate expressions for these derivatives from the above-mentioned paper. In contrast to the spherical harmonic expansions, these alternative series directly depend on the geopotential coefficients ${\bar{{C}}_{n,m}}$ and ${\bar{{S}}_{n,m}}$ . Each term of the series for the first-order derivatives is represented by a sum of these coefficients, which are multiplied by linear combinations of at most two spherical harmonics. For the second-order derivatives, the geopotential coefficients are multiplied by linear combinations of at most three spherical harmonics. As compared to existing non-singular expressions for the geopotential derivatives, the new expressions have a more simple structure. They depend only on the conventional spherical harmonics and do not depend on the first- and second-order derivatives of the associated Legendre functions. The basic equations of the second kind are inferred from the linear equations, constructed in the cited paper, which express the coefficients of the spherical harmonic series for the first- and second-order derivatives in terms of the geopotential coefficients. These equations are converted into recurrent relations from which the coefficients ${\bar{{C}}_{n,m}}$ and ${\bar{{S}}_{n,m}}$ are determined on the basis of the spherical harmonic coefficients of each derivative. The latter coefficients can be estimated from the values of the geopotential derivatives by the quadrature formulas or the least-squares approach. The new expressions of two kinds can be applied for spherical harmonic synthesis and analysis. In particular, they might be incorporated in geopotential modeling on the basis of the orbit data from the CHAMP, GRACE and GOCE missions, and the gradiometry data from the GOCE mission. 相似文献
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Sridevi Jade Malay Mukul V. K. Gaur Kireet Kumar T. S. Shrungeshwar G. S. Satyal Rakesh Kumar Dumka Saigeetha Jagannathan M. B. Ananda P. Dileep Kumar Souvik Banerjee 《Journal of Geodesy》2014,88(6):539-557
We present new insights on the time-averaged surface velocities, convergence and extension rates along arc-normal transects in Kumaon, Garhwal and Kashmir–Himachal regions in the Indian Himalaya from 13 years of high-precision Global Positioning System (GPS) time series (1995–2008) derived from GPS data at 14 GPS permanent and 42 campaign stations between $29.5{-}35^{\circ }\hbox {N}$ and $76{-}81^{\circ }\hbox {E}$ . The GPS surface horizontal velocities vary significantly from the Higher to Lesser Himalaya and are of the order of 30 to 48 mm/year NE in ITRF 2005 reference frame, and 17 to 2 mm/year SW in an India fixed reference frame indicating that this region is accommodating less than 2 cm/year of the India–Eurasia plate motion ( ${\sim }4~\hbox {cm/year}$ ). The total arc-normal shortening varies between ${\sim }10{-}14~\hbox {mm/year}$ along the different transects of the northwest Himalayan wedge, between the Indo-Tsangpo suture to the north and the Indo-Gangetic foreland to the south indicating high strain accumulation in the Himalayan wedge. This convergence is being accommodated differentially along the arc-normal transects; ${\sim } 5{-}10~\hbox {mm/year}$ in Lesser Himalaya and 3–4 mm/year in Higher Himalaya south of South Tibetan Detachment. Most of the convergence in the Lesser Himalaya of Garhwal and Kumaon is being accommodated just south of the Main Central Thrust fault trace, indicating high strain accumulation in this region which is also consistent with the high seismic activity in this region. In addition, for the first time an arc-normal extension of ${\sim }6~\hbox {mm/year}$ has also been observed in the Tethyan Himalaya of Kumaon. Inverse modeling of GPS-derived surface deformation rates in Garhwal and Kumaon Himalaya using a single dislocation indicate that the Main Himalayan Thrust is locked from the surface to a depth of ${\sim }15{-}20~\hbox {km}$ over a width of 110 km with associated slip rate of ${\sim }16{-}18~\hbox {mm/year}$ . These results indicate that the arc-normal rates in the Northwest Himalaya have a complex deformation pattern involving both convergence and extension, and rigorous seismo-tectonic models in the Himalaya are necessary to account for this pattern. In addition, the results also gave an estimate of co-seismic and post-seismic motion associated with the 1999 Chamoli earthquake, which is modeled to derive the slip and geometry of the rupture plane. 相似文献
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基于$\frac{{{{\bar{P}}}_{nm}}\left( \cos \theta \right)}{\sin \theta }\left( m>0 \right)$的非奇异递推公式,给出了基于球坐标的引力矢量和垂线偏差非奇异计算公式;针对极点λ可任意取值引起的地方指北坐标系方向的不确定性问题,证明了引力矢量在转换到地心直角坐标系后不随λ的变化而变化,即与λ的取值无关。最终的数值计算结果表明,直角坐标系下的非奇异计算公式与本文提出的球坐标下的非奇异计算公式所得计算结果绝对值差异小于10-16m/s2,证明了该非奇异公式的正确性。最后总结了所有引力位球函数一阶导、二阶导非奇异性计算的一般思路。 相似文献
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为简化传统正轴等角圆锥投影求解基准纬度时繁琐的迭代算法,引入平均纬度和平均纬差的概念,借助计算机代数系统Mathematica,在平均纬差处级数展开,导出了基于球体模型的正轴等角圆锥投影求解基准纬度的非迭代算法。以全国和不同纬差的省区为例,将其与传统椭球迭代算法进行对比分析。结果表明,推导的基于球体模型的非迭代公式计算基准纬度B0、B1、B2的相对误差最大值为2.011%,长度变形的相对误差小于1×10-6,基本可满足全国以及各省区地图制图的精度要求,从而验证了所研究算法的精确性与实用性。 相似文献