正交距离圆曲线拟合方法   总被引：2，自引：0，他引：2  

丁克良  刘全利  陈翔 《测绘科学》2008,(Z1)

在分析圆曲线拟合准则基础上,提出采用正交最小二乘法拟合圆曲线。该方法以圆曲线正交距离残差平方和极小为准则。基于间接平差原理详细推导了相关模型和算法,并以实际算例说明了该方法的效果。  相似文献   

On the multivariate total least-squares approach to empirical coordinate transformations. Three algorithms   总被引：2，自引：1，他引：1  

Burkhard Schaffrin  Yaron A. Felus 《Journal of Geodesy》2008,82(6):373-383

The multivariate total least-squares (MTLS) approach aims at estimating a matrix of parameters, Ξ, from a linear model (Y−E _Y = (X−E _X ) · Ξ) that includes an observation matrix, Y, another observation matrix, X, and matrices of randomly distributed errors, E _Y and E _X . Two special cases of the MTLS approach include the standard multivariate least-squares approach where only the observation matrix, Y, is perturbed by random errors and, on the other hand, the data least-squares approach where only the coefficient matrix X is affected by random errors. In a previous contribution, the authors derived an iterative algorithm to solve the MTLS problem by using the nonlinear Euler–Lagrange conditions. In this contribution, new lemmas are developed to analyze the iterative algorithm, modify it, and compare it with a new ‘closed form’ solution that is based on the singular-value decomposition. For an application, the total least-squares approach is used to estimate the affine transformation parameters that convert cadastral data from the old to the new Israeli datum. Technical aspects of this approach, such as scaling the data and fixing the columns in the coefficient matrix are investigated. This case study illuminates the issue of “symmetry” in the treatment of two sets of coordinates for identical point fields, a topic that had already been emphasized by Teunissen (1989, Festschrift to Torben Krarup, Geodetic Institute Bull no. 58, Copenhagen, Denmark, pp 335–342). The differences between the standard least-squares and the TLS approach are analyzed in terms of the estimated variance component and a first-order approximation of the dispersion matrix of the estimated parameters.  相似文献   

联合多种测高数据确定中国海及其邻域1．5′×1．5′重力异常     

王虎彪  王勇  陆洋  周旭华 《武汉大学学报(信息科学版)》2008,33(12):1292-1295

联合多种测高资料和Geosat/GM波形重构数据,基于EIGEN_CG01C重力场模型,采用沿轨迹加权最小二乘方法和逆Vening-Meinesz公式,确定了中国海及其邻域1.5′×1.5′重力异常。将计算结果与最新船测资料进行了比较,标准差为3.37×10-5m.s-2。  相似文献   

PLS法与隧道围岩稳定性分类   总被引：5，自引：0，他引：5  

解华明  丁华 《物探与化探》2003,27(4):320-322

围岩稳定性是隧道工程支护设计的基本参数,采用偏最小二乘回归法,综合考虑多因变量影响因素,对隧道围岩稳定性分类进行回归建模,并取得较好效果.  相似文献   

A Least-squares Approach to Depth Determination from Numerical Horizontal Self-potential Gradients     

E. M. Abdelrahman  H. S. Saber  K. S. Essa  M. A. Fouda 《Pure and Applied Geophysics》2004,161(2):399-411

We have developed a least-squares minimization approach to depth determination of a buried ore deposit from numerical horizontal gradients obtained from self-potential (SP) data using filters of successive window lengths (graticule spacings). The problem of depth determination from SP gradients has been transformed into the problem of finding a solution to a nonlinear equation of the form f(z)=0. Formulas have been derived for vertical and horizontal cylinders and spheres. Procedures are also formulated to estimate the electrical dipole moment and the polarization angle. The method is applied to synthetic data with and without random noise. Finally, the validity of the method is tested on two field examples. In both cases, the depth obtained is found to be in a very good agreement with that obtained from drilling information.  相似文献   

部分变量误差模型的整体抗差最小二乘估计     

赵俊  归庆明 《测绘学报》2016,45(5):552-559

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   

配置法在局部大地水准面精化中的实例研究     

钟波  罗志才 《地理空间信息》2006,4(6):19-21

从最小二乘配置方法的基本原理出发,以我国某地区范围内1km分辨率的大地水准面高模型数据为例,根据实用公式计算了试验区大地水准面高的协方差值后,采用多项式函数模型和高斯函数模型分别拟合了该地区大地水准面高的局部协方差函数,并对试验区内18个检核点做了推估计算。根据推估值(Nfit)与实测值(NGPSL)的比较分析表明,虽然多项式协方差函数模型略优于高斯协方差函数模型,但它们都能以厘米级的精度拟合局部大地水准面,这表明了配置法用于精化厘米级大地水准面的有效性。  相似文献   

GPS变形监测动态数据处理中卡尔曼滤波的应用     

高雅萍  冯晓亮 《海洋测绘》2006,26(4):36-38

介绍了卡尔曼滤波的基本原理,针对常规GPS变形监测数据处理中存在着不连续、非实时的缺点,结合卡尔曼滤波的特点,运用三峡实测数据对GPS变形监测动态数据处理中卡尔曼滤波的应用进行研究。并采用各点点位位移速度图对所建立的函数模型进行验证,同时对状态方程的建立及初始值的选取进行分析总结。  相似文献   

应用最小二乘法建立钾长石释光测年标准生长曲线     

杨宏宇  赵晖  王兴繁 《中国沙漠》2019,39(1):97-104

标准生长曲线（Standardised Growth Curve,SGC）法的提出为高效快速地测定释光样品的等效剂量（D_e）值提供了可能。不同实验室的放射源剂量率、操作流程、仪器误差等的不同会导致SGC参数的不同。运用最小二乘法标准化实验剂量校正后的信号L_ri/T_ri*D_e得到一条本实验室的标准生长曲线,用来快速得到等效剂量值。通过R软件实现了最小二乘法标准化过程,建立了50、100、150、200、250℃激发温度下的钾长石的标准生长曲线,分析发现250℃下的SGC收敛性最好,由于此温度下的信号衰退率可忽略不计,因此,我们用250℃激发温度下的SGC方程来估计样品的等效剂量。比较250℃ SGC D_e和250℃ MET-pIRIR D_e的一致性,发现在0~500 Gy范围内用SGC法估计的D_e和MET-pIRIR法估计的D_e非常接近,表明了此范围内SGC法的可靠性,而在>600 Gy范围内出现较大差别。一方面,此范围内用于拟合SGC的数据点较少导致高剂量区域内拟合的方程参数不够准确;另一方面,600 Gy与SGC对应的饱和剂量水平值844.5 Gy已经接近,所以在>600 Gy区域测出的D_e很可能出现较大偏差。因此需在今后工作中逐步积累更多样品,完善SGC参数,使其也能胜任较老年龄样品。  相似文献   

Singular value decomposition and cluster analysis as regression diagnostics tools for geodetic applications     

Markus Vennebusch  Axel Nothnagel  Hansjörg Kutterer 《Journal of Geodesy》2009,83(9):877-891

It is well known that high-leverage observations significantly affect the estimation of parameters. In geodetic literature, mainly redundancy numbers are used for the detection of single high-leverage observations or of single redundant observations. In this paper a further objective method for the detection of groups of important and less important (and thus redundant) observations is developed. In addition, the parameters which are predominantly affected by these groups of observations are identified. This method thus complements other diagnostics tools, such as, e.g., multiple row diagnostics methods as described in statistical literature (see, e.g., Belsley et al. in Regression diagnostics: identifying influential data and sources of collinearity. Wiley, New York, 1980). The method proposed in this paper is based on geometric aspects of adjustment theory and uses the singular value decomposition of the design matrix of an adjustment problem together with cluster analysis methods for regression diagnostics. It can be applied to any geodetic adjustment problem and can be used for the detection of (groups of) observations that significantly affect the estimated parameters or that are of negligible impact. One of the advantages of the proposed method is the improvement of the reliability of observation plans and thus the reduction of the impact of individual observations (and outliers) on the estimated parameters. This is of particular importance for the very long baseline interferometry technique which serves as an application example of the regression diagnostics tool.  相似文献