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   

A recursive decomposition algorithm for network seismic reliability evaluation     

Jie Li  Jun He 《地震工程与结构动力学》2002,31(8):1525-1539

A new probabilistic analytical approach to evaluate seismic system reliability of large lifeline systems is presented in this paper. The algorithm takes the shortest path from the source to the terminal of a node weight or edge weight network as decomposition policy, using the Boolean laws of set operation and probabilistic operation principal, a recursive decomposition process then could be constructed. For a general weight network, the modified Torrieri method (NTR/T method) is introduced to combine with the suggested algorithm. Therefore, the recursive decomposition algorithm may be applied to evaluate the seismic reliability of general lifeline systems. A series of case studies, including a practical district electric power network system and a large urban water supply system, show that the suggested algorithm supplies a useful probabilistic analysis means for the seismic reliability evaluation of large lifeline systems. Copyright © 2002 John Wiley & Sons, Ltd.  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   

System identification of instrumented bridge systems     

Yalin Arici  Khalid M. Mosalam 《地震工程与结构动力学》2003,32(7):999-1020

Several recorded motions for seven bridge systems in California during recent earthquakes were analysed using parametric and non‐parametric system identification (SI) methods. The bridges were selected considering the availability of an adequate array of accelerometers and accounting for different structural systems, materials, geometry and soil types. The results of the application of SI methods included identification of modal frequencies and damping ratios. Excellent fits of the recorded motion in the time domain were obtained using parametric methods. The multi‐input/single‐output SI method was a suitable approach considering the instrumentation layout for these bridges. Use of the constructed linear filters for prediction purposes was also demonstrated for three bridge systems. Reasonable prediction results were obtained considering the various limitations of the procedure. Finally, the study was concluded by identifying the change of the modal frequencies and damping of a particular bridge system in time using recursive filters. Copyright © 2003 John Wiley & Sons, Ltd.  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   

Local Oceanic Vertical Deflection Determination with Gravity Data Along a Profile     

Jianbo Wang  Xin Liu  Yi Shen  Qiaoli Kong 《Marine Geodesy》2018,41(1):24-43

Deflections of the vertical (DOVs) over oceans cannot be directly measured, which restricts their applications. A local covariance function of anomalous potential is put forward in this paper in conjunction with the least-squares collocation (LSC) method to compute the oceanic DOVs utilization of oceanic gravity data along a profile. The covariance functions of gravity field quantities have been derived directly as functions of x, y and z without the need to introduce coordinate transformations corresponding to along- or cross-profile components. In the proposed methodology, gravity data along a profile were used to calculate the residual gravity anomaly using the remove-compute-restore technique. The residual gravity anomaly was used to calculate the parameters of the proposed covariance function of the local anomalous gravity field, which was used in the LSC to compute the residual DOVs along the profile. The residual DOVs added model DOVs to recover the DOVs along the profile. The results of a simulation experiment prove that the proposed methodology is feasible and effective.  相似文献   

Calibration of paired watersheds: Utility of moving sums in presence of externalities          下载免费PDF全文

Herbert Ssegane  Devendra M. Amatya  Augustine Muwamba  George M. Chescheir  Tim Appelboom  E.W. Tollner  Jami E. Nettles  Mohamed A. Youssef  François Birgand  R.W. Skaggs 《水文研究》2017,31(20):3458-3471

Historically, paired watershed studies have been used to quantify the hydrological effects of land use and management practices by concurrently monitoring 2 similar watersheds during calibration (pretreatment) and post‐treatment periods. This study characterizes seasonal water table and flow response to rainfall during the calibration period and tests a change detection technique of moving sums of recursive residuals (MOSUM) to select calibration periods for each control–treatment watershed pair when the regression coefficients for daily water table elevation were most stable to minimize regression model uncertainty. The control and treatment watersheds were 1 watershed of 3–4‐year‐old intensely managed loblolly pine (Pinus taeda L.) with natural understory, 1 watershed of 3–4‐year‐old loblolly pine intercropped with switchgrass (Panicum virgatum), 1 watershed of 14–15‐year‐old thinned loblolly pine with natural understory (control), and 1 watershed of switchgrass only. The study period spanned from 2009 to 2012. Silvicultural operational practices during this period acted as external factors, potentially shifting hydrologic calibration relationships between control and treatment watersheds. MOSUM results indicated significant changes in regression parameters due to silvicultural operations and were used to identify stable relationships for water table elevation. None of the calibration relationships developed using this method were significantly different from the classical calibration relationship based on published historical data. We attribute that to the similarity of historical and 2010–2012 leaf area index on control and treatment watersheds as moderated by the emergent vegetation. Although the MOSUM approach does not eliminate the need for true calibration data or replace the classic paired watershed approach, our results show that it may be an effective alternative approach when true data are unavailable, as it minimizes the impacts of external disturbances other than the treatment of interest.  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