共查询到20条相似文献，搜索用时 109 毫秒
1.
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
2.
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
3.
本文通过理论变换将断面区域转变为基于测量断面原始观测数据测角的平面直角坐标系中函数曲线在自变量取值范围内与坐标轴所夹的区域的方法,给出数值处理方法的推证及面积计算公式,并对常见的几种形状进行了验算,结果表明该方法可以替代坐标法计算光滑边界的不规则断面的面积,具有较好的实用性。同时,计算公式也比较适合计算机编程实现面积的自动计算。 相似文献
4.
针对观测向量和系数矩阵权分配不合理、验前随机模型不准确的情况,以部分误差变量（partial errors-in-variables,PEIV）模型为基础,推导了附有相对权比的总体最小二乘平差算法;通过在平差准则中加入相对权比,自适应调整观测向量和系数矩阵随机元素对模型参数估计的贡献,给出了确定相对权比的验前单位权方差法和判别函数最小化迭代算法,该算法普遍适用于一般性的系数矩阵和权矩阵。通过直线拟合和坐标转换模拟算例的比较分析,发现当观测值和系数矩阵的验前单位权方差已知,且较准确时,验前单位权方差法确定相对权比和参数估计的效果较好;而以${{\overline{\mathit{{\mathit{\Phi}}}}}_{1}}\left( \hat{\varepsilon },{{{\hat{\varepsilon }}}_{a}} \right)={{\hat{\varepsilon }}^{\text{T}}}\hat{\varepsilon }+\hat{\varepsilon }_{a}^{\text{T}}{{\hat{\varepsilon }}_{a}} $作为判别函数是判别函数最小化迭代算法中效果最好的。 相似文献
5.
四种改进积分法的低空扰动引力计算 总被引：1，自引：0，他引：1
针对Stokes积分方法计算扰动引力中计算点从空中趋近地面时存在积分奇异和不连续的问题,该文提出了去中央奇异点法、奇异点积分值修正法、中央格网加密算法和改进积分式法4种改进Stokes积分的计算公式,并进行了实验计算。计算结果表明:近地空间范围内,4种改进算法都能在一定程度上改进原始积分的奇异性问题;相同条件下,奇异点积分值修正法和改进积分式法计算精度最高,适宜于低空计算;改进积分式法通过理论推导,得到了从球外部到球面统一、连续且无奇异的改进Stokes积分公式,理论严谨。 相似文献
6.
非心摄动引力的快速计算方法研究 总被引：4，自引：0，他引：4
给出了球谐函数不含阶次 (n,m)调制的递推公式 ,推导出非心引力矢量、引力张量的快速计算格式 ,给出了相应的算法。该算法优于传统正常化递推求和算法 ,减少了运算次数 ,使计算速度提高了 5倍。对低轨卫星预报、卫星重力测量反演、动力法定轨等的响应时间都具有重要贡献。 相似文献
7.
空间直角坐标转换需要计算包括尺度系数在内的七参数,目前关于尺度系数的计算方法较多,但计算结果互有差异.本文基于奇异值分解算法推导了经典最小二乘(LS)准则及整体最小二乘(TLS)准则下尺度系数的计算公式,并结合案例采用布罗伊登-弗莱彻-戈德法布-香农(BFGS)优化算法验证了公式的准确性.本文还对经典最小二乘准则、整体... 相似文献
8.
针对传统的均衡重力异常方式基于平面近似,积分范围较小、计算公式的适用性受限、表征的信息量有限的问题,该文在球坐标下分析艾黎-海斯卡宁(Airy-Hesikanen)均衡模型。以计算点向径为半径,将地形分为布格球壳和粗糙地形两部分,计算其地形影响和均衡改正。在实验区,选用补偿深度21km、密度差0.678g/cm3的模型参数,采用该文公式和传统公式计算均衡重力异常,并比较分析其计算值。结果表明,以球近似Airy-Hesikanen均衡模型计算均衡重力异常值,在小积分范围以及平坦地区,与传统公式计算值的精度相当;但随着积分半径增加,球近似Airy-Hesikanen均衡模型计算值精度不断提高、变化更平缓,说明球近似AiryHesikanen均衡模型代替平面近似Airy-Hesikanen均衡模型应用于重力问题研究更为符合地球实际情况。 相似文献
9.
10.
提出一种由ＧＰＳ独立观测边组成闭合环的各坐标分量闭合差计算ＧＰＳ平面控制全中误差的公式。给出了根据地心直角坐标系各坐标分量计算平面上环闭合差的简化公式。根据《工程测量规范》各等级三角网、三边网的主要精度指标,计算了相应等级ＧＰＳ平面控制网的全中误差指标。 相似文献
11.
扰动重力梯度的非奇异表示 总被引：5，自引：0，他引：5
在局部指北坐标系中用地心球坐标来表示扰动重力梯度张量,当计算点趋近于两极时,由于Legendre函数的一阶和二阶导数以及分母上所含余纬的正弦函数,将导致扰动重力梯度张量的计算出现无穷大。因此,本文引入了Legendre函数的一阶和二阶导数以及 无奇异性的计算公式,并且进一步推导了 无奇异性的计算公式。在将Legendre函数的一阶和二阶导数以及 、 无奇异性的计算公式代入到扰动重力梯度张量各分量的求解中时,又充分考虑了m等于0,1,2以及其它量时的复杂情况,建立了扰动重力梯度张量各分量无奇异性的详细计算模型。通过模拟实验表明,本文所建立的详细计算模型不仅能够完全满足当前卫星重力梯度张量计算的精度要求,而且模型稳定、可靠、易于编程实现。 相似文献
12.
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
13.
This paper presents a unified approach to the least squares spherical harmonic analysis of the acceleration vector and Eötvös tensor (gravitational gradients) in an arbitrary orientation. The Jacobian matrices are based on Hotine’s equations that hold in the Earth-fixed Cartesian frame and do not need any derivatives of the associated Legendre functions. The implementation was confirmed through closed-loop tests in which the simulated input is inverted in the least square sense using the rotated Hotine’s equations. The precision achieved is at the level of rounding error with RMS about $10^{-12}{-}10^{-14}$ m in terms of the height anomaly. The second validation of the linear model is done with help from the standard ellipsoidal correction for the gravity disturbance that can be computed with an analytic expression as well as with the rotated equations. Although the analytic expression for this correction is only of a limited accuracy at the submillimeter level, it was used for an independent validation. Finally, the equivalent of the ellipsoidal correction, called the effect of the normal, has been numerically obtained also for other gravitational functionals and some of their combinations. Most of the numerical investigations are provided up to spherical harmonic degree 70, with degree 80 for the computation time comparison using real GRACE data. The relevant Matlab source codes for the design matrices are provided. 相似文献
14.
An algorithm for the determination of the spherical harmonic coefficients of the terrestrial gravitational field representation from the analysis of a kinematic orbit solution of a low earth orbiting GPS-tracked satellite is presented and examined. A gain in accuracy is expected since the kinematic orbit of a LEO satellite can nowadays be determined with very high precision, in the range of a few centimeters. In particular, advantage is taken of Newton's Law of Motion, which balances the acceleration vector with respect to an inertial frame of reference (IRF) and the gradient of the gravitational potential. By means of triple differences, and in particular higher-order differences (seven-point scheme, nine-point scheme), based upon Newton's interpolation formula, the local acceleration vector is estimated from relative GPS position time series. The gradient of the gravitational potential is conventionally given in a body-fixed frame of reference (BRF) where it is nearly time independent or stationary. Accordingly, the gradient of the gravitational potential has to be transformed from spherical BRF to Cartesian IRF. Such a transformation is possible by differentiating the gravitational potential, given as a spherical harmonics series expansion, with respect to Cartesian coordinates by means of the chain rule, and expressing zero- and first-order Ferrer's associated Legendre functions in terms of Cartesian coordinates. Subsequently, the BRF Cartesian coordinates are transformed into IRF Cartesian coordinates by means of the polar motion matrix, the precession–nutation matrices and the Greenwich sidereal time angle (GAST). In such a way a spherical harmonic representation of the terrestrial gravitational field intensity with respect to an IRF is achieved. Numerical tests of a resulting Gauss–Markov model document not only the quality and the high resolution of such a space gravity spectroscopy, but also the problems resulting from noise amplification in the acceleration determination process. 相似文献
15.
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
16.
从球冠谐理论出发,详细推导了球冠坐标系下扰动重力梯度的无奇异性计算公式。基于Tikhonov正则化方法,利用GOCE卫星实际观测数据解算局部重力场球冠谐模型。数值计算表明,基于扰动重力梯度的球冠谐分析建模方法能够有效地恢复局部重力场中的短波信号,与GO_CONS_GCF_2_DIR_R5模型的差异在±0.3×10~(-5) m/s~2水平。 相似文献
17.
为提高利用逆Vening-Meinesz公式反演测高重力中央区效应的精度，视中央区为矩形域，将垂线偏差分量表示成双二次多项式插值形式，引入非奇异变换，推导出了重力异常的计算公式。以低纬度区域2'×2'的垂线偏差实际数据为背景场进行了计算，结果表明，当中央区包含4个网格时，传统公式与推导出的重力异常计算公式误差的最大值大于1 mGal。推导出的公式可为高精度测高重力中央区效应的计算提供理论依据。 相似文献
18.
Optimized formulas for the gravitational field of a tesseroid 总被引：7，自引：3，他引：4
Various tasks in geodesy, geophysics, and related geosciences require precise information on the impact of mass distributions on gravity field-related quantities, such as the gravitational potential and its partial derivatives. Using forward modeling based on Newton’s integral, mass distributions are generally decomposed into regular elementary bodies. In classical approaches, prisms or point mass approximations are mostly utilized. Considering the effect of the sphericity of the Earth, alternative mass modeling methods based on tesseroid bodies (spherical prisms) should be taken into account, particularly in regional and global applications. Expressions for the gravitational field of a point mass are relatively simple when formulated in Cartesian coordinates. In the case of integrating over a tesseroid volume bounded by geocentric spherical coordinates, it will be shown that it is also beneficial to represent the integral kernel in terms of Cartesian coordinates. This considerably simplifies the determination of the tesseroid’s potential derivatives in comparison with previously published methodologies that make use of integral kernels expressed in spherical coordinates. Based on this idea, optimized formulas for the gravitational potential of a homogeneous tesseroid and its derivatives up to second-order are elaborated in this paper. These new formulas do not suffer from the polar singularity of the spherical coordinate system and can, therefore, be evaluated for any position on the globe. Since integrals over tesseroid volumes cannot be solved analytically, the numerical evaluation is achieved by means of expanding the integral kernel in a Taylor series with fourth-order error in the spatial coordinates of the integration point. As the structure of the Cartesian integral kernel is substantially simplified, Taylor coefficients can be represented in a compact and computationally attractive form. Thus, the use of the optimized tesseroid formulas particularly benefits from a significant decrease in computation time by about 45 % compared to previously used algorithms. In order to show the computational efficiency and to validate the mathematical derivations, the new tesseroid formulas are applied to two realistic numerical experiments and are compared to previously published tesseroid methods and the conventional prism approach. 相似文献
19.
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
20.
The integral formulas of the associated Legendre functions 总被引：1，自引：0，他引：1
A new kind of integral formulas for ${\bar{P}_{n,m} (x)}$ is derived from the addition theorem about the Legendre Functions when n ? m is an even number. Based on the newly introduced integral formulas, the fully normalized associated Legendre functions can be directly computed without using any recursion methods that currently are often used in the computations. In addition, some arithmetic examples are computed with the increasing degree recursion and the integral methods introduced in the paper respectively, in order to compare the precisions and run-times of these two methods in computing the fully normalized associated Legendre functions. The results indicate that the precisions of the integral methods are almost consistent for variant x in computing ${\bar{P}_{n,m} (x)}$ , i.e., the precisions are independent of the choice of x on the interval [0,1]. In contrast, the precisions of the increasing degree recursion change with different values on the interval [0,1], particularly, when x tends to 1, the errors of computing ${\bar{P}_{n,m} (x)}$ by the increasing degree recursion become unacceptable when the degree becomes larger and larger. On the other hand, the integral methods cost more run-time than the increasing degree recursion. Hence, it is suggested that combinations of the integral method and the increasing degree recursion can be adopted, that is, the integral methods can be used as a replacement for the recursive initials when the recursion method become divergent. 相似文献