共查询到20条相似文献,搜索用时 15 毫秒
1.
Stanley W. Shepperd 《Journal of Geodesy》1982,56(2):95-105
A recursive method is derived for computing the Molodenskii truncation error coefficients at altitude for the altitude-generalized
Stokes integral. Furthermore, the Cook truncation error coefficients at altitude corresponding to the generalized Vening-Meinesz
integral are derived in terms of the Molodenskii coefficients. Also, the gravity disturbance truncation error coefficients
at altitude are related to the Molodenskii coefficients. By combining these results, it is shown how the truncation error
for the complete gravity disturbance vector at altitude may be computed recursively. 相似文献
2.
TSVD是大地测量病态问题解算的常用有效方法。影响TSVD解算效果的关键因素是截断参数,现有截断参数确定方法可提供有效的截断参数,但仍难以给出最优截断参数。以均方误差最小为准则确定截断参数是一种理论依据较充分的截断参数确定方法,但均方误差计算所需的模型参数真值在实际应用中无法获得,导致该方法难以给出理论最优截断参数。鉴于此,本文研究了基于均方误差影响下(方差与偏差联合影响)参数估值变化特性的TSVD截断参数确定方法。通过TSVD依次截掉小奇异值,获得奇异值截掉前后的方差与参数估值变化,利用两者变化分析确定偏差影响,避免依赖参数真值计算偏差,从而确定出均方误差最小理论下的截断参数。数值与应用试验结果表明,本文方法确定的截断参数可有效改善TSVD解算效果,是一种行之有效的截断参数确定方法。 相似文献
3.
Improved convergence rates for the truncation error in gravimetric geoid determination 总被引:2,自引:2,他引:0
When Stokes's integral is used over a spherical cap to compute a gravimetric estimate of the geoid, a truncation error results
due to the neglect of gravity data over the remainder of the Earth. Associated with the truncation error is an error kernel
defined over these two complementary regions. An important observation is that the rate of decay of the coefficients of the
series expansion for the truncation error in terms of Legendre polynomials is determined by the smoothness properties of the
error kernel. Previously published deterministic modifications of Stokes's integration kernel involve either a discontinuity
in the error kernel or its first derivative at the spherical cap radius. These kernels are generalised and extended by constructing
error kernels whose derivatives at the spherical cap radius are continuous up to an arbitrary order. This construction is
achieved by smoothly continuing the error kernel function into the spherical cap using a suitable degree polynomial. Accordingly,
an improved rate of convergence of the spectral series representation of the truncation error is obtained.
Received: 21 April 1998 / Accepted: 4 October 1999 相似文献
4.
A Meissl-modified Vaníček and Kleusberg kernel to reduce the truncation error in gravimetric geoid computations 总被引:3,自引:2,他引:1
A deterministic modification of Stokes's integration kernel is presented which reduces the truncation error when regional
gravity data are used in conjunction with a global geopotential model to compute a gravimetric geoid. The modification makes
use of a combination of two existing modifications from Vaníček and Kleusberg and Meissl. The former modification applies
a root mean square minimisation to the upper bound of the truncation error, whilst the latter causes the Fourier series expansion
of the truncation error to coverage to zero more rapidly by setting the kernel to zero at the truncation radius. Green's second
identity is used to demonstrate that the truncation error converges to zero faster when a Meissl-type modification is made
to the Vaníček and Kleusberg kernel. A special case of this modification is proposed by choosing the degree of modification
and integration cap-size such that the Vaníček and Kleusberg kernel passes through zero at the truncation radius.
Received: 14 October 1996 / Accepted: 20 October 1997 相似文献
5.
Meissel-Stokes核函数应用于区域大地水准面分析 总被引:1,自引:0,他引:1
为提高区域大地水准面计算精度,基于EGM2008地球重力场位系数模型分析Meissel-Stokes核函数、截断误差系数以及截断误差。选取实验区,采用移去-恢复法评价Meissel-Stokes核函数计算大地水准面的精度。结果表明:Meissel-Stokes核函数及其截断误差系数收敛速度快;截断误差小且稳定。在积分半径不易扩展的情况下,应用Meissel-Stokes核函数计算区域大地水准面,比标准Stokes计算大地水准面精度略高。 相似文献
6.
在评估重力场模型计算空间扰动引力精度时,对模型截断误差常采用阶方差方法。文中将6种经典的重力异常阶方差模型与现有超高阶重力场模型的阶方差进行比较,TSD模型与重力场模型的差值最小。根据重力异常阶方差模型TSD,文中分析不同高度、不同阶次利用重力场模型计算空中扰动引力时截断误差的影响。实验结果表明:36阶模型截断误差最大径向和水平方向分别为26.455 1mGal、25.946 3mGal;360阶模型截断误差最大径向和水平方向分别为9.969 0mGal、9.960 9 mGal;2160阶模型截断误差最大径向和水平方向分别为2.538 5 mGal、2.538 1mGal;2160阶模型计算空中扰动引力时,即使在低空附近,截断误差在2.5mGal以内,计算高度超过5km,截断误差可以忽略;超过400km的高度,都可以用36阶模型计算,截断误差在1mGal以内。 相似文献
7.
8.
Recurrence relations have been derived for truncation error coefficients of the extended Stokes' function and its partial
derivatives required in the computation of the disturbing gravity vector at any elevation above the earth's surface. The corresponding
formulae, the example of values of the truncation error coefficients for H=30.1 km and ψ0=30∘ and the estimations of truncation error are given in this article.
Received: 26 January 1996 / Accepted: 11 June 1997 相似文献
9.
Brian Farelly 《Journal of Geodesy》1991,65(2):92-101
Six sources of error in the use of Fourier methods for the conversion of geoid heights to gravity anomalies are considered. The errors due to spherical approximation are unimportant. The errors due to approximations in Stokes' integral may be eliminated by use of the gravity coating rather than the gravity anomaly. The chord-to-arc error and the truncation error may be reduced by using a reference field. Tapering of the edges of the measurement window reduces the truncation error. The long-wavelength components of the high degree spherical harmonics cause small offsets in the resulting gravity anomalies. The errors due to the plane approximation can be reduced by appropriate choice of map projection and area of integration. 相似文献
10.
S. Roy Schubert 《Journal of Geodesy》1968,42(4):427-434
Recently much work has been done concerning the behavior of the truncation errors of the integral formulas of Stokes and Vening
Meinesz. In our paper we examine the theoretical foundations of truncation error behavior. 相似文献
11.
Some modifications of Stokes' formula that account for truncation and potential coefficient errors 总被引:1,自引:1,他引:0
Stokes' formula from 1849 is still the basis for the gravimetric determination of the geoid. The modification of the formula,
originating with Molodensky, aims at reducing the truncation error outside a spherical cap of integration. This goal is still
prevalent among various modifications. In contrast to these approaches, some least-squares types of modification that aim
at reducing the truncation error, as well as the error stemming from the potential coefficients, are demonstrated. The least-squares
estimators are provided in the two cases that (1) Stokes' kernel is a priori modified (e.g. according to Molodensky's approach)
and (2) Stokes' kernel is optimally modified to minimize the global mean square error. Meissl-type modifications are also
studied. In addition, the use of a higher than second-degree reference field versus the original (Pizzetti-type) reference
field is discussed, and it is concluded that the former choice of reference field implies increased computer labour to achieve
the same result as with the original reference field.
Received: 14 December 1998 / Accepted: 4 October 1999 相似文献
12.
Y. Hagiwara 《Journal of Geodesy》1972,46(4):453-466
A general formula giving Molodenskii coefficientsQ
n of the truncation errors for the geoidal height is introduced in this paper. A relation betweenQ
n andq
n, Cook’s truncation function, is also obtained. Cook (1951) has treated the truncation errors for the deflection of the vertical
in the Vening Meinesz integration. Molodenskii et al. (1962) have also derived the truncation error formulas for the deflection
of the vertical. It is proved in this paper that these two formulas are equivalent. 相似文献
13.
本文讨论了FFT估计高程异常及Romberg算法解求截断系数的有关问题;并利用雪林-拉普阶方差估计FFT法的误差值,指出ψ_0=1°.0的球帽是最佳选择。 相似文献
14.
本文介绍了建立刚体地球章动序列的地球物理方法。依据固体潮的理论,建立了一个新的刚体地球章动序列,章动项的系数截断到0.0001mas,在考虑二阶效应的情况下,一共包括了304项。 相似文献
15.
J. Y. Chen 《Journal of Geodesy》1982,56(1):9-26
Summary The application of combined data (satellite and terrestrial data) to the practical computation of height anomalies or the
deflections of the vertical was originally suggested by (Molodensky et al. 1962). This idea usually leads to the modification
of Stokes' or Vening-Meinesz' functions in the integration procedure. In the recent decade there were various suggestions
in this regard especially for the computation of height anomalies. For example, a considerable mathematical insight into the
modification of Stokes' function and the truncation of its integral has been provided by (Meissl 1971, Houtze et al. 1979,
Rapp 1980, Jekeli 1980).
Five different methods for computing deflections of the vertical by modifying Vening-Meinesz' function are studied and compared
with each other. The corresponding formulae, the values of the coefficients in each method and the estimations of their corresponding
potential coefficient error and truncation error are given in this article.
This paper was written at the Institut f. Angewandte Geod?sie, Technische Universit?t Graz, Austria. 相似文献
16.
17.
向下延拓航空重力数据的Tikhonov双参数正则化法 总被引:2,自引:0,他引:2
为了避免正则化参数对向下延拓过程可靠成分的修正影响,提出了Tikhonov双参数正则化法。引进截断参数,将法矩阵的奇异值分为相对较大的奇异值(可靠部分)和相对较小的奇异值(不可靠部分);引进正则化参数,只对法矩阵的小奇异值进行修正,以抑制高频误差对向下延拓解的影响。采用改进的广义交互确认法(GCV)确定截断参数和正则化参数。基于EGM2008重力场模型仿真了一组航空重力数据,验证了该方法对航空重力数据向下延拓过程的有效性。 相似文献
18.
Investigating the propagation mechanism of unmodelled systematic errors on coordinate time series estimated using least squares 总被引:6,自引:8,他引:6
The propagation of unmodelled systematic errors into coordinate time series computed using least squares is investigated,
to improve the understanding of unexplained signals and apparent noise in geodetic (especially GPS) coordinate time series.
Such coordinate time series are invariably based on a functional model linearised using only zero and first-order terms of
a (Taylor) series expansion about the approximate coordinates of the unknown point. The effect of such truncation errors is
investigated through the derivation of a generalised systematic error model for the simple case of range observations from
a single known reference point to a point which is assumed to be at rest by the least squares model but is in fact in motion.
The systematic error function for a one pseudo-satellite two-dimensional case, designed to be as simple but as analogous to
GPS positioning as possible, is quantified. It is shown that the combination of a moving reference point and unmodelled periodic
displacement at the unknown point of interest, due to ocean tide loading, for example, results in an output coordinate time
series containing many periodic terms when only zero and first-order expansion terms are used in the linearisation of the
functional model. The amplitude, phase and period of these terms is dependent on the input amplitude, the locations of the
unknown point and reference point, and the period of the reference point's motion. The dominant output signals that arise
due to truncation errors match those found in coordinate time series obtained from both simulated data and real three-dimensional
GPS data. 相似文献
19.
重点围绕远程飞行器飞行轨道控制保障需求,开展了空中扰动引力计算和地面重力异常测量精度指标及海洋重力测量测线布设方案的分析与论证。首先通过解析和简化飞行器导航误差解表达式,定量估计了地球重力场对远程飞行器飞行轨迹的影响,并以一定量值的落点偏差为限定指标,研究论证了空中扰动引力的计算精度要求。在此基础上,通过对地面重力异常截断误差及数据传播误差的估计和分析,研究确定了地面/海面网格平均重力异常的观测分辨率和计算精度指标。以此为依据,提出了相对应的海洋重力测量测线布设方案,并通过数值计算验证了所提方案的合理性和有效性。 相似文献
20.
L. E. Sjöberg 《Journal of Geodesy》1999,73(7):362-366
The well-known International Association of Geodesy (IAG) approach to the atmospheric geoid correction in connection with
Stokes' integral formula leads to a very significant bias, of the order of 3.2 m, if Stokes' integral is truncated to a limited
region around the computation point. The derived truncation error can be used to correct old results. For future applications
a new strategy is recommended, where the total atmospheric geoid correction is estimated as the sum of the direct and indirect
effects. This strategy implies computational gains as it avoids the correction of direct effect for each gravity observation,
and it does not suffer from the truncation bias mentioned above. It can also easily be used to add the atmospheric correction
to old geoid estimates, where this correction was omitted. In contrast to the terrain correction, it is shown that the atmospheric
geoid correction is mainly of order H of terrain elevation, while the term of order H
2 is within a few millimetres.
Received: 20 May 1998 / Accepted: 19 April 1999 相似文献