共查询到20条相似文献,搜索用时 31 毫秒
1.
Markku Heikkinen 《Journal of Geodesy》1979,53(3):239-245
The Honkasalo term is discussed and the author arrives at the conclusion that its application to gravimetric observations
is harmful and should be avoided. 相似文献
2.
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
3.
M. K. Paul 《Journal of Geodesy》1973,47(4):413-425
Neglecting distant zones in the computation of geoidal height using Stokes' formula gives rise to some truncation error. This
truncation error is expressible as a weighted summation of the zonal harmonic components of the gravity anomaly. Making use
of the well-known properties of Legendre polynomials, a compact method of computing these theoretical coefficients has been
developed in this paper. 相似文献
4.
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
5.
A solution to the downward continuation effect on the geoid determined by Stokes' formula 总被引:2,自引:1,他引:2
L.E. Sjöberg 《Journal of Geodesy》2003,77(1-2):94-100
The analytical continuation of the surface gravity anomaly to sea level is a necessary correction in the application of Stokes'
formula for geoid estimation. This process is frequently performed by the inversion of Poisson's integral formula for a sphere.
Unfortunately, this integral equation corresponds to an improperly posed problem, and the solution is both numerically unstable,
unless it is well smoothed, and tedious to compute. A solution that avoids the intermediate step of downward continuation
of the gravity anomaly is presented. Instead the effect on the geoid as provided by Stokes' formula is studied directly. The
practical solution is partly presented in terms of a truncated Taylor series and partly as a truncated series of spherical
harmonics. Some simple numerical estimates show that the solution mostly meets the requests of a 1-cm geoid model, but the
truncation error of the far zone must be studied more precisely for high altitudes of the computation point. In addition,
it should be emphasized that the derived solution is more computer efficient than the detour by Poisson's integral.
Received: 6 February 2002 / Accepted: 18 November 2002
Acknowledgements. Jonas ?gren carried out the numerical calculations and gave some critical and constructive remarks on a draft version of
the paper. This support is cordially acknowledged. Also, the thorough work performed by one unknown reviewer is very much
appreciated. 相似文献
6.
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
7.
The effects of the deviations of sea surface topography from the geoid are estimated for terrestrial geoid computations as
obtained from Stokes' formula. The results are based on an equal-area expansion of Lisitzin's sea surface topography data
in a spherical harmonic series. It is realized that those data affect mainly the harmonics of degree n≤10. Consequently, in
geoids obtained from combination solutions (where low harmonics are dominated by harmonics as obtained from differential orbit
improvement) the sea surface topography effects are relatively small. 相似文献
8.
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
9.
关于Stokes公式的球面卷积和平面卷积的注记 总被引:2,自引:0,他引:2
晁定波 《武汉大学学报(信息科学版)》2003,28(6):651-654
讨论了Stokes公式球面卷积和平面卷积形式的近似性和严密性问题,分析了Stokes函数球面卷积形式和平面卷积形式的关系,推导了其间的差值表达式,估算了最大差值及其对计算大地水准面差距的误差影响。同时指出,将顾及Stokes函数全项的平面卷积公式称为严密公式的提法,仅仅是相对仅顾及Stokes函数首项的简单平面卷积公式而言,认为更合理的提法应该是“高精度Stokes平面近似卷积公式”。理论分析表明,球面卷积不可能严格转化为等效的平面卷积。 相似文献
10.
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
11.
12.
Four different implementations of Stokes' formula are employed for the estimation of geoid heights over Sweden: the Vincent
and Marsh (1974) model with the high-degree reference gravity field but no kernel modifications; modified Wong and Gore (1969)
and Molodenskii et al. (1962) models, which use a high-degree reference gravity field and modification of Stokes' kernel;
and a least-squares (LS) spectral weighting proposed by Sj?berg (1991). Classical topographic correction formulae are improved
to consider long-wavelength contributions. The effect of a Bouguer shell is also included in the formulae, which is neglected
in classical formulae due to planar approximation. The gravimetric geoid is compared with global positioning system (GPS)-levelling-derived
geoid heights at 23 Swedish Permanent GPS Network SWEPOS stations distributed over Sweden. The LS method is in best agreement,
with a 10.1-cm mean and ±5.5-cm standard deviation in the differences between gravimetric and GPS geoid heights. The gravimetric
geoid was also fitted to the GPS-levelling-derived geoid using a four-parameter transformation model. The results after fitting
also show the best consistency for the LS method, with the standard deviation of differences reduced to ±1.1 cm. For comparison,
the NKG96 geoid yields a 17-cm mean and ±8-cm standard deviation of agreement with the same SWEPOS stations. After four-parameter
fitting to the GPS stations, the standard deviation reduces to ±6.1 cm for the NKG96 geoid. It is concluded that the new corrections
in this study improve the accuracy of the geoid. The final geoid heights range from 17.22 to 43.62 m with a mean value of
29.01 m. The standard errors of the computed geoid heights, through a simple error propagation of standard errors of mean
anomalies, are also computed. They range from ±7.02 to ±13.05 cm. The global root-mean-square error of the LS model is the
other estimation of the accuracy of the final geoid, and is computed to be ±28.6 cm.
Received: 15 September 1999 / Accepted: 6 November 2000 相似文献
13.
解析延拓高阶解的推导方法与比较分析 总被引:1,自引:0,他引:1
利用迭代求导法、直接求导法推导了解析延拓高阶解公式,并与经典递推方法进行了比较分析。利用迭代求导法得到了重力异常径向导数在球近似下的通用递推公式,该公式表明,解析延拓的经典递推求解方法实际上是忽略小项的近似,在忽略小项后,迭代求导法与递推法的形式是一样的。虽然直接求导法可以提高计算速度,但利用5°×5°实验区的重力数据进行解析延拓实验的结果表明,直接求导法获得的犵2项数值较其他方法偏小0.1~0.4mGal,这种差异的产生主要由于计算误差引起的。 相似文献
14.
Loffeld双基公式将多接收阵合成孔径声纳的系统函数分解为准收发合置项和收发分置畸变项。针对该模型,在二维频域定量分析了相位误差,结果显示该方法能满足高分辨成像。在此基础上提出了一种新的成像方法,首先在二维频域通过距离向数据分块的方式补偿收发分置畸变相位中的距离空变项;然后,在二维时域对各接收阵元的数据进行顺序重排,以实现多阵元数据的收发合置转换;最后,采用距离-多谱勒算法对收发合置转换后的数据进行成像,便得到高分辨图像。仿真和实测数据处理结果验证了该方法的有效性。 相似文献
15.
《测量评论》2013,45(84):268-274
AbstractIn the E.S.R., viii, 59, 191–194 (January 1946), J.H. Cole gives a very simple formula for finding the length of long lines on the spheroid (normal section arcs), given the coordinates of the end points. In the course of the computation the approximate azimuth of one end of the line is found, the error over a 500-mile line being of the order of 3″ or 4″. If the formula is amended so that the azimuth at the other end of the line is used in computing the length of the arc, the error is then less than 0″·1 over such a distance. An extra term is now given which makes this azimuth virtually correct over any distance. Numerical tests show that Cole's formula for length and the new one for azimuth are very accurate and convenient in all azimuths and latitudes. 相似文献
16.
根据两点数值微分公式建立了基于二元样条函数的规则格网数字高程模型(DEM)的表面表达模型,得出了基于二元样条函数的传递误差公式。公式表明,二元样条函数的DEM传递误差与双线性多项式的传递误差相同。但由于样条函数的DEM表面建模误差低于线性多项式的DEM表面建模误差,因此,基于样条函数的DEM表面模型具有更高的精度。 相似文献
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19.
A new technique to determine geoid and orthometric heights from satellite positioning and geopotential numbers 总被引:1,自引:0,他引:1
L. E. Sjöberg 《Journal of Geodesy》2006,80(6):304-312
This paper takes advantage of space-technique-derived positions on the Earth’s surface and the known normal gravity field to determine the height anomaly from geopotential numbers. A new method is also presented to downward-continue the height anomaly to the geoid height. The orthometric height is determined as the difference between the geodetic (ellipsoidal) height derived by space-geodetic techniques and the geoid height. It is shown that, due to the very high correlation between the geodetic height and the computed geoid height, the error of the orthometric height determined by this method is usually much smaller than that provided by standard GPS/levelling. Also included is a practical formula to correct the Helmert orthometric height by adding two correction terms: a topographic roughness term and a correction term for lateral topographic mass–density variations. 相似文献
20.
在脉冲星导航中,角位置误差是主要的误差源之一。因此本文基于X射线脉冲星导航,提出了一种修正扩维无迹卡尔曼滤波(MASUKF)算法进行角位置误差的改进。MASUKF算法在原扩维无迹卡尔曼滤波(ASUKF)算法的基础上加入了Roamer延迟的高阶项,并将其作为误差项,将修改后的误差项代入状态方程与量测方程中,即可进行仿真分析。在仿真中,首先将ASUKF算法与UKF算法进行对比仿真模拟试验,结果显示ASUKF算法能显著地提高约45 m的定位精度,在X、Y、Z 3方向的速度误差估计精度约提高了20%;然后比较ASUKF与MASUKF算法,结果显示MASUKF算法较ASUKF算法的速度误差与位置误差的估计精度均提高2%以上。 相似文献