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1.
The consistency of the Chang’E-1 and SELENE reference frames as realized by the footprint positions of laser altimetry measurements
of the lunar surface during both missions was analyzed using a global 12-parameter model for small (with respect to unity)
deformations and rigid body motions. The rigid body motion and deformation parameters between the two reference frames estimated
from nearly-colocated without tie measurements are found to be consistent, i.e., nearly zero for the estimates of the translations,
rotations and shear parameters. However, the estimated three strain parameters, which are similar in magnitude and sign, reveal
a prominent scale difference, between the Chang’E-1 and SELENE reference frames, of about 0.9 × 10−5. The scale difference can be attributed to calibration of the data sets using the known coordinates of the lunar laser ranging
stations all located on the near side of the Moon. 相似文献
2.
Santiago Belda Robert Heinkelmann José M. Ferrándiz Tobias Nilsson Harald Schuh 《Journal of Geodesy》2017,91(2):135-149
Precise transformation between the celestial reference frames (CRF) and terrestrial reference frames (TRF) is needed for many purposes in Earth and space sciences. According to the Global Geodetic Observing System (GGOS) recommendations, the accuracy of positions and stability of reference frames should reach 1 mm and 0.1 mm year\(^{-1}\), and thus, the Earth Orientation Parameters (EOP) should be estimated with similar accuracy. Different realizations of TRFs, based on the combination of solutions from four different space geodetic techniques, and CRFs, based on a single technique only (VLBI, Very Long Baseline Interferometry), might cause a slow degradation of the consistency among EOP, CRFs, and TRFs (e.g., because of differences in geometry, orientation and scale) and a misalignment of the current conventional EOP series, IERS 08 C04. We empirically assess the consistency among the conventional reference frames and EOP by analyzing the record of VLBI sessions since 1990 with varied settings to reflect the impact of changing frames or other processing strategies on the EOP estimates. Our tests show that the EOP estimates are insensitive to CRF changes, but sensitive to TRF variations and unmodeled geophysical signals at the GGOS level. The differences between the conventional IERS 08 C04 and other EOP series computed with distinct TRF settings exhibit biases and even non-negligible trends in the cases where no differential rotations should appear, e.g., a drift of about 20 \(\upmu \)as year\(^{-1 }\)in \(y_{\mathrm{pol }}\) when the VLBI-only frame VTRF2008 is used. Likewise, different strategies on station position modeling originate scatters larger than 150 \(\upmu \)as in the terrestrial pole coordinates. 相似文献
3.
Volker Tesmer Johannes Boehm Robert Heinkelmann Harald Schuh 《Journal of Geodesy》2007,81(6-8):409-421
This paper compares estimated terrestrial reference frames (TRF) and celestial reference frames (CRF) as well as position time-series in terms of systematic differences, scale, annual signals and station position repeatabilities using four different tropospheric mapping functions (MF): The NMF (Niell Mapping Function) and the recently developed GMF (Global Mapping Function) consist of easy-to-handle stand-alone formulae, whereas the IMF (Isobaric Mapping Function) and the VMF1 (Vienna Mapping Function 1) are determined from numerical weather models. All computations were performed at the Deutsches Geodätisches Forschungsinstitut (DGFI) using the OCCAM 6.1 and DOGS-CS software packages for Very Long Baseline Interferometry (VLBI) data from 1984 until 2005. While it turned out that CRF estimates only slightly depend on the MF used, showing small systematic effects up to 0.025 mas, some station heights of the computed TRF change by up to 13 mm. The best agreement was achieved for the VMF1 and GMF results concerning the TRFs, and for the VMF1 and IMF results concerning scale variations and position time-series. The amplitudes of the annual periodical signals in the time-series of estimated heights differ by up to 5 mm. The best precision in terms of station height repeatability is found for the VMF1, which is 5–7% better than for the other MFs. 相似文献
4.
The Meissl scheme for the geodetic ellipsoid 总被引：2，自引：1，他引：1
We present a variant of the Meissl scheme to relate surface spherical harmonic coefficients of the disturbing potential of
the Earth’s gravity field on the surface of the geodetic ellipsoid to surface spherical harmonic coefficients of its first- and second-order normal derivatives on the same or any other ellipsoid.
It extends the original (spherical) Meissl scheme, which only holds for harmonic coefficients computed from geodetic data
on a sphere. In our scheme, a vector of solid spherical harmonic coefficients of one quantity is transformed into spherical
harmonic coefficients of another quantity by pre-multiplication with a transformation matrix. This matrix is diagonal for
transformations between spheres, but block-diagonal for transformations involving the ellipsoid. The computation of the transformation
matrix involves an inversion if the original coefficients are defined on the ellipsoid. This inversion can be performed accurately
and efficiently (i.e., without regularisation) for transformation among different gravity field quantities on the same ellipsoid,
due to diagonal dominance of the matrices. However, transformations from the ellipsoid to another surface can only be performed
accurately and efficiently for coefficients up to degree and order 520 due to numerical instabilities in the inversion. 相似文献
5.
Benedikt Soja Richard S. Gross Claudio Abbondanza Toshio M. Chin Michael B. Heflin Jay W. Parker Xiaoping Wu Tobias Nilsson Susanne Glaser Kyriakos Balidakis Robert Heinkelmann Harald Schuh 《Journal of Geodesy》2018,92(9):1063-1077
The Global Geodetic Observing System requirement for the long-term stability of the International Terrestrial Reference Frame is 0.1 mm/year, motivated by rigorous sea level studies. Furthermore, high-quality station velocities are of great importance for the prediction of future station coordinates, which are fundamental for several geodetic applications. In this study, we investigate the performance of predictions from very long baseline interferometry (VLBI) terrestrial reference frames (TRFs) based on Kalman filtering. The predictions are computed by extrapolating the deterministic part of the coordinate model. As observational data, we used over 4000 VLBI sessions between 1980 and the middle of 2016. In order to study the predictions, we computed VLBI TRF solutions only from the data until the end of 2013. The period of 2014 until 2016.5 was used to validate the predictions of the TRF solutions against the measured VLBI station coordinates. To assess the quality, we computed average WRMS values from the coordinate differences as well as from estimated Helmert transformation parameters, in particular, the scale. We found that the results significantly depend on the level of process noise used in the filter. While larger values of process noise allow the TRF station coordinates to more closely follow the input data (decrease in WRMS of about 45%), the TRF predictions exhibit larger deviations from the VLBI station coordinates after 2014 (WRMS increase of about 15%). On the other hand, lower levels of process noise improve the predictions, making them more similar to those of solutions without process noise. Furthermore, our investigations show that additionally estimating annual signals in the coordinates does not significantly impact the results. Finally, we computed TRF solutions mimicking a potential real-time TRF and found significant improvements over the other investigated solutions, all of which rely on extrapolating the coordinate model for their predictions, with WRMS reductions of almost 50%. 相似文献
6.
Based upon a data set of 25 points of the Baltic Sea Level Project, second campaign 1993.4, which are close to mareographic
stations, described by (1) GPS derived Cartesian coordinates in the World Geodetic Reference System 1984 and (2) orthometric
heights in the Finnish Height Datum N60, epoch 1993.4, we have computed the primary geodetic parameter W
0(1993.4) for the epoch 1993.4 according to the following model. The Cartesian coordinates of the GPS stations have been converted
into spheroidal coordinates. The gravity potential as the additive decomposition of the gravitational potential and the centrifugal
potential has been computed for any GPS station in spheroidal coordinates, namely for a global spheroidal model of the gravitational
potential field. For a global set of spheroidal harmonic coefficients a transformation of spherical harmonic coefficients
into spheroidal harmonic coefficients has been implemented and applied to the global spherical model OSU 91A up to degree/order
360/360. The gravity potential with respect to a global spheroidal model of degree/order 360/360 has been finally transformed
by means of the orthometric heights of the GPS stations with respect to the Finnish Height Datum N60, epoch 1993.4, in terms
of the spheroidal “free-air” potential reduction in order to produce the spheroidal W
0(1993.4) value. As a mean of those 25 W
0(1993.4) data as well as a root mean square error estimation we computed W
0(1993.4)=(6 263 685.58 ± 0.36) kgal × m. Finally a comparison of different W
0 data with respect to a spherical harmonic global model and spheroidal harmonic global model of Somigliana-Pizetti type (level
ellipsoid as a reference, degree/order 2/0) according to The Geodesist's Handbook 1992 has been made.
Received: 7 November 1996 / Accepted: 27 March 1997 相似文献
7.
将轮胎调和分析引入电离层TEC的模型化过程中,建立了基于轮胎调和分析的电离层TEC球谐系数模型,并对该模型进行详细的验证和分析。结果表明,本文模型计算精度高,系数截断为15阶时,恢复误差全年统计不超过4%,且除南、北极区外球谐模型具有很好的适用性。然后对该模型系数的时间序列特性进行了函数估计：引入逐级余差建模方法,使用趋势函数、功率谱分析、ARMA模型对球谐系数的时间序列进行分析,找出了模型系数时间序列变化的规律,构建了预报模型,实现了基于模型系数的预报,并对预报系数的精度变化问题和系数本身短期预报的数据积累时间进行分析,最终通过TEC的预报,验证了模型的精度。 相似文献
8.
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
9.
R. H. Rapp 《Journal of Geodesy》1971,45(3):283-297
The undulations of the geoid may be computed from spherical harmonic potential coefficients of the earth’s gravitational field.
This paper examines three procedures that reflect various points of view on how this computation should be carried out. One
method requires only the flattening of a reference ellipsoid to be defined while the other two methods require a complete
definition of the parameters of the ellipsoid. It was found that the various methods give essentially the same undulations
provided that correct parameters are chosen for the reference ellipsoid. A discussion is given on how these parameters are
chosen and numerical results are reported using recent potential coefficient determinations. 相似文献
10.
地球参考框架是一切测绘活动、地球科学研究的物理基础。目前,地球参考框架常采用长期解的形式,即利用一组全球分布的基准站在某一参考历元的坐标和速度来表示。由于观测有误差,且各基准站又具有非线性变化,故需要对不同历元的瞬时地球参考框架进行累积,形成稳定的长期参考框架。以不同历元观测数据得到的瞬时参考框架成果为输入,构建了一种基于多历元观测数据建立参考框架长期累积解的融合模型。从坐标转换模型和测站坐标的时变模型出发,详细推导了建立长期解的函数模型,依据该函数模型的秩亏数设计了转换参数的内约束基准。采用2010-08—2014-12的国际全球导航卫星系统服务第2次处理结果进行试算,并与国际地球参考框架2014成果进行了对比。结果表明,X、Y、Z方向标准偏差分别为3.45 ?mm、4.04 mm、2.84 mm,速度精度分别为1.53 mm/a、1.46 mm/a、1.21 mm/a,X、Y、Z方向的加权均方根误差优于3 ?mm。 相似文献
11.
Mathis Bloßfeld Sergei Rudenko Alexander Kehm Natalia Panafidina Horst Müller Detlef Angermann Urs Hugentobler Manuela Seitz 《Journal of Geodesy》2018,92(9):1003-1021
In this paper, we consistently estimate geodetic parameters such as weekly 3-D station coordinates, Earth orientation parameters (EOP) including daily x/y-pole coordinates and the excess length of day \(\Delta \hbox {LOD}\), and selected weekly Earth’s gravitational field (Stokes) coefficients up to degree and order 6 from Satellite Laser Ranging measurements to up to 11 geodetic satellites. The SLR constellation consists of LAGEOS-1/2, Etalon-1/2, Stella, Starlette, Ajisai, Larets, LARES, BLITS and WESTPAC, and its observations cover a time span of 38 years ranging from February 16, 1979, to April 30, 2017. If multiple satellites with various altitudes and orbit inclinations are combined, correlations between estimated parameters are significantly reduced. This allows us (i) to investigate the ability of satellite constellations to reduce existing correlations and (ii) to estimate reliable parameters with higher precision compared to the standard 4-satellite constellation (LAGEOS-1/2, Etalon-1/2) which is currently used by the International Laser Ranging Service for the determination of the Terrestrial Reference Frame (TRF) and EOP products. In particular, the Stokes coefficients, EOP and TRF datum parameters (three translations, three rotations, one scale factor), which are highly correlated with satellite-specific orbit parameters, are improved. From our investigations, we found for an 11-satellite solution compared to the above-mentioned 4-satellite solution a decrease in the scatter of the TRF datum parameters of up to 37%, the transformation residuals are decreased by up to 22%, the scatter of the EOP is decreased by up to 22%, and their mean values are decreased by up to 84% w.r.t. the reference solutions. The largest improvement is obtained for the Stokes coefficients which significantly benefit from a combination of multiple satellites (inclinations and orbit altitudes). In total, single coefficients are improved by up to 93% and the overall improvement is up to 74%. Moreover, it could be clearly identified that Ajisai significantly disturbs the TRF solution due to an erroneous center-of-mass correction. We further quantify the impact of specific satellites on the determination of different geodetic parameters and finally evaluate the potential of the existing SLR-tracked spherical satellite constellation to support the goals of GGOS. 相似文献
12.
应用文献 [1 ]推导出的球谐系数与椭球谐系数的转换关系 ,给出了椭球界面下Neumann边值问题的积分解 相似文献
13.
Multiple Parameter Regularization: Numerical Solutions and Applications to the Determination of Geopotential from Precise Satellite Orbits 总被引：1，自引：0，他引：1
Kaula’s rule of thumb has been used in producing geopotential models from space geodetic measurements, including the most recent models from satellite gravity missions CHAMP. Although Xu and Rummel (Manuscr Geod 20 8–20, 1994b) suggested an alternative regularization method by introducing a number of regularization parameters, no numerical tests have ever been conducted. We have compared four methods of regularization for the determination of geopotential from precise orbits of COSMIC satellites through simulations, which include Kaula’s rule of thumb, one parameter regularization and its iterative version, and multiple parameter regularization. The simulation results show that the four methods can indeed produce good gravitational models from the precise orbits of centimetre level. The three regularization methods perform much better than Kaula’s rule of thumb by a factor of 6.4 on average beyond spherical harmonic degree 5 and by a factor of 10.2 for the spherical harmonic degrees from 8 to 14 in terms of degree variations of root mean squared errors. The maximum componentwise improvement in the root mean squared error can be up to a factor of 60. The simplest version of regularization by multiplying a positive scalar with a unit matrix is sufficient to better determine the geopotential model. Although multiple parameter regularization is theoretically attractive and can indeed eliminate unnecessary regularization for some of the harmonic coefficients, we found that it only improved its one parameter version marginally in this COSMIC example in terms of the mean squared error. 相似文献
14.
The derivatives of the Earth gravitational potential are considered in the global Cartesian Earth-fixed reference frame. Spherical
harmonic series are constructed for the potential derivatives of the first and second orders on the basis of a general expression
of Cunningham (Celest Mech 2:207–216, 1970) for arbitrary order derivatives of a spherical harmonic. A common structure of
the series for the potential and its first- and second-order derivatives allows to develop a general procedure for constructing
similar series for the potential derivatives of arbitrary orders. The coefficients of the derivatives are defined by means
of recurrence relations in which a coefficient of a certain order derivative is a linear function of two coefficients of a
preceding order derivative. The coefficients of the second-order derivatives are also presented as explicit functions of three
coefficients of the potential. On the basis of the geopotential model EGM2008, the spherical harmonic coefficients are calculated
for the first-, second-, and some third-order derivatives of the disturbing potential T, representing the full potential V, after eliminating from it the zero- and first-degree harmonics. The coefficients of two lowest degrees in the series for
the derivatives of T are presented. The corresponding degree variances are estimated. The obtained results can be applied for solving various
problems of satellite geodesy and celestial mechanics. 相似文献
15.
E. Doukakis 《Journal of Geodesy》1977,51(4):295-300
The transformation of the instantaneous terrestrial coordinate system to the mean or average earth-fixed one is parameterized
by the polar motion components which are continuously changing in time. Using the non-symmetricity of the connection coefficients
connecting the above frames the errors (“misclosures”) are estimated which would be present if the instantaneous frame would
be used as the geodetic reference frame. 相似文献
16.
Combinations of station coordinates and velocities from independent space-geodetic techniques have long been the standard
method to realize robust global terrestrial reference frames (TRFs). In principle, the particular strengths of one observing
method can compensate for weaknesses in others if the combination is properly constructed, suitable weights are found, and
accurate co-location ties are available. More recently, the methodology has been extended to combine time-series of results
at the normal equation level. This allows Earth orientation parameters (EOPs) to be included and aligned in a fully consistent
way with the TRF. While the utility of such multi-technique combinations is generally recognized for the reference frame,
the benefits for the EOPs are yet to be quantitatively assessed. In this contribution, which is a sequel to a recent paper
on co-location ties (Ray and Altamimi in J Geod 79(4–5): 189–195, 2005), we have studied test combinations of very long baseline
interferometry (VLBI) and Global Positioning System (GPS) time-series solutions to evaluate the effects on combined EOP measurements
compared with geophysical excitations. One expects any effect to be small, considering that GPS dominates the polar motion
estimates due to its relatively dense and uniform global network coverage, high precision, continuous daily sampling, and
homogeneity, while VLBI alone observes UT1-UTC. Presently, although clearly desirable, we see no practical method to rigorously
include the GPS estimates of length-of-day variations due to significant time-varying biases. Nevertheless, our results, which
are the first of this type, indicate that more accurate polar motion from GPS contributes to improved UT1-UTC results from
VLBI. The situation with combined polar motion is more complex. The VLBI data contribute directly only very slightly, if at
all, with an impact that is probably affected by the weakness of the current VLBI networks (small size and sparseness) and
the quality of local ties relating the VLBI and GPS frames. Instead, the VLBI polar motion information is used primarily in
rotationally aligning the VLBI and GPS frames, thereby reducing the dependence on co-location tie information. Further research
is needed to determine an optimal VLBI-GPS combination strategy that yields the highest quality EOP estimates. Improved local
ties (including internal systematic effects within the techniques) will be critically important in such an effort. 相似文献
17.
P. Moore 《Journal of Geodesy》1987,61(3):223-234
Starlette was launched in 1975 in order to study temporal variations in the Earth’s gravity field; in particular, tidal and
Earth rotation effects. For the period April 1983 to April 1984 over12,700 normal points of laser ranging data to Starlette have been sub-divided into49 near consecutive 5–6 day arcs. Normal equations for each arc as obtained from a least-squares data reduction procedure, were
solved for ocean tidal parameters along with other geodetic and geodynamic parameters. The tidal parameters are defined relative
to Wahr’s body tides and Wahr’s nutation model and show fair agreement with other satellite derived results and those obtained
from spherical harmonic decomposition of global ocean tidal models. 相似文献
18.
Prediction of vertical deflections from high-degree spherical harmonic synthesis and residual terrain model data 总被引：6，自引：4，他引：2
Christian Hirt 《Journal of Geodesy》2010,84(3):179-190
This study demonstrates that in mountainous areas the use of residual terrain model (RTM) data significantly improves the
accuracy of vertical deflections obtained from high-degree spherical harmonic synthesis. The new Earth gravitational model
EGM2008 is used to compute vertical deflections up to a spherical harmonic degree of 2,160. RTM data can be constructed as
difference between high-resolution Shuttle Radar Topography Mission (SRTM) elevation data and the terrain model DTM2006.0
(a spherical harmonic terrain model that complements EGM2008) providing the long-wavelength reference surface. Because these
RTM elevations imply most of the gravity field signal beyond spherical harmonic degree of 2,160, they can be used to augment
EGM2008 vertical deflection predictions in the very high spherical harmonic degrees. In two mountainous test areas—the German
and the Swiss Alps—the combined use of EGM2008 and RTM data was successfully tested at 223 stations with high-precision astrogeodetic
vertical deflections from recent zenith camera observations (accuracy of about 0.1 arc seconds) available. The comparison
of EGM2008 vertical deflections with the ground-truth astrogeodetic observations shows root mean square (RMS) values (from
differences) of 3.5 arc seconds for ξ and 3.2 arc seconds for η, respectively. Using a combination of EGM2008 and RTM data for the prediction of vertical deflections considerably reduces
the RMS values to the level of 0.8 arc seconds for both vertical deflection components, which is a significant improvement
of about 75%. Density anomalies of the real topography with respect to the residual model topography are one factor limiting
the accuracy of the approach. The proposed technique for vertical deflection predictions is based on three publicly available
data sets: (1) EGM2008, (2) DTM2006.0 and (3) SRTM elevation data. This allows replication of the approach for improving the
accuracy of EGM2008 vertical deflection predictions in regions with a rough topography or for improved validation of EGM2008
and future high-degree spherical harmonic models by means of independent ground truth data. 相似文献
19.
The upward-downward continuation of a harmonic function like the gravitational potential is conventionally based on the direct-inverse
Abel-Poisson integral with respect to a sphere of reference. Here we aim at an error estimation of the “planar approximation”
of the Abel-Poisson kernel, which is often used due to its convolution form. Such a convolution form is a prerequisite to
applying fast Fourier transformation techniques. By means of an oblique azimuthal map projection / projection onto the local
tangent plane at an evaluation point of the reference sphere of type “equiareal” we arrive at a rigorous transformation of
the Abel-Poisson kernel/Abel-Poisson integral in a convolution form. As soon as we expand the “equiareal” Abel-Poisson kernel/Abel-Poisson
integral we gain the “planar approximation”. The differences between the exact Abel-Poisson kernel of type “equiareal” and
the “planar approximation” are plotted and tabulated. Six configurations are studied in detail in order to document the error
budget, which varies from 0.1% for points at a spherical height H=10km above the terrestrial reference sphere up to 98% for points at a spherical height H = 6.3×106km.
Received: 18 March 1997 / Accepted: 19 January 1998 相似文献
20.
Christopher Kotsakis 《Journal of Geodesy》2008,82(4-5):261-260
Transforming height information that refers to an ellipsoidal Earth reference model, such as the geometric heights determined
from GPS measurements or the geoid undulations obtained by a gravimetric geoid solution, from one geodetic reference frame
(GRF) to another is an important task whose proper implementation is crucial for many geodetic, surveying and mapping applications.
This paper presents the required methodology to deal with the above problem when we are given the Helmert transformation parameters
that link the underlying Cartesian coordinate systems to which an Earth reference ellipsoid is attached. The main emphasis
is on the effect of GRF spatial scale differences in coordinate transformations involving reference ellipsoids, for the particular
case of heights. Since every three-dimensional Cartesian coordinate system ‘gauges’ an attached ellipsoid according to its
own accessible scale, there will exist a supplementary contribution from the scale variation between the involved GRFs on
the relative size of their attached reference ellipsoids. Neglecting such a scale-induced indirect effect corrupts the values
for the curvilinear geodetic coordinates obtained from a similarity transformation model, and meter-level apparent offsets
can be introduced in the transformed heights. The paper explains the above issues in detail and presents the necessary mathematical
framework for their treatment.
An erratum to this article can be found at 相似文献