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1.
Efficient gravity field recovery from GOCE gravity gradient observations   总被引：4，自引：2，他引：2  
 An efficient algorithm is proposed for gravity field recovery from Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) satellite gravity gradient observations. The mathematical model is formulated in the time domain, which allows the inclusion of realistic observational noise models. The algorithm combines the iterative solution of the normal equations, using a Richardson-type iteration scheme, with the fast computation of the right-hand side of the normal equations in each iteration step by a suitable approximation of the design matrix. The convergence of the iteration is investigated, error estimates are provided, and the unbiasedness of the method is proved. It is also shown that the method does not converge to the solution of the normal equations. The performance of the approach for white noise and coloured noise is demonstrated along a simulated GOCE orbit up to spherical harmonic degree and order 180. The results also indicate that the approximation error may be neglected. Received: 30 November 1999 / Accepted: 31 May 2000  相似文献   

2.
A fast iterative method for gravity field determination from low Earth satellite orbit coordinates has been developed and implemented successfully. The method is based on energy conservation and avoids problems related to orbit dynamics and initial state. In addition, the particular geometry of a repeat orbit is exploited by using a very efficient iterative estimation scheme, in which a set of normal equations is approximated by a sparse block-diagonal equivalent. Recovery experiments for spherical harmonic gravity field models up to degree and order 80 and 120 were conducted based on a 29-day simulated data set of orbit coordinates. The method was found to be very flexible and could be easily adapted to include observations of non-conservative accelerations, such as (to be) provided by satellites like CHAMP, GRACE, and GOCE. A serious drawback of the method is its large sensitivity to satellite velocity errors. Existing orbit determination strategies need to be altered or augmented to include algorithms that focus on optimizing the accuracy of estimated velocities.  相似文献   

3.
Regularization of gravity field estimation from satellite gravity gradients   总被引：6，自引：1，他引：6  
 The performance of the L-curve criterion and of the generalized cross-validation (GCV) method for the Tikhonov regularization of the ill-conditioned normal equations associated with the determination of the gravity field from satellite gravity gradiometry is investigated. Special attention is devoted to the computation of the corner point of the L-curve, to the numerically efficient computation of the trace term in the GCV target function, and to the choice of the norm of the residuals, which is important for the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) in the presence of colored observation noise. The trace term in the GCV target function is estimated using an unbiased minimum-variance stochastic estimator. The performance analysis is based on a simulation of gravity gradients along a 60-day repeat circular orbit and a gravity field recovery complete up to degree and order 300. Randomized GCV yields the optimal regularization parameter in all the simulations if the colored noise is properly taken into account. Moreover, it seems to be quite robust against the choice of the norm of the residuals. It performs much better than the L-curve criterion, which always yields over-smooth solutions. The numerical costs for randomized GCV are limited provided that a reasonable first guess of the regularization parameter can be found. Received: 17 May 2001 / Accepted: 17 January 2002  相似文献   

4.
C. Hwang 《Journal of Geodesy》2001,75(2-3):117-136
 COSMIC is a joint Taiwan–US mission to study the atmosphere using the Global Positioning System (GPS) occultation technique. Improved formulas are developed for the radial, along-track, and cross-track perturbations, which are more accurate than the commonly used order-zero formulas. The formulas are used to simulate gravity recovery using the geodetic GPS data of COSMIC in the operational phase. Results show that the EGM96 model can be improved up to degree 26 using 1 year of COSMIC data. TOPEX/POSEIDON altimeter data are used to derive a temporal gravity variation. COSMIC cannot reproduce this gravity variation perfectly because of data noise and orbital configuration, but the recovered field clearly shows the gravity signature due to mass movement in an El Ni?o. Received: 3 March 2000 / Accepted: 10 November 2000  相似文献   

5.
多种跟踪组合卫星重力场恢复方法初探   总被引：2，自引：0，他引：2  
将卫星地面跟踪、高低卫星跟踪和低低卫星跟踪恢复重力场的原理进行统一 ,导出了两种能充分综合多种跟踪观测的卫星重力场恢复基本观测方程。在建立基本观测量与重力场参数的函数传输关系的基础上 ,对目前存在的重力场恢复算法给出了直观的解释 ,并以距离二次变率为重力场恢复的基本观测量 ,提出了一种能组合各种卫星跟踪观测量的动态 /动力组合定轨和重力场恢复方法。  相似文献   

6.
The passive satellite GFZ-1 has been orbiting the Earth since April 1995. The purpose of this mission is to improve the current knowledge of the Earth's gravity field by analysing gravitational orbit perturbations observed at unique low altitudes, below 400 km. GFZ-1 is one target of the international satellite laser ranging ground network. An evaluation of the first 30 months of GFZ-1 laser tracking data led to a new version of the global GRIM4-S4 satellite-only gravity field model: GRIM4-S4G. Information was obtained from GFZ-1 data for spherical harmonic coefficients up to degree 100, which was not possible in any earlier satellite-only gravity field solution. GFZ-1's contribution to a global 5 × 5° geoid and gravity field representations is moderate but visible with a 1 cm and 0.1 mGal gain in accuracy on a level of 75 cm and 5 mGal, respectively. Received: 10 November 1998 / Accepted: 19 April 1999  相似文献   

7.
For many years, the gravity field of the Earth was only seen by satellite geodesy as the main factor affecting the orbit and consequently it was retrieved together with a number of other orbital perturbations. Since the advent of a new generation of accelerometers, non-gravitational perturbations can be separated from the gravity effects and a new era of gravity field estimates from space has been born. During preparatory data analysis for new missions performed by the geodetic community, three approaches have been proposed and numerically tested: the brute force method (direct approach), the semi-analytical (time-wise) method and the space-wise method. In particular, the time-wise method takes advantage of the incoming time flow of data and, after performing a Fourier transform of the observation equations, exploits the prevailing block diagonal structure of the normal equations to estimate the spherical harmonic coefficients of the gravity field. Complementary to this is the space-wise approach, which goes back to the traditional computation of the harmonic coefficients by an integration technique or by least-squares collocation. Some advantages and disadvantages are peculiar to both methods, particularly the space-wise approach, which has for a long time ignored the marked signature of the noise spectrum due to the specific measuring conditions of space-borne accelerometers. The application of a proper Wiener filter, exploiting the correlation along the orbit, embedded into an iterative scheme, seems to be the answer. The solution to this major problem of the space-wise approach is illustrated and simulation results are discussed.  相似文献   

8.
Summary.  GFZ Potsdam and GRGS Toulouse/Grasse jointly developed a new pair of global models of the Earth's gravity field to satisfy the requirements of the recent and future geodetic and altimeter satellite missions. A precise gravity model is a prerequisite for precise satellite orbit restitution, tracking station positioning and altimeter data reduction. According to different applications envisaged, the new model exists in two parallel versions: the first one being derived exclusively from satellite tracking data acquired on 34 satellites, the second one further incorporating satellite altimeter data over the oceans and terrestrial gravity data. The most recent “satellite-only” gravity model is labelled GRIM4-S4 and the “combined” gravity model GRIM4-C4. The models are solutions in spherical harmonics and have a resolution up to degree and order 60 plus a few resonance terms in the case of GRIM4-S4, and up to degree/order 72 in the case of GRIM4-C4, corresponding to a spatial resolution of 555 km at the Earth's surface. The gravitational coefficients were estimated in a rigorous least squares adjustment simultaneously with ocean tidal terms and tracking station position parameters, so that each gravity model is associated with a consistent ocean tide model and a terrestrial reference frame built up by over 300 optical, laser and Doppler tracking stations. Comprehensive quality tests with external data and models, and test arc computations over a wide range of satellites have demonstrated the state-of-the-art capabilities of both solutions in long-wavelength geoid representation and in precise orbit computation. Received 1 February 1996; Accepted 17 July 1996  相似文献   

9.
Summary Two methods are discussed for the processing of altimetry data. For the first method it is assumed that the altimetry data, may be analyzed independent of the orbit computation for the satellite that carries the altimeter. Because of the high accuracy of the altimetry data, which can only be fully utilized if it is also introduced into the orbit computations, the second method deals with a simultaneous processing of altimetry data, orbit tracking, and gravity anomalies for the continents. To represent the gravity field, the potential of a simple layer is chosen whose unknown density is assumed to be constant over surface elements into which the surface of the earth is divided. Depending on the accuracy and the amount of the altimetry data, the surface elements for the density values are chosen smaller or larger, so that a very flexible representation of the earth’s gravity field is obtained. Because of the amount and the resolution of the altimetry data a large number of density values have to be determined in a least squares adjustment. To facilitate the computations, buffer zones are introduced so that the large system of normal equations can be broken up into small independent subsystems. Shortened version of a paper presented to the 14 th International Congress of Surveyors in Washington, Sept. 1974.  相似文献   

10.
采用星载GPS观测数据与简化动力学定轨方法,在方程中引入伪随机脉冲参数,从而实现对Swarm卫星的精密定轨. 详细分析了不同阶次的GOCO06s地球重力场模型对Swarm卫星简化动力学定轨精度的影响,对比了PGM2000a、EIGEN-2、EGM2008以及GECO重力场模型展开到100阶次时Swarm卫星解算的轨道精度. 结果表明:当GOCO06s地球重力场模型阶次处于30～100阶次时,Swarm-A、Swarm-B和Swarm-C卫星在径向、切向、法向上的定轨精度随着GOCO06s阶次的不断增加而越来越高,而在高于100阶次时,定轨精度基本稳定,且在各方向定轨精度优于3 cm. 此外,采用100阶次GECO、EGM2008和GOCO06s模型对三颗Swarm卫星进行定轨,解算的轨道精度相当,且要高于同阶次其他重力场模型的定轨结果.   相似文献   

11.
Gravitational perturbation theory for intersatellite tracking   总被引：7，自引：0，他引：7  
 An analytical gravitational perturbation theory for the intersatellite tracking range and range-rate measurement between two satellites is developed. The satellite-to-satellite tracking (SST) range data measure the difference between the position perturbations of two satellites along the direction of the intersatellite range. The SST range-rate data measure the difference between the velocity perturbations along the direction of the intersatellite range, and the difference of the position perturbation along the direction perpendicular to the intersatellite range (cross-range). The SST range and range rate depend on different orbital excitations for mapping the gravity field. For the Gravity Recovery and Climate Experiment (GRACE), approximately 97% of the geopotential coefficient pairs produce perturbations with a root-mean-square larger than 1 m on the range and 0.1 m/sec on the range rate based on the EGM96 gravity field truncated at degree and order 140. Results in this study showed that ocean tides produce significant perturbations in the range and range-rate measurements. An ocean tide field with a higher degree and order (>70) is required to model the ocean tide perturbations on the intersatellite range and range-rate measurement. Received: 17 May 2000 / Accepted: 3 September 2001  相似文献   

12.
本文研究了联合卫星观测数据和重力异常数据确定超高阶重力场模型的理论方法,并使用EGM2008模型重力异常和GOCE（gravity field and ocean circulation explorer）观测数据构建了重力场模型SGG-UGM-1。重点研究了由球面格网重力异常快速构建超高阶重力场模型的块对角最小二乘方法,将OpenMP技术引入到块对角最小二乘中以提高计算效率,并基于模拟数据验证了方法及算法和软件模块的正确性。采用本文制定的联合解算策略,利用GOCE重力卫星观测数据构建的220阶次法方程和EGM2008模型重力异常构建的2159阶次块对角法方程,联合求解了2159阶次的重力场模型SGG-UGM-1。将SGG-UGM-1与EGM2008、EIGEN-6C2、EIGEN-6C4等超高阶模型在频谱域内进行了比较分析,结果表明SGG-UGM-1相对参考模型的系数误差较小,且在220阶次内的系数精度相比EGM2008模型有了提高。采用中国与美国的GPS/水准数据和毛乌素测区的航空重力观测数据对这些模型进行了外符合精度的检验。检核结果表明,在中国区域,SGG-UGM-1模型大地水准面的精度在EIGEN-6C2和EIGEN-6C4两个模型之间,优于GOSG-EGM模型和EGM2008模型,与美国区域几个模型的精度相当。利用毛乌素测区的航空重力数据对几个模型进行了检核,结果表明SGG-UGM-1模型计算的重力扰动精度与EGM2008、EIGEN-6C4模型相当,优于GOSG-EGM模型和EIGEN-6C2模型。  相似文献   

13.
Global gravity field models have been determined based on kinematic orbits covering an observation period of one year beginning from March 2002. Three different models have been derived up to a maximum degree of n=90 of a spherical harmonic expansion of the gravitational potential. One version, ITG-CHAMP01E, has been regularized beginning from degree n=40 upwards, based on the potential coefficients of the gravity field model EGM96. A second model, ITG-CHAMP01K, has been determined based on Kaulas rule of thumb, also beginning from degree n=40. A third version, ITG-CHAMP01S, has been determined without any regularization. The physical model of the gravity field recovery technique is based on Newtons equation of motion, formulated as a boundary value problem in the form of a Fredholm-type integral equation. The observation equations are formulated in the space domain by dividing the one-year orbit into short sections of approximately 30-minute arcs. For every short arc, a variance factor has been determined by an iterative computation procedure. The three gravity field models have been validated based on various criteria, and demonstrate the quality of not only the gravity field recovery technique but also the kinematically determined orbits.  相似文献   

14.
 Starting from the analytical theory of perturbed␣circular motions presented in Celestial Mechanics (Bois 1994) and from specific extended formulations of the perturbations in a uniformly rotating plane of constant inclination, this paper presents an extended formulation of the solution. The actual gain made through this extension is the establishment of a first-order predictive theory written in spherical coordinates and thus free of singularities, whose perturbations are directly expressed in the local orbital frame generally used in satellite geodesy. This new formulation improves the generality, the precision and the field of applications of the theory. It is particularly devoted to the analysis of satellite position perturbations for satellites in low eccentricity orbits usually used for many Earth observation applications. An application to the TOPEX/Poseidon (T/P) orbit is performed. In particular, contour maps are provided which show the geographical location of orbit differences coming from geopotential coefficient differences of two recent gravity field models. Comparison of predicted radial and along-track orbit differences with respect to numerical results provided by the French group (CNES, in Toulouse) in charge of the T/P orbit are convincing. Received 22 January 1996; Accepted 19 September 1996  相似文献   

15.
 A prerequisite for the success of future gravity missions like the European Gravity field and steady-state Ocean Circulation Explorer (GOCE) is a precise orbit determination (POD). A detailed simulation study has been carried out to assess the achievable orbit accuracy based on satellite-to-satellite tracking (SST) by the US global positioning system (GPS) and in conjunction the implications for gravity field determination. An orbit accuracy at the few centimeter level seems possible, sufficient to support the GOCE gravity mission and in particular its gravity gradiometer. Received: 21 January 2000 / Accepted: 4 July 2000  相似文献   

16.
Throughout 2004 the GRACE (Gravity Recovery And Climate Experiment) orbit contracted slowly to yield a sparse repeat track of 61 revolutions every 4 days on 19 September 2004. As a result, we show from linear perturbation theory that geopotential information previously available to fully resolve a gravity field every month of 120× 120 (degree by order) in spherical harmonics was compressed then into about one-fourth of the necessary observation space. We estimate from this theory that the ideal gravity field resolution in September 2004 was only about 30 × 30. More generally, we show that any repeat-cycle mission for geopotential recovery with full resolution L × L requires the number of orbit-revolutions-to-repeat to be greater than 2L.  相似文献   

17.
Three GOCE-based gravity field solutions have been computed by ESA’s high-level processing facility and were released to the user community. All models are accompanied by variance-covariance information resulting either from the least squares procedure or a Monte-Carlo approach. In order to obtain independent external quality parameters and to assess the current performance of these models, a set of independent tests based on satellite orbit determination and geoid comparisons is applied. Both test methods can be regarded as complementary because they either investigate the performance in the long wavelength spectral domain (orbit determination) or in the spatial domain (geoid comparisons). The test procedure was applied to the three GOCE gravity field solutions and to a number of selected pre-launch models for comparison. Orbit determination results suggest, that a pure GOCE gravity field model does not outperform the multi-year GRACE gravity field solutions. This was expected as GOCE is designed to improve the determination of the medium to high frequencies of the Earth gravity field (in the range of degree and order 50 to 200). Nevertheless, in case of an optimal combination of GOCE and GRACE data, orbit determination results should not deteriorate. So this validation procedure can also be used for testing the optimality of the approach adopted for producing combined GOCE and GRACE models. Results from geoid comparisons indicate that with the 2 months of GOCE data a significant improvement in the determination of the spherical harmonic spectrum of the global gravity field between degree 50 and 200 can be reached. Even though the ultimate mission goal has not yet been reached, especially due to the limited time span of used GOCE data (only 2 months), it was found that existing satellite-only gravity field models, which are based on 7 years of GRACE data, can already be enhanced in terms of spatial resolution. It is expected that with the accumulation of more GOCE data the gravity field model resolution and quality can be further enhanced, and the GOCE mission goal of 1–2 cm geoid accuracy with 100 km spatial resolution can be achieved.  相似文献   

18.
 Equations expressing the covariances between spherical harmonic coefficients and linear functionals applied on the anomalous gravity potential, T, are derived. The functionals are the evaluation functionals, and those associated with first- and second-order derivatives of T. These equations form the basis for the prediction of spherical harmonic coefficients using least-squares collocation (LSC). The equations were implemented in the GRAVSOFT program GEOCOL. Initially, tests using EGM96 were performed using global and regional sets of geoid heights, gravity anomalies and second-order vertical gravity gradients at ground level and at altitude. The global tests confirm that coefficients may be estimated consistently using LSC while the error estimates are much too large for the lower-order coefficients. The validity of an error estimate calculated using LSC with an isotropic covariance function is based on a hypothesis that the coefficients of a specific degree all belong to the same normal distribution. However, the coefficients of lower degree do not fulfil this, and this seems to be the reason for the too-pessimistic error estimates. In order to test this the coefficients of EGM96 were perturbed, so that the pertubations for a specific degree all belonged to a normal distribution with the variance equal to the mean error variance of the coefficients. The pertubations were used to generate residual geoid heights, gravity anomalies and second-order vertical gravity gradients. These data were then used to calculate estimates of the perturbed coefficients as well as error estimates of the quantities, which now have a very good agreement with the errors computed from the simulated observed minus calculated coefficients. Tests with regionally distributed data showed that long-wavelength information is lost, but also that it seems to be recovered for specific coefficients depending on where the data are located. Received: 3 February 2000 / Accepted: 23 October 2000  相似文献   

19.
When the orbit of the Landsat I spacecraft was liberated to natural forces, the loss of observations to the remote sensing community was balanced by a modest gain for geodesy. The orbit’s long ground-track repeat period of eighteen days gives rise to a shallow resonance with fourteenth, twenty-eighth and forty-second order terms in the geopotential. A single continuous span of twenty-four days of Unified S-Band tracking data, collected at a single station in 1976, has been analyzed to define constraints on the dominant resonance terms of these orders and of fourteenth-order fringe resonance effects depending on the eccentricitye≈.002. Tracking observations from other stations collected during 1974 and 1975 gave essentially the same results, which provided error estimates for the lumped resonance coefficients. The application of the resonance model can considerably improve the definition and prediction of the Landsat 1 orbit. Direct numerical estimates of the influence coefficients in the resonance constraint equations were made to confirm the accuracy of analytical expressions which allow the equations to be applied to geopotential fields of arbitrarily high degree and order. Several recently derived gravity fields were tested against the Landsat resonance constraints and their comparative agreement is discussed.  相似文献   

20.
Summary The concept of satellite-to-satellite tracking measuring the relative velocity of two orbiting satellites spaced some hundreds kilometers on a close orbit, provides now possibilities for the investigation of the Earth’s gravity field. In the paper only medium and short wave length effects affecting the measured relative velocity have been considered. Collocation is used in such an analysis of local geoid improvement, because this method allows to combine heterogeneous data in a consistent way. Covariance functions relevant for the particular case of a circular equatorial orbit are given. Two kinds of observation equations have been formulated. The choice of observation equation with regard to satellites configuration is discussed. It is found that it is sufficient to have a limited number of satellite-to-satellite observations in a 7o×7o area around the estimation point with distances between profiles of about 1o.5 and between the two satellites forming the pair of 200+350 km; the altitude of satellite-to-satellite observations should be as low as possible. The accuracy of the geoid determination strongly depends on the degree and order of the reference field used. An accuracy of about ±1 m can be achieved with an assumed reference field of (40,40). The influence of measuring errors is discussed and it is shown that only satellite-to-satellite observations with accuracy better then 0.1 mm/sec will give an improvement of the geoid. Finally, some results on the combination of low-low satellite-to-satellite tracking and terrestrial gravity data are given. The proposed method seems to be especially interesting for unsurveyed areas. Furthermore, it has the practical advantage that only a local coverage data is needed.  相似文献   

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