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1.
When planning a satellite gravity gradiometer (SGG) mission, it is important to know the quality of the quantities to be recovered
at ground level as a function of e.g. satellite altitude, data type and sampling rate, and signal variance and noise. This
kind of knowledge may be provided either using the formal error estimates of wanted quantities using least-squares collocation
(LSC) or by comparing simulated data at ground level with results computed by methods like LSC or Fast Fourier Transform (FFT).
Results of a regional gravity field recovery in a 10o×20o area surrounding the Alps using LSC and FFT are reported. Data used as observations in satellite altitude (202 or161 km) and for comparison at ground level were generated using theOSU86F coefficient set, complete to degree 360. These observations are referred to points across simulated orbits. The simulated
quantities were computed for a 45 days mission period and 4 s sampling. A covariance function which also included terms above
degree 360 was used for prediction and error estimation. This had the effect that the formal error standard deviation for
gravity anomalies were considerably larger than the standard deviations of predicted minus simulated quantities. This shows
the importance of using data with frequency content above degree 360 in simulation studies. Using data at202 km altitude the standard deviation of the predicted minus simulated data was equal to8.3 mgal for gravity and0.33 m for geoid heights. 相似文献
2.
Calibrating the GOCE accelerations with star sensor data and a global gravity field model 总被引:1,自引:0,他引:1
A reliable and accurate gradiometer calibration is essential for the scientific return of the gravity field and steady-state
ocean circulation explorer (GOCE) mission. This paper describes a new method for external calibration of the GOCE gradiometer
accelerations. A global gravity field model in combination with star sensor quaternions is used to compute reference differential
accelerations, which may be used to estimate various combinations of gradiometer scale factors, internal gradiometer misalignments
and misalignments between star sensor and gradiometer. In many aspects, the new method is complementary to the GOCE in-flight
calibration. In contrast to the in-flight calibration, which requires a satellite-shaking phase, the new method uses data
from the nominal measurement phases. The results of a simulation study show that gradiometer scale factors can be estimated
on a weekly basis with accuracies better than 2 × 10−3 for the ultrasensitive and 10−2 for the less sensitive axes, which is compatible with the requirements of the gravity gradient error. Based on a 58-day data
set, scale factors are found that can reduce the errors of the in-flight-calibrated measurements. The elements of the complete
inverse calibration matrix, representing both the internal gradiometer misalignments and scale factors, can be estimated with
accuracies in general better than 10−3. 相似文献
3.
Burkhard Schaffrin 《Journal of Geodesy》1989,63(4):395-404
The now classical collocation method in geodesy has been derived byH. Moritz (1970; 1973) within an appropriate Mixed Linear Model. According toB. Schaffrin (1985; 1986) even a generalized form of the collocation solution can be proved to represent a combined estimation/prediction
procedure of typeBLUUE (Best Linear Uniformly Unbiased Estimation) for the fixed parameters, and of type inhomBLIP (Best inhomogeneously LInear Prediction) for the random effects with not necessarily zero expectation. Moreover, “robust collocation” has been introduced by means of homBLUP (Best homogeneously Linear weakly Unbiased Prediction) for the random effects together with a suitableLUUE for the fixed parameters. Here we present anequivalence theorem which states that the robust collocation solution in theoriginal Mixed Linear Model can identically be derived as traditionalLESS (LEast Squares Solution) in amodified Mixed Linear Model without using artifacts like “pseudo-observations”. This allows us a nice interpretation of “robust collocation”
as an adjustment technique in the presence of “weak prior information”. 相似文献
4.
C. C. Tscherning 《Journal of Geodesy》1978,52(1):85-92
The term “entity” covers, when used in the field of electronic data processing, the meaning of words like “thing”, “being”,
“event”, or “concept”. Each entity is characterized by a set of properties.
An information element is a triple consisting of an entity, a property and the value of a property. Geodetic information is
sets of information elements with entities being related to geodesy. This information may be stored in the form ofdata and is called ageodetic data base provided (1) it contains or may contain all data necessary for the operations of a particular geodetic organization, (2)
the data is stored in a form suited for many different applications and (3) that unnecessary duplications of data have been
avoided.
The first step to be taken when establishing a geodetic data base is described, namely the definition of the basic entities
of the data base (such as trigonometric stations, astronomical stations, gravity stations, geodetic reference-system parameters,
etc...).
Presented at the “International Symposium on Optimization of Design and Computation of Control Networks”, Sopron, Hungary,
July 1977. 相似文献
5.
The problem of the convergence of the collocation solution to the true gravity field was defined long ago (Tscherning in Boll
Geod Sci Affini 39:221–252, 1978) and some results were derived, in particular by Krarup (Boll Geod Sci Affini 40:225–240,
1981). The problem is taken up again in the context of the stochastic interpretation of collocation theory and some new results
are derived, showing that, when the potential T can be really continued down to a Bjerhammar sphere, we have a quite general convergence property in the noiseless case.
When noise is present in data, still reasonable convergence results hold true.
“Democrito che ’l mondo a caso pone” “Democritus who made the world stochastic” Dante Alighieri, La Divina Commedia, Inferno, IV – 136 相似文献
6.
Regularization of geopotential determination from satellite data by variance components 总被引:11,自引:18,他引:11
Different types of present or future satellite data have to be combined by applying appropriate weighting for the determination
of the gravity field of the Earth, for instance GPS observations for CHAMP with satellite to satellite tracking for the coming
mission GRACE as well as gradiometer measurements for GOCE. In addition, the estimate of the geopotential has to be smoothed
or regularized because of the inversion problem. It is proposed to solve these two tasks by Bayesian inference on variance
components. The estimates of the variance components are computed by a stochastic estimator of the traces of matrices connected
with the inverse of the matrix of normal equations, thus leading to a new method for determining variance components for large
linear systems. The posterior density function for the variance components, weighting factors and regularization parameters
are given in order to compute the confidence intervals for these quantities. Test computations with simulated gradiometer
observations for GOCE and satellite to satellite tracking for GRACE show the validity of the approach.
Received: 5 June 2001 / Accepted: 28 November 2001 相似文献
7.
The problem of “global height datum unification” is solved in the gravity potential space based on: (1) high-resolution local
gravity field modeling, (2) geocentric coordinates of the reference benchmark, and (3) a known value of the geoid’s potential.
The high-resolution local gravity field model is derived based on a solution of the fixed-free two-boundary-value problem
of the Earth’s gravity field using (a) potential difference values (from precise leveling), (b) modulus of the gravity vector
(from gravimetry), (c) astronomical longitude and latitude (from geodetic astronomy and/or combination of (GNSS) Global Navigation
Satellite System observations with total station measurements), (d) and satellite altimetry. Knowing the height of the reference
benchmark in the national height system and its geocentric GNSS coordinates, and using the derived high-resolution local gravity
field model, the gravity potential value of the zero point of the height system is computed. The difference between the derived
gravity potential value of the zero point of the height system and the geoid’s potential value is computed. This potential
difference gives the offset of the zero point of the height system from geoid in the “potential space”, which is transferred
into “geometry space” using the transformation formula derived in this paper. The method was applied to the computation of
the offset of the zero point of the Iranian height datum from the geoid’s potential value W
0=62636855.8 m2/s2. According to the geometry space computations, the height datum of Iran is 0.09 m below the geoid. 相似文献
8.
G. Balmino D. Letoquart F. Barlier M. Ducasse A. Bernard B. Sacleux C. Bouzat J. J. Runavot X. Le Pichon M. Souriau 《Journal of Geodesy》1984,58(2):151-179
Résumé Une des techniques de détermination fine et globale du champ de gravitation terrestre U est la gradiométrie spatiale, dans
laquelle on mesure à bord d'un satellite sur orbite basse certaines combinations linéaires des composantes du tenseur ∂2 U/∂xi ∂xj dans des axes {x
i
} liés au satellite. Un tel projet, appelé GRADIO, est actuellement à l'étude en France et pourrait aboutir à partir de 1990.
Après avoir rappelé les objectifs scientifiques d'une telle mission, nous en donnons les spécifications—étayées par une série
d'études analytiques; nous définissons ensuite le satellite porteur et ses caractères techniques, en insistant sur les points
délicats de la faisabilité (facteurs d'échelle des micro-accéléromètres constituant l'appareil, connaissance de l'attitude...)
et en présentant des idées de solution en cours d'approfondissement.
Summary Satellite gradiometry arises as one of the methods for improving our knowledge of the global Earth gravity field at high resolution: by means of micro-accelerometers on board a low orbiting spacecraft, linear combination of the gravity tensor components ∂2 U/∂xi ∂xj are measured in a satellite-fixed reference frame {x i }. Based on this technique, a project named GRADIO is presently under study in France and could fly in 1990 at the earliest. After the scientific objectives of that experiment have been reviewed, the measurement specifications are given as coming from various analytical studies. The platform and its characteristics are then defined: the critical realization problems (scale factors of the micro-accelerometers, spacecraft attitude control and restitution) are pointed out together with some ideas for their solution which are under analysis and require further study.相似文献
9.
Considering present attempts to develop a gradiometer with an accuracy between 10−3
E and 10−4
E, two applications for such a device have been studied: (a) mapping the gravitational field of the Earth, and (b) estimating
the geocentric distance of a satellite carrying the instrument. Given a certain power spectrum for the signal and 10−4
E (rms) of white measurement noise, the results of an error analysis indicate that a six-month mission in polar orbit at a height
of 200 km, with samples taken every three seconds, should provide data for estimating the spherical harmonic potential coefficients
up to degree and order 300 with less than 50% error, and improve the coefficients through degree 30 by up to four orders of
magnitude compared to existing models. A simulation study based on numerical orbit integrations suggests that a simple adjustment
of the initial conditions based on gradiometer data could produce orbits where the geocentric distance is accurate to 10 cm
or better, provided the orbits are 2000 km high and some improvement in the gravity field up to degree 30 is first achieved.
In this sense, the gravity-mapping capability of the gradiometer complements its use in orbit refinement. This idea can be
of use in determining orbits for satellite altimetry. Furthermore, by tracking the gradiometer-carrying spacecraft when it
passes nearly above a terrestrial station, the geocentric distance of this station can also be estimated to about one decimeter
accuracy. This principle could be used in combination with VLBI and other modern methods to set up a world-wide 3-D network
of high accuracy. 相似文献
10.
Summary Satellite gradiometry is studied as a means to improve the geoid in local areas from a limited data coverage. Least-squares
collocation is used for this purpose because it allows to combine heterogeneous data in a consistent way and to estimate the
integrated effect of the attenuated spectrum. In this way accuracy studies can be performed in a general and reliable manner.
It is shown that only three second-order gradients contribute significantly to the estimation of the geoidal undulations and
that it is sufficient to have gradiometer data in a 5°×5° area around the estimation point. The accuracy of the geoid determination
is strongly dependent on the degree and order of the reference field used. An accuracy of about ±1 m can be achieved with
a reference field of (12, 12). There is an optimal satellite altitude for each reference field and this altitude may be higher
than 300 km for a field of low degree and order. The influence of measuring errors is discussed and it is shown that only
gradiometer data with accuracies better than ±0.05 E will give a significant improvement of the geoid. Finally, some results
on the combination of satellite gradiometry and terrestrial gravity measurements are given.
The proposed method seems to be well suited for local geoid determinations down to the meter range. It is especially interesting
for unsurveyed and difficult areas because no terrestrial measurements are necessary. Furthermore, it has the practical advantage
that only a local data coverage is needed. 相似文献
11.
Gravity gradient modeling using gravity and DEM 总被引:2,自引:0,他引:2
A model of the gravity gradient tensor at aircraft altitude is developed from the combination of ground gravity anomaly data
and a digital elevation model. The gravity data are processed according to various operational solutions to the boundary-value
problem (numerical integration of Stokes’ integral, radial-basis splines, and least-squares collocation). The terrain elevation
data are used to reduce free-air anomalies to the geoid and to compute a corresponding indirect effect on the gradients at
altitude. We compare the various modeled gradients to airborne gradiometric data and find differences of the order of 10–20 E
(SD) for all gradient tensor elements. Our analysis of these differences leads to a conclusion that their source may be primarily
measurement error in these particular gradient data. We have thus demonstrated the procedures and the utility of combining
ground gravity and elevation data to validate airborne gradiometer systems. 相似文献
12.
A spatiospectral localization method is discussed for processing the global geopotential coefficients from satellite mission
data to investigate time-variable gravity. The time-variable mass variation signal usually appears associated with a particular
geographical area yielding inherently regional structure, while the dependence of the satellite gravity errors on a geographical
region is not so evident. The proposed localization amplifies the signal-to-noise ratio of the (non-stationary) time-variable
signals in the geopotential coefficient estimates by localizing the global coefficients to the area where the signal is expected
to be largest. The results based on localization of the global satellite gravity coefficients such as Gravity Recovery And
Climate Experiment (GRACE) and Gravity and Ocean Circulation Explorer (GOCE) indicate that the coseismic deformation caused
by great earthquakes such as the 2004 Sumatra–Andaman earthquake can be detected by the low-low tracking and the gradiometer
data within the bandwidths of spherical degrees 15–30 and 25–100, respectively. However, the detection of terrestrial water
storage variation by GOCE gradiometer is equivocal even after localization. 相似文献
13.
Regional geoid determination in Antarctica utilizing airborne gravity and topography data 总被引:2,自引:2,他引:0
Mirko Scheinert Jan Müller Reinhard Dietrich Detlef Damaske Volkmar Damm 《Journal of Geodesy》2008,82(7):403-414
Antarctica is the only continent that suffers major gaps in terrestrial gravity data coverage. To overcome this problem and
to close these gaps as well as to densify the global satellite gravity field solutions, the International Association of Geodesy
(IAG) Commission Project 2.4 “Antarctic Geoid” was set into action. This paper reviews the current situation concerning the
gravity field in Antarctica. It is shown that airborne geophysical surveys are the most promising tools to gain new gravity
data in Antarctica. In this context, a number of projects to be carried out during the International Polar Year 2007/2008
will contribute to this goal. To demonstrate the feasibility of the regional geoid improvement in Antarctica, we present a
case study using gravity and topography data of the southern Prince Charles Mountains, East Antarctica. During the processing,
the remove–compute– restore (RCR) technique and least-squares collocation (LSC) were applied. Adding signal parts of up to
6 m to the global gravity field model that was used as a basis, the calculated regional quasigeoid reveals the dominant features
of bedrock topography in that region, namely the graben structure of the Lambert glacier system. The accuracy of the improved
regional quasigeoid is estimated to be at the level of 15 cm. 相似文献
14.
Computation of spherical harmonic coefficients and their error estimates using least-squares collocation 总被引:4,自引:0,他引:4
C. C. Tscherning 《Journal of Geodesy》2001,75(1):12-18
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
15.
Johannes Bouman Sietse Rispens Thomas Gruber Radboud Koop Ernst Schrama Pieter Visser Carl Christian Tscherning Martin Veicherts 《Journal of Geodesy》2009,83(7):659-678
One of the products derived from the gravity field and steady-state ocean circulation explorer (GOCE) observations are the
gravity gradients. These gravity gradients are provided in the gradiometer reference frame (GRF) and are calibrated in-flight
using satellite shaking and star sensor data. To use these gravity gradients for application in Earth scienes and gravity
field analysis, additional preprocessing needs to be done, including corrections for temporal gravity field signals to isolate
the static gravity field part, screening for outliers, calibration by comparison with existing external gravity field information
and error assessment. The temporal gravity gradient corrections consist of tidal and nontidal corrections. These are all generally
below the gravity gradient error level, which is predicted to show a 1/f behaviour for low frequencies. In the outlier detection, the 1/f error is compensated for by subtracting a local median from the data, while the data error is assessed using the median absolute
deviation. The local median acts as a high-pass filter and it is robust as is the median absolute deviation. Three different
methods have been implemented for the calibration of the gravity gradients. All three methods use a high-pass filter to compensate
for the 1/f gravity gradient error. The baseline method uses state-of-the-art global gravity field models and the most accurate results
are obtained if star sensor misalignments are estimated along with the calibration parameters. A second calibration method
uses GOCE GPS data to estimate a low-degree gravity field model as well as gravity gradient scale factors. Both methods allow
to estimate gravity gradient scale factors down to the 10−3 level. The third calibration method uses high accurate terrestrial gravity data in selected regions to validate the gravity
gradient scale factors, focussing on the measurement band. Gravity gradient scale factors may be estimated down to the 10−2 level with this method. 相似文献
16.
I. N. Tziavos 《Journal of Geodesy》1987,61(2):177-197
Mean gravity anomalies, deflections of the vertical, and a geopotential model complete to degree and order180 are combined in order to determine geoidal heights in the area bounded by [34°≦ϕ≤42°, 18°≦λ≦28°]. Moreover, employing point
gravity anomalies simultaneously with the above data, an attempt is made to predict deflections of the vertical in the same
area. The method used in the computations is least squares collocation. Using empirical covariance functions for the data,
the suitable errors for the different sources of observations, and the optimum cap radius around each point of evaluation,
an accuracy better than±0.60m for geoidal heights and±1″.5 for deflections of the vertical is obtained taking into account existing systematic effects. This accuracy refers to the
comparison between observed and predicted values. 相似文献
17.
The determination of high frequency variations in UT-1 and a component of pole position from a single pass of Doppler observations
of a Navy Navigation Satellite is affected by instrument errors and uncertainties in the gravity field and atmospheric drag
forces used in computing the satellite orbit. For elevation angles above20°, instrument errors contribute about2 msec to the determination of UT-1 and “.03 to the determination of pole position. Gravity and drag errors contribute about 0“.03
of correlated error. But gravity errors may be inferred by statistical analysis of residuuls after drag errors are reduced
by drag-compensating devices aboard future Navy Navigation Satellites. Since20 Doppler stations nominally acquire about100 passes each day, daily observations of UT-1 and pole position could achieve precisions of0.2 msec and “.005, respectively, assuming half the passes contribute to the determination of each component of pole position. The
current accuracy of Doppler results for two day solutions is about50 cm for pole position and1 msec for high frequency variations in UT-1. 相似文献
18.
LUO Jia LI Jiancheng CHAO Dingbo 《地球空间信息科学学报》2003,6(1):19-23
1 IntroductionTodeveloptheoceanwidelyanddeeply ,weneedabundantoceaninformation .Asanessentialpartofsuchinformation ,seafloortopographyplaysaveryimportantroleinavarietyofmarineactivities .However,thehighcostforoceanbathymetricsurveyinglimitstheapplicationo… 相似文献
19.
This research deals with some theoretical and numerical problems of the downward continuation of mean Helmert gravity disturbances.
We prove that the downward continuation of the disturbing potential is much smoother, as well as two orders of magnitude smaller
than that of the gravity anomaly, and we give the expression in spectral form for calculating the disturbing potential term.
Numerical results show that for calculating truncation errors the first 180∘ of a global potential model suffice. We also discuss the theoretical convergence problem of the iterative scheme. We prove
that the 5′×5′ mean iterative scheme is convergent and the convergence speed depends on the topographic height; for Canada, to achieve an
accuracy of 0.01 mGal, at most 80 iterations are needed. The comparison of the “mean” and “point” schemes shows that the mean
scheme should give a more reasonable and reliable solution, while the point scheme brings a large error to the solution.
Received: 19 August 1996 / Accepted: 4 February 1998 相似文献
20.
P. Schwintzer C. Reigber A. Bode Z. Kang S. Y. Zhu F.-H. Massmann J. C. Raimondo R. Biancale G. Balmino J. M. Lemoine B. Moynot J. C. Marty F. Barlier Y. Boudon 《Journal of Geodesy》1997,71(4):189-208
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