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1.
R. Lehmann 《Journal of Geodesy》1999,73(9):491-500
A review of recent progress and current activities towards an improved formulation and solution of geodetic boundary value
problems is given. Improvements stimulated and required by the dramatic changes of the real world of geodetic measurements
are focused upon. Altimetry–gravimetry problems taking into account various scenarios of non-homogeneous data coverage are
discussed in detail. Other problems are related to free geodetic datum parameters, most of all the vertical datum, overdetermination
or additional constraints imposed by satellite geodetic observations or models. Some brief remarks are made on pseudo-boundary
value problems for geoid determination and on purely gravitational boundary-value problems.
Received: 17 March 1999 / Accepted: 19 April 1999 相似文献
2.
The source position time-series for many of the frequently observed radio sources in the NASA geodetic very long baseline
interferometry (VLBI) program show systematic linear and non-linear variations of as much as 0.5 mas (milli-arc-seconds) to
1.0 mas, due mainly to source structure changes. In standard terrestrial reference frame (TRF) geodetic solutions, it is a
common practice to only estimate a global source position for each source over the entire history of VLBI observing sessions.
If apparent source position variations are not modeled, they produce corresponding systematic variations in estimated Earth
orientation parameters (EOPs) at the level of 0.02–0.04 mas in nutation and 0.01–0.02 mas in polar motion. We examine the
stability of position time-series of the 107 radio sources in the current NASA geodetic source catalog since these sources
have relatively dense observing histories from which it is possible to detect systematic variations. We consider different
strategies for handling source instabilities where we (1) estimate the positions of unstable sources for each session they
are observed, or (2) estimate spline parameters or rate parameters for sources chosen to fit the specific variation seen in
the position-time series. We found that some strategies improve VLBI EOP accuracy by reducing the biases and weighted root
mean square differences between measurements from independent VLBI networks operating simultaneously. We discuss the problem
of identifying frequently observed unstable sources and how to identify new sources to replace these unstable sources in the
NASA VLBI geodetic source catalog. 相似文献
3.
Combining the geodetic models of vertical crustal deformation 总被引：6，自引：0，他引：6
Different kinds of analytical models of vertical curstal deformation have both advantages and disadvantages, and are appropriate
to different deformation patterns. It is difficult to identify which deformation model is most suitable for a particular deformation
area. In order to obtain a more precise and reliable analytical result, the combined model based on forecast theory has been
approached. As a result, the fitting ability of single models is significantly improved. The combined model still possesses
the same important features as the single models, which enable transferal of the derived crustal deformation information,
within or even outside the time span of the data coverage, from geodetic sites to any user-specified locations where geodetic
data may not exist. Examples are presented of both numerical simulation and a real-life situation, and the results are analysed
in detail to demonstrate the efficiency of the proposed methodology.
Received: 26 January 1998 / Accepted 14 August 1998 相似文献
4.
Data weighting and solution assessment in combination 总被引：4，自引：0，他引：4
A data weighting method for combining different geodetic data based on statistical tests of the residuals is discussed. By
requiring the residuals of combination solution to be white Gaussian as a sample of random noise, the relative weight factors
can be determined internally, independent of external comparisons. To achieve this goal and to assess the solution, the Pearson
χ2 and higher-order moments of residuals are used to measure quantitatively the discrepancies between the residuals and white
Gaussian noise.
Received: 30 June 1998 / Accepted: 19 April 1999 相似文献
5.
Robust estimation of geodetic datum transformation 总被引：18，自引：1，他引：17
Y. Yang 《Journal of Geodesy》1999,73(5):268-274
The robust estimation of geodetic datum transformation is discussed. The basic principle of robust estimation is introduced.
The error influence functions of the robust estimators, together with those of least-squares estimators, are given. Particular
attention is given to the robust initial estimates of the transformation parameters, which should have a high breakdown point
in order to provide reliable residuals for the following estimation. The median method is applied to solve for robust initial
estimates of transformation parameters since it has the highest breakdown point. A smooth weight function is then used to
improve the efficiency of the parameter estimates in successive iterative computations. A numerical example is given on a
datum transformation between a global positioning system network and the corresponding geodetic network in China. The results
show that when the coordinates are contaminated by outliers, the proposed method can still give reasonable results.
Received: 25 September 1997 / Accepted: 1 March 1999 相似文献
6.
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
7.
Atmospheric Angular Momentum Time-Series: Characterization of their Internal Noise and Creation of a Combined Series 总被引：1，自引：0，他引：1
The atmosphere induces variations in Earth rotation. These effects are classically computed using the “angular momentum approach”. In this method, the variations in Earth rotation are estimated from the variations in the atmospheric angular momentum (AAM). Several AAM time-series are available from different meteorological centers. However, the estimation of atmospheric effects on Earth rotation differs when using one atmospheric model or the other. The purpose of this work is to build an objective criterion that justifies the use of one series in particular. Because the atmosphere is not the only cause of Earth rotation variations, this criterion cannot rely only on a comparison of AAM series with geodetic data. Instead, we determine the quality of each series by making an estimation of their noise level, using a generalized formulation of the “three-cornered hat method”. We show the existence of a link between the noise of the AAM series and their correlation with geodetic data: a noisy series is usually less correlated with Earth orientation data. As the quality of the series varies in time, we construct a combined AAM series, using time-dependent weights chosen so that the noise level of the combined series is minimal. To determine the influence of a minimal noise level on the correlation with geodetic data, we compute the correlation between the combined series and Earth orientation data. We note that the combined series is always amongst the best correlated series, which confirms the link established before. The quality criterion, while totally independent of Earth orientation observations, appears to be physically convincing when atmospheric and geodetic data are compared 相似文献
8.
In the linear estimation problem associated with an experiment that is exactly repeated a number of times, the estimation
parameters may naturally be partitioned into two groups, those that are common to all repetitions, and those that are particular
to each repeat experiment. We derive least-squares solutions that minimise in norm either group of parameters, as also the
trace of the corresponding covariance matrix. These solutions are applied to the station adjustment of triangulation surveying,
and to the estimation problem of satellite radar altimetry: to estimate simultaneously mean sea surface heights and residual
radial orbit errors, while minimising the norm of either group of parameters. This altimetry problem is considered in the
cases of collinear, local crossover and global crossover data.
Received: 6 January 1997 / Accepted: 21 December 1998 相似文献
9.
Research on the deformations in Qinghai-Tibet plateau and its margins by inverting seismic moment tensors and GPS velocities 总被引：1，自引：0，他引：1
We have determined approximate average rates of deformation in the Qinghai-Tibet plateau and its margins from the GPS data for last 10 years and the moment tensors from earthquakes between 1900 and 1999.We also determined the strain rate (seismic strain rate) associated with the seismic deformation using 254 Mw≥5.0 earthquakes,and estimated the shortening and extension rates for every block in the area as well.We also estimated the strain rate (geodetic strain rate)by 80 GPS sites' velocity vectors and analyzed characteristic of kinematics by two kinds of strain rates and discussed earthquake potential in the area.As a result,the deformation rates from seismic moment tensors and from GPS velocities are basically agreed with each other.It is feasible to analyze seismic risk by comparing geodetic strain rate with seismic strain rate based on the opinion that strain energy will be released through earthquake.It is concluded that there is no strong earthquake potential (＞M7) in the Qinghai-Tibet plateau and its margins,but there is earthquake potential (＞M5) in middle Tibet in a few years. 相似文献
10.
A. A. Seemkooei 《Journal of Geodesy》2001,75(4):227-233
The proper and optimal design and subsequent assessment of geodetic networks is an integral part of most surveying engineering
projects. Optimization and design are carried out before the measurements are actually made. A geodetic network is designed
and optimized in terms of high reliability and the results are compared with those obtained by the robustness analysis technique.
The purpose of an optimal design is to solve for both the network configuration (first-order design) and observations accuracy
(second-order design) in order to meet the desired criteria. For this purpose, an analytical method is presented for performing
the first-order design, second-order design, and/or the combined design. In order to evaluate the geometrical strength of
a geodetic network, the results of robustness analysis are displayed in terms of robustness in rotation, robustness in shear,
and robustness in scale. Results showed that the robustness parameters were affected by redundancy numbers. The largest robustness
parameters were due to the observations with minimum redundancy numbers.
Received: 14 August 2000 / Accepted: 2 January 2001 相似文献
11.
The differential equations which generate a general conformal mapping of a two-dimensional Riemann manifold found by Korn
and Lichtenstein are reviewed. The Korn–Lichtenstein equations subject to the integrability conditions of type vectorial Laplace–Beltrami
equations are solved for the geometry of an ellipsoid of revolution (International Reference Ellipsoid), specifically in the
function space of bivariate polynomials in terms of surface normal ellipsoidal longitude and ellipsoidal latitude. The related
coefficient constraints are collected in two corollaries. We present the constraints to the general solution of the Korn–Lichtenstein
equations which directly generates Gau?–Krüger conformal coordinates as well as the Universal Transverse Mercator Projection
(UTM) avoiding any intermediate isometric coordinate representation. Namely, the equidistant mapping of a meridian of reference
generates the constraints in question. Finally, the detailed computation of the solution is given in terms of bivariate polynomials
up to degree five with coefficients listed in closed form.
Received: 3 June 1997 / Accepted: 17 November 1997 相似文献
12.
It is shown that also in a rank deficient Gauss-Markov model higher weights of the observations automatically improve the
precision of the estimated parameters as long as they are computed in thesame datum. However, the amount of improvement in terms of the trace of the dispersion matrix isminimum for the so-called “free datum” which corresponds to the pseudo-inverse normal equations matrix. This behaviour together with its consequences is discussed
by an example with special emphasis on geodetic networks for deformation analysis. 相似文献
13.
The crossover adjustment plays a central role in the processing of satellite altimeter measurements. The usual procedure
is to form sea surface height differences at crossover points, solve for the radial orbit error (with due attention to the
singular nature of the estimation problem) and then to construct altimetric sea-level maps using the mean sea surface heights
at the crossover points. Our approach is very different, to make direct use of measurements at crossover points without differencing
and to estimate simultaneously orbit parameters, mean sea surface height and sea surface height variability in a single, unified
adjustment. The technique is suited for repeat data over an area small enough that adjoining passes may be considered to be
parallel and to permit the solution of a set of linear equations of dimension equal to the number of crossover points. The
size of the numerical problem is almost independent of the number of repeat cycles of the altimeter mission. Explicit recognition
is given to the rank defect of the least-squares estimation problem; we show that, for an orbit model with r parameters, the rank defect of the local crossover problem is exactly r
2. The defect may be overcome by choosing an appropriate set of constraints – either giving a best fit of mean sea surface
heights to a reference surface, or minimising orbit parameters, or a minimum norm solution in which both mean sea surface
heights and orbit parameters are minimised. There is no need to choose a reference pass, all passes are treated equally and
data gaps are easily accommodated. Numerical results are presented for the south-western Indian Ocean, based on the first
2 years of altimeter data from the Geosat Exact Repeat Mission.
Received: 31 May 1996 / Accepted: 19 April 1997 相似文献
14.
Geodetic measurements from 1963 through 1994 are used to estimate horizontal strain rates across the Red River fault near
Thac Ba, Vietnam. Whether or not this fault system is currently active is a subject of some debate. By combining: (1) triangulation
from 1963, (2) triangulation in 1983, and (3) Global Positioning System (GPS) observations in 1994, horizontal shear strain
rates are estimated without imposing any prior information on fixed stations. The estimated rates of shear strain in ten triangular
subnetworks surrounding the fault trace are not significantly different from zero at 95% confidence. The maximum rate of dextral
shear is less than 0.3 μrad/year in all but one of the triangles. The estimates help bound the slip rate in a simple elastic
dislocation model for a locked, vertical strike-slip fault. By assuming a locking depth of 5–20 km, the most likely values
for the deep slip rate are between 1 and 5 mm/year of right-lateral motion. These values delimit the 23% confidence interval.
At 95% confidence, the slip rate estimate falls between 7 mm/year of left-lateral motion and 15 mm/year of right-lateral motion.
Received: 18 November 1997 / Accepted: 28 January 1999 相似文献
15.
16.
G. Even-Tzur 《Journal of Geodesy》2002,76(8):455-461
The performance of geodetic monitoring networks is heavily influenced by the configuration of the measured GPS vectors. As
an effective design of the GPS measurements will decrease GPS campaign costs and increase the accuracy and reliability of
the entire network, the identification of the preferred GPS vectors for measurement has been highlighted as a core problem
in the process of deformation monitoring. An algorithm based on a sensitivity analysis of the network, as dependent upon a
postulated velocity field, is suggested for the selection of the optimal GPS vectors. Relevant mathematical and statistical
concepts are presented as the basis for an improved method of vector configuration design. A sensitivity analysis of the geodetic
geodynamic network in the north of Israel is presented, where the method is examined against two deformation models, the Simple
Transform Fault and the Locked Fault. The proposed method is suggested as a means for the improvement of the design of monitoring
networks, a common practice worldwide.
Received: 30 July 2001 / Accepted: 3 June 2002
Acknowledgments. It is my pleasant duty to thank the Survey of Israel and Dr. E. Ostrovsky for providing the variance–covariance matrix of
the G1 network in northern Israel. I would like to thank the reviewers of this paper for their constructive and helpful remarks. 相似文献
17.
A Quaternion-based Geodetic Datum Transformation Algorithm 总被引：1，自引：1，他引：1
This paper briefly introduces quaternions to represent rotation parameters and then derives the formulae to compute quaternion, translation and scale parameters in the Bursa–Wolf geodetic datum transformation model from two sets of co-located 3D coordinates. The main advantage of this representation is that linearization and iteration are not needed for the computation of the datum transformation parameters. We further extend the formulae to compute quaternion-based datum transformation parameters under constraints such as the distance between two fixed stations, and develop the corresponding iteration algorithm. Finally, two numerical case studies are presented to demonstrate the applications of the derived formulae. 相似文献
18.
R. Lehmann 《Journal of Geodesy》1997,71(9):533-540
Geodetic surface integrals play an important role in the numerical solution of geodetic boundary-value problems. In many
cases they can be evaluated using fast methods in the frequency domain (FFT). However, this is not possible in general, because
the domain of integration may be non-trivial (as is the surface of the Earth), the kernel function may not be of convolution
type, or the data distribution may be heterogeneous. Therefore, fast evaluation strategies are also required in the space
domain. They are more difficult to design because only one property is left where a more or less fast evaluation strategy
can be built upon: the potential type of the kernel function. Consequently, the idea is not to replace well-established frequency
domain techniques, but to supplement them. Our approach to this problem goes in two directions: (1) we use advanced cubature
methods where the integration nodes automatically densify in the vicinity of the evaluation points; (2) we use powerful computer
hardware, namely MIMD computers with distributed memory. This enables us to evaluate geodetic surface integrals of any practical
complexity in reasonable time and accuracy. This is shown in a numerical example.
Received: 7 May 1996 / Accepted:17 March 1997 相似文献
19.
. The excess radio-path delay due to the atmospheric water vapor, the wet delay, can be derived from water vapor radiometer
(WVR) measurements. WVR data used for external calibration of space geodetic measurements are not always acquired in the directions
of the space geodetic signal sources, thus extrapolation and interpolation methods for the wet delay are needed. We evaluate
three different methods using approximately 10 days of WVR measurements. Two methods, the gradient method and turbulence method,
use the directional information in the data, while the third method used is linear regression in time regardless of the direction
of the observations. The turbulence method yielded at least 10% less RMS estimation error than the errors from the other two
methods.
Received: 20 May 1997 / Accepted: 15 December 1997 相似文献
20.
Summary . It is well known that for the comparison and combination of geodetic networks their heterogeneous datum definitions are
well to be considered. Various algorithms have been developed for this purpose. As an alternative concept to deal with hybrid
datum problems, the operator parallel sum of matrices is introduced in this paper. To begin with, a definition is given and some basic properties are explained. To demonstrate
the usefulness of the operator, two practical applications are given. The first deals with the estimation of parameters describing
the deformation of two networks which are to be compared to each other. The second one treats the estimation of parameters
representing the heterogeneous datum definitions of two networks which are to be merged into a hybrid network. It will be
shown that – regardless of the datum definitions of the preadjusted individual networks – the parallel sum of matrices can
be used to simplify the algorithms applied for the estimation of those parameters.
Received 15 December 1995; Accepted 24 September 1996 相似文献