共查询到20条相似文献,搜索用时 31 毫秒
1.
Least-squares prediction using an empirically deduced local covariance function was performed to investigate the temporal
change in the rates of vertical crustal movements in the Tohoku district, Japan. Levelling data covering an area of approximately
450 × 275 km2 observed between 1966 and 1995 were used and the results shown in the form of contour maps. Firstly we derived a covariance
function of the rates of vertical crustal movement with a Gaussian form function. We used this function to estimate the spatial
distribution of the rates of vertical crustal movements. By the present method, a steady tilt of the Tohoku district to the
east, toward the Japan Trench and an areal uplift in the southwestern part were well reproduced. Moreover, a significant temporal
change in vertical movement rates is clearly seen.
Received: 15 July 1996 相似文献
2.
Procedures to calculate mean sea surface heights and gravity anomalies from altimeter-derived sea surface heights and along-track
sea surface slopes using the least-squares collocation procedure are derived. The slope data is used when repeat track averaging
is not possible to reduce ocean variability effects. Tests were carried out using Topex, Geosat, ERS-1 [35-day and 168-day
(2 cycle)] data. Calculations of gravity anomalies in the Gulf Stream region were made using the sea surface height and slope
data. Tests were also made correcting the sea surface heights for dynamic ocean topography calculated from a degree 360 expansion
of data from the POCM-4B global ocean circulation model. Comparisons of the anomaly predictions were carried out with ship
data using anomalies calculated for this paper as well as others.
Received: 19 August 1996 / Accepted: 14 April 1997 相似文献
3.
The success rate and precision of GPS ambiguities 总被引:8,自引:1,他引:7
P. J. G. Teunissen 《Journal of Geodesy》2000,74(3-4):321-326
An application of a theorem on the optimality of integer least-squares (LS) is described. This theorem states that the integer
LS estimator maximizes the ambiguity success rate within the class of admissible integer estimators. This theorem is used
to show how the probability of correct integer estimation depends on changes in the second moment of the ambiguity `float'
solution. The distribution of the `float' solution is considered to be a member of the broad family of elliptically contoured
distributions. Eigenvalue-based bounds for the ambiguity success rate are obtained.
Received: 11 January 1999 / Accepted: 2 November 1999 相似文献
4.
In the framework of a boundary value problem (BVP), when areas on the boundary are void of data the solution of the problem
becomes undetermined and clearly more difficult. Physically, this could be the situation in which a gradiometer on a satellite
on a perfectly circular orbit covers a sphere with measured second radial derivatives: if the satellite orbit is not polar,
there are caps at satellite altitude which are not covered by data. A solution is presented based on an iterative algorithm,
under the hypothesis of using a finite-dimensional model as is usually done in the time-wise approach. The convergence of
the iterative solution is proved and a numerical example is shown to confirm the theoretical result.
Received: 14 August 2000 / Accepted: 12 April 2001 相似文献
5.
The mixed spherical map projections of equiareal, cylindric type are based upon the Lambert projection and the sinusoidal
Sanson–Flamsteed projection. These cylindric and pseudo-cylindric map projections of the sphere are generalized to the ellipsoid
of revolution (biaxial ellipsoid). They are used in consequence by two lemmas to generate a horizontal and a vertical weighted
mean of equiareal cylindric map projections of the ellipsoid of revolution. Its left–right deformation analysis via further
results leads to the left–right principal stretches/eigenvalues and left–right eigenvectors/eigenspace, as well as the maximal
left–right angular distortion for these new mixed cylindric map projections of ellipsoidal type. Detailed illustrations document
the cartographic synergy of mixed cylindric map projections.
Received: 23 April 1996 / Accepted: 19 April 1997 相似文献
6.
Apropos laser tracking to GPS satellites 总被引:3,自引:0,他引:3
. Laser tracking to GPS satellites (PRN5 and 6) provides an opportunity to compare GPS and laser systems directly and to combine
data of both in a single solution. A few examples of this are given in this study. The most important results of the analysis
are that (1) daily SLR station coordinate solutions could be generated with a few cm accuracy; (2) coordinates of nine stations
were determined in a 2.3-year-long arc solution; (3) the contribution of laser data on the `SLR-GPS' combined orbit, resulting
from the simultaneous processing of SLR and GPS data, is significant and (4) laser-only orbits have an accuracy of 10–20 cm,
1-day predictions of SLR orbits differ from IGS orbits by about 20–40 cm, 2-day predictions by 50–60 cm.
Received: 1 October 1996 / Accepted: 14 February 1997 相似文献
7.
E. W. Grafarend 《Journal of Geodesy》2001,75(7-8):363-390
In a comparison of the solution of the spherical horizontal and vertical boundary value problems of physical geodesy it is
aimed to construct downward continuation operators for vertical deflections (surface gradient of the incremental gravitational
potential) and for gravity disturbances (vertical derivative of the incremental gravitational potential) from points on the
Earth's topographic surface or of the three-dimensional (3-D) Euclidean space nearby down to the international reference sphere
(IRS). First the horizontal and vertical components of the gravity vector, namely spherical vertical deflections and spherical
gravity disturbances, are set up. Second, the horizontal and vertical boundary value problem in spherical gravity and geometry
space is considered. The incremental gravity vector is represented in terms of vector spherical harmonics. The solution of
horizontal spherical boundary problem in terms of the horizontal vector-valued Green function converts vertical deflections
given on the IRS to the incremental gravitational potential external in the 3-D Euclidean space. The horizontal Green functions
specialized to evaluation and source points on the IRS coincide with the Stokes kernel for vertical deflections. Third, the
vertical spherical boundary value problem is solved in terms of the vertical scalar-valued Green function. Fourth, the operators
for upward continuation of vertical deflections given on the IRS to vertical deflections in its external 3-D Euclidean space
are constructed. Fifth, the operators for upward continuation of incremental gravity given on the IRS to incremental gravity
to the external 3-D Euclidean space are generated. Finally, Meissl-type diagrams for upward continuation and regularized downward
continuation of horizontal and vertical gravity data, namely vertical deflection and incremental gravity, are produced.
Received: 10 May 2000 / Accepted: 26 February 2001 相似文献
8.
New solutions for the geodetic coordinate transformation 总被引:5,自引:2,他引:5
G. C. Jones 《Journal of Geodesy》2002,76(8):437-446
The Cartesian-to-geodetic-coordinate transformation is approached from a new perspective. Existence and uniqueness of geodetic
representation are presented, along with a clear geometric picture of the problem and the role of the ellipse evolute. A new
solution is found with a Newton-method iteration in the reduced latitude; this solution is proved to work for all points in
space. Care is given to error propagation when calculating the geodetic latitude and height.
Received: 9 August 2001 / Accepted: 27 March 2002
Acknowledgments. The author would like to thank the Clifford W.␣Tompson scholarship fund, Dr. Brian DeFacio, the University of Missouri College
of Arts &Sciences, and the United States Air Force. He also thanks a reviewer for suggesting and providing a prototype MATLAB
code. A MATLAB program for the iterative sequence is presented at the end of the paper (Appendix A). 相似文献
9.
The standard analytical approach which is applied for constructing geopotential models OSU86 and earlier ones, is based on
reducing the boundary value equation to a sphere enveloping the Earth and then solving it directly with respect to the potential
coefficients
n,m
. In an alternative procedure, developed by Jekeli and used for constructing the models OSU91 and EGM96, at first an ellipsoidal
harmonic series is developed for the geopotential and then its coefficients
n,m
e
are transformed to the unknown
n,m
. The second solution is more exact, but much more complicated. The standard procedure is modified and a new simple integral
formula is derived for evaluating the potential coefficients. The efficiency of the standard and new procedures is studied
numerically. In these solutions the same input data are used as for constructing high-degree parts of the EGM96 models. From
two sets of
n,m
(n≤360,|m|≤n), derived by the standard and new approaches, different spectral characteristics of the gravity anomaly and the geoid undulation
are estimated and then compared with similar characteristics evaluated by Jekeli's approach (`etalon' solution). The new solution
appears to be very close to Jekeli's, as opposed to the standard solution. The discrepancies between all the characteristics
of the new and `etalon' solutions are smaller than the corresponding discrepancies between two versions of the final geopotential
model EGM96, one of them (HDM190) constructed by the block-diagonal least squares (LS) adjustment and the other one (V068)
by using Jekeli's approach. On the basis of the derived analytical solution a new simple mathematical model is developed to
apply the LS technique for evaluating geopotential coefficients.
Received: 12 December 2000 / Accepted: 21 June 2001 相似文献
10.
L. E. Sjöberg 《Journal of Geodesy》2002,76(2):115-120
The problems of intersection on the sphere and ellipsoid are studied. On the sphere, the problem of intersection along great
circles is explicitly solved. On the ellipsoid, each of the problems of intersection along arcs of constant azimuth, normal
sections and geodesic lines is solved without any limitation on arc length. In the last case the solution is based on the
Newton–Raphson method of iteration including numerical integration.
Received: 11 April 2001 / Accepted: 3 September 2001 相似文献
11.
A general scheme is given for the solution in a least-squares sense of the geodetic boundary value problem in a spherical,
constant-radius approximation, both uniquely and overdetermined, for a large class of observations. The only conditions are
that the relation of the observations to the disturbing potential is such that a diagonalization in the spectrum can be found
and that the error-covariance function of the observations is isotropic and homogeneous. Most types of observations used in
physical geodesy can be adjusted to fit into this approach. Examples are gravity anomalies, deflections of the vertical and
the second derivatives of the gravity potential.
Received: 3 November 1999 / Accepted: 25 September 2000 相似文献
12.
A solution to the downward continuation effect on the geoid determined by Stokes' formula 总被引:2,自引:1,他引:2
L.E. Sjöberg 《Journal of Geodesy》2003,77(1-2):94-100
The analytical continuation of the surface gravity anomaly to sea level is a necessary correction in the application of Stokes'
formula for geoid estimation. This process is frequently performed by the inversion of Poisson's integral formula for a sphere.
Unfortunately, this integral equation corresponds to an improperly posed problem, and the solution is both numerically unstable,
unless it is well smoothed, and tedious to compute. A solution that avoids the intermediate step of downward continuation
of the gravity anomaly is presented. Instead the effect on the geoid as provided by Stokes' formula is studied directly. The
practical solution is partly presented in terms of a truncated Taylor series and partly as a truncated series of spherical
harmonics. Some simple numerical estimates show that the solution mostly meets the requests of a 1-cm geoid model, but the
truncation error of the far zone must be studied more precisely for high altitudes of the computation point. In addition,
it should be emphasized that the derived solution is more computer efficient than the detour by Poisson's integral.
Received: 6 February 2002 / Accepted: 18 November 2002
Acknowledgements. Jonas ?gren carried out the numerical calculations and gave some critical and constructive remarks on a draft version of
the paper. This support is cordially acknowledged. Also, the thorough work performed by one unknown reviewer is very much
appreciated. 相似文献
13.
When standard boundary element methods (BEM) are used in order to solve the linearized vector Molodensky problem we are confronted with
two problems: (1) the absence of O(|x|−2) terms in the decay condition is not taken into account, since the single-layer ansatz, which is commonly used as representation
of the disturbing potential, is of the order O(|x|−1) as x→∞. This implies that the standard theory of Galerkin BEM is not applicable since the injectivity of the integral operator
fails; (2) the N×N stiffness matrix is dense, with N typically of the order 105. Without fast algorithms, which provide suitable approximations to the stiffness matrix by a sparse one with O(N(logN)
s
), s≥0, non-zero elements, high-resolution global gravity field recovery is not feasible. Solutions to both problems are proposed.
(1) A proper variational formulation taking the decay condition into account is based on some closed subspace of co-dimension
3 of the space of square integrable functions on the boundary surface. Instead of imposing the constraints directly on the
boundary element trial space, they are incorporated into a variational formulation by penalization with a Lagrange multiplier.
The conforming discretization yields an augmented linear system of equations of dimension N+3×N+3. The penalty term guarantees the well-posedness of the problem, and gives precise information about the incompatibility
of the data. (2) Since the upper left submatrix of dimension N×N of the augmented system is the stiffness matrix of the standard BEM, the approach allows all techniques to be used to generate
sparse approximations to the stiffness matrix, such as wavelets, fast multipole methods, panel clustering etc., without any
modification. A combination of panel clustering and fast multipole method is used in order to solve the augmented linear system
of equations in O(N) operations. The method is based on an approximation of the kernel function of the integral operator by a degenerate kernel
in the far field, which is provided by a multipole expansion of the kernel function. Numerical experiments show that the fast
algorithm is superior to the standard BEM algorithm in terms of CPU time by about three orders of magnitude for N=65 538 unknowns. Similar holds for the storage requirements. About 30 iterations are necessary in order to solve the linear
system of equations using the generalized minimum residual method (GMRES). The number of iterations is almost independent
of the number of unknowns, which indicates good conditioning of the system matrix.
Received: 16 October 1999 / Accepted: 28 February 2001 相似文献
14.
The global positioning system (GPS) model is distinctive in the way that the unknown parameters are not only real-valued,
the baseline coordinates, but also integers, the phase ambiguities. The GPS model therefore leads to a mixed integer–real-valued
estimation problem. Common solutions are the float solution, which ignores the ambiguities being integers, or the fixed solution,
where the ambiguities are estimated as integers and then are fixed. Confidence regions, so-called HPD (highest posterior density)
regions, for the GPS baselines are derived by Bayesian statistics. They take care of the integer character of the phase ambiguities
but still consider them as unknown parameters. Estimating these confidence regions leads to a numerical integration problem
which is solved by Monte Carlo methods. This is computationally expensive so that approximations of the confidence regions
are also developed. In an example it is shown that for a high confidence level the confidence region consists of more than
one region.
Received: 1 February 2001 / Accepted: 18 July 2001 相似文献
15.
Dual algebraic formulation of differential GPS 总被引:1,自引:0,他引:1
A new approach to differential GPS is presented. The corresponding theoretical framework calls on elementary concepts of
algebraic graph theory. The notion of double difference, which is related to that of closure in the sense of Kirchhoff, is
revisited in this context. The Moore–Penrose pseudo-inverse of the closure operator plays a key role in the corresponding
dual formulation. This approach, which is very attractive from a conceptual point of view, sheds a new light on the Teunissen
formulation.
Received: 21 May 2002 / Accepted: 18 November 2002
Correspondence to: A. Lannes 相似文献
16.
The problem of phase ambiguity resolution in global positioning system (GPS) theory is considered. The Bayesian approach
is applied to this problem and, using Monte Carlo simulation to search over the integer candidates, a practical expression
for the Bayesian estimator is obtained. The analysis of the integer grid points inside the search ellipsoid and their evolution
with time, while measurements are accumulated, leads to the development of a Bayesian theory based on a mathematical mixture
model for the ambiguity.
Received: 29 March 2001 / Accepted: 3 September 2001 相似文献
17.
Richard Thomas 《Journal of Geographical Systems》2001,3(3):283-301
This paper applies a compartmental epidemic model to estimating the mixing relations that support the transfer of HIV infection
between risk populations within the countries of Western Europe. To this end, a space-time epidemic model with compartments
representing countries with populations specified to be at high (gay men and intravenous drug injectors ever with AIDS) and
low (the remainder who are sexually active) risk is described. This model also allows for contacts between susceptible and
infectious individuals by both local and international travel. This system is calibrated to recorded AIDS incidence and the
best-fit solution provides estimates of variations in the rates of mixing between the compartments together with a reconstruction
of the transmission pathway. This solution indicates that, for all the countries, AIDS incidence among those at low risk is
expected to remain extremely small relative to their total number. A sensitivity analysis of the low risk partner acquisition
rate, however, suggests this endemic state might be fragile within Europe during this century. The discussion examines the
relevance of these mixing relationships for the maintenance of disease control.
Received: 4 May 2000 / Accepted: 9 July 2000 相似文献
18.
Possible improvement of Earth orientation forecast using autocovariance prediction procedures 总被引:3,自引:2,他引:1
Autocovariance prediction has been applied to attempt to improve polar motion and UT1-UTC predictions. The predicted polar
motion is the sum of the least-squares extrapolation model based on the Chandler circle, annual and semiannual ellipses, and
a bias fit to the past 3 years of observations and the autocovariance prediction of these extrapolation residuals computed
after subtraction of this model from pole coordinate data. This prediction method has been applied also to the UT1-UTC data,
from which all known predictable effects were removed, but the prediction error has not been reduced with respect to the error
of the current prediction model. However, the results show the possibility of decreasing polar motion prediction errors by
about 50 for different prediction lengths from 50 to 200 days with respect to the errors of the current prediction model.
Because of irregular variations in polar motion and UT1-UTC, the accuracy of the autocovariance prediction does depend on
the epoch of the prediction. To explain irregular variations in x, y pole coordinate data, time-variable spectra of the equatorial components of the effective atmospheric angular momentum, determined
by the National Center for Environmental Prediction, were computed. These time-variable spectra maxima for oscillations with
periods of 100–140 days, which occurred in 1985, 1988, and 1990 could be responsible for excitation of the irregular short-period
variations in pole coordinate data. Additionally, time-variable coherence between geodetic and atmospheric excitation function
was computed, and the coherence maxima coincide also with the greatest irregular variations in polar motion extrapolation
residuals.
Received: 22 October 1996 / Accepted: 16 September 1997 相似文献
19.
The recovery of a full set of gravity field parameters from satellite gravity gradiometry (SGG) is a huge numerical and computational
task. In practice, parallel computing has to be applied to estimate the more than 90 000 harmonic coefficients parameterizing
the Earth's gravity field up to a maximum spherical harmonic degree of 300. Three independent solution strategies (preconditioned
conjugate gradient method, semi-analytic approach, and distributed non-approximative adjustment), which are based on different
concepts, are assessed and compared both theoretically and on the basis of a realistic-as-possible numerical simulation regarding
the accuracy of the results, as well as the computational effort. Special concern is given to the correct treatment of the
coloured noise characteristics of the gradiometer. The numerical simulations show that the three methods deliver nearly identical
results—even in the case of large data gaps in the observation time series. The newly proposed distributed non-approximative
adjustment approach, which is the only one of the three methods that solves the inverse problem in a strict sense, also turns
out to be a feasible method for practical applications.
Received: 17 December 2001 / Accepted: 17 July 2002
Acknowledgments. We would like to thank Prof. W.-D. Schuh, Institute of Theoretical Geodesy, University of Bonn, for providing us with the
serial version of the PCGMA algorithm, which forms the basis for the parallel PCGMA package developed at our institute. This
study was partially performed in the course of the GOCE project `From E?tv?s to mGal+', funded by the European Space Agency
(ESA) under contract No. 14287/00/NL/DC.
Correspondence to: R. Pail 相似文献
20.
Quality-control issues relating to instantaneous ambiguity resolution for real-time GPS kinematic positioning 总被引:23,自引:3,他引:23
S. Han 《Journal of Geodesy》1997,71(6):351-361
An integrated method for the instantaneous ambiguity resolution using dual-frequency precise pseudo-range and carrier-phase
observations is suggested in this paper. The algorithm combines the search procedures in the coordinate domain, the observation
domain and the estimated ambiguity domain (and therefore benefits from the integration of their most positive elements). A
three-step procedure is then proposed to enhance the reliability of the ambiguity resolution by: (1) improving the stochastic
model for the double-differenced functional model in real time; (2) refining the criteria which distinguish the integer ambiguity
set that generates the minimum quadratic form of residuals from that corresponding to the second minimum one; and (3) developing
a fault detection and adaptation procedure. Three test scenarios were considered, one static baseline (11.3 km) and two kinematic
experiments (baseline lengths from 5.2 to 13.7 km). These showed that the mean computation time for one epoch is less than
0.1 s, and that the success rate reaches 98.4% (compared to just 68.4% using standard ratio tests).
Received: 5 June 1996; Accepted: 16 January 1997 相似文献