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Very Long Baseline Interferometry (VLBI) is one of the new techniques which will probably dominate geodesy and geophysics
in the near future. Its main advantage lies in the fact that it brings the accuracy of direction measurements to a level previously
possible only for range measurements. This closes the gap between powerful range determination techniques such as laser ranging
and the much less accurate determination of directions through photographic tracking of artificial earth satellites.
The technique is geometric in the sense that the relevant observations are independent of the gravity field of the earth.
However, the “orbits” of the observed extragalactic radio sources with respect to an earth-fixed system are dominated and
perturbed by the rotation of the earth with respect to inertial frame. This allows the determination of polar motion, precession-nutation
and length-of-the-day variations, and the technique becomes also “dynamic” in this respect.
The capability of determining the geometry of a network of stations within a short time interval and with a centimeter level
accuracy also allows the study of the variation of network geometry with time caused by earth tides and other periodic or
secular station drifts.
The main objective of the present work is the exploration of the capabilities of VLBI for the recovery of earth rotation and
network geometry parameters. For this purpose, a number of characteristic experimental designs based on present and candidate
for the near future station locations is chosen. The results from the analysis of simulated observations for each particular
design are presented in the paper.
Presented at IAG International Symposium on “Optimization of Design and Computation of Control Networks”, Sopron, Hungary,
4–10 July 1977. 相似文献
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Sans résumé
The online version of the original article can be found at 相似文献
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A. Dermanis 《Journal of Geodesy》1998,72(2):71-100
Motivated by the existing theory of the geometric characteristics of linear generalized inverses of linear mappings, an attempt
is made to establish a corresponding mathematical theory for nonlinear generalized inverses of nonlinear mappings in finite-
dimensional spaces. The theory relies on the concept of fiberings consisting of disjoint manifolds (fibers) in which the domain
and range spaces of the mappings are partitioned. Fiberings replace the quotient spaces generated by some characteristic subspaces
in the linear case. In addition to the simple generalized inverse, the minimum-distance and the x
0-nearest generalized inverse are introduced and characterized, in analogy with the least-squares and the minimum-norm generalized
inverses of the linear case. The theory is specialized to the geodetic mapping from network coordinates to observables and
the nonlinear transformations (Baarda's S-transformations) between different solutions are defined with the help of transformation parameters obtained from the solution
of nonlinear equations. In particular, the transformations from any solution to an x
0-nearest solution (corresponding to Meissl's inner solution) are given for two- and three-dimensional networks for both the
similarity and the rigid transformation case. Finally the nonlinear theory is specialized to the linear case with the help
of the singular-value decomposition and algebraic expressions with specific geometric meaning are given for all possible types
of generalized inverses.
Received: 11 April 1996 / Accepted: 19 April 1997 相似文献
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GPS Solutions - New tools in the form of angular deficiency indices are developed for the physical interpretation of numerically detected rank deficiencies or weaknesses, in terms of defects or... 相似文献
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Summary. Within the framework of Newtonian kinematics VLBI observations are analysed with respect to estimability of geodetic and astrometric quantities. An Earth model of either rigid or deformable type is designed; instrumental clock offsets and clock drifts are included. Observational patterns are studied in all detail reviewed in seven tables. Appendix A is an introduction to the set-up of the observational model for a deformable Earth both in terms of coordinate-free and coordinate-related geometry. Appendix B is a study of the invariance characteristics of VLBI observations. Interrelations of three fundamental quantities, length unit, time unit and velocity of light are discussed. An overall result of an Earth model of deformable type is the need of simultaneous observations to more than one source; VLBI time delay observations cannot distinguish between secular changes of network size (expansion or shrinking) and a common secular drift (deceleration or acceleration) of clocks used. 相似文献
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Athanasios Dermanis 《Journal of Geodesy》1985,59(3):247-274
A study of the role of coordinate frame definitions in the determination of crustal deformation parameters is first carried
out for the theoretical case where displacement information between two discrete time epochs is continuously available for
all area points. The obtained results are next applied to the realistic case where the required continuous information is
derived by means of an interpolation of the known coordinate variations at the points of a horizontal geodetic network.
The problem is different from the usual one of frame-invariant interpolation, since not only the domain of definition, but
also the interpolated quantities, depend on independent choices of coordinate frames.
Specific necessary and sufficient conditions for the invariance of derived crustal deformation parameters are given for linear
type of interpolations of either the coordinates at the second epoch or of the displacements.
With the help of the above conditions the invariance characteristics of two commonly used types of linear interpolations are
finally derived, in order to illustrate the practical significance of the results. 相似文献
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By considering a deformable geodetic network, deforming in a linear-in-time mode, according to a coordinate-invariant model, it becomes possible to get an insight into the rank deficiency of the stacking procedure, which is the standard method for estimating initial station coordinates and constant velocities, from coordinate time series. Comparing any two out of the infinitely many least squares estimates of stacking unknowns (initial station coordinates, velocity components and transformation parameters for the reference system in each data epoch), it is proven that the two solutions differ only by a linear-in-time trend in the transformation parameters. These pass over to the initial coordinates (the constant term) and to the velocity estimates (the time coefficient part). While the difference in initial coordinates is equivalent to a change of the reference system at the initial epoch, the differences in velocity components do not comply with those predicted by the same change of reference system for all epochs. Consequently, the different velocity component estimates, obtained by introducing different sets of minimal constraints, correspond to physically different station velocities, which are therefore non-estimable quantities. The theoretical findings are numerically verified for a global, a regional and a local network, by obtaining solutions based on four different types of minimal constraints, three usual algebraic ones (inner or partial inner) and the lately introduced kinematic constraints. Finally, by resorting to the basic ideas of Felix Tisserand, it is explained why the station velocities are non-estimable quantities in a very natural way. The problem of the optimal choice of minimal constraints and, hence, of the corresponding spatio-temporal reference system is shortly discussed. 相似文献
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Athanasios Dermanis 《Journal of Geodesy》1987,61(4):297-309
The Bruns formula is generalized to three dimensions with the derivation of equations expressing the height anomaly vector
or the geoid undulation vector as a function of the disturbing gravity potential and its spatial derivatives. It is shown
that the usual scalar Bruns formula provides not the separation along the normal to the reference ellipsoid but the component
of the relevant spatial separation along the local direction of normal gravity. The above results which hold for any type
of normal potential are specialized for the usual Somigliana-Pizzetti normal field so that the components of the geoid undulation
vector are expressed as functions of the parameters of the reference ellipsoid, the disturbing potential and its spatial derivatives
with respect to three types of curvilinear coordinates, ellipsoidal, geodetic and spherical. Finally the components of the
geoid undulation vector are related to the deflections of the vertical in a spherical approximation. 相似文献
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InformationsPublication Available
Proceedings of the 2nd Hotine Marussi Symposium on Mathematical Geodesy edited by F. Sacerdote—F. Sansò 相似文献
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