Showing papers in "Journal of Geodesy in 1980"
TL;DR: In this paper, the authors reviewed several concepts for utilizing GPS signals and described the reconstructed carrier phase method, which is being pursued by the Defense Mapping Agency, National Oceanic and Atmospheric Administration, and the U.S. Geological Survey.
Abstract: The development of relatively inexpensive satellite receivers in the early 1970's has resulted in cost-effective applications of satellites for a variety of geodetic surveying needs. Currently achievable accuracies range from 10 to 20 centimeters. The NAVSTAR Global Positioning System, now under development by the Department of Defense, incorporates advanced technology which has the potential capability of revolutionizing satellite geodesy. Several concepts for utilizing GPS signals are briefly reviewed, and another concept, called the reconstructed carrier phase method, is described in some detail. This concept is being pursued by the Defense Mapping Agency, National Oceanic and Atmospheric Administration, and the U.S. Geological Survey. These agencies have numerous requirements for accurate positioning. Several prototype receivers are planned to be available for testing in mid-1982. These receivers should be highly portable, consume little power, and obtain base line accuracies of several centimeters in several hours of observation time. However, water vapor radiometers will be needed in order to achieve the full accuracy. Initial simulation results utilizing the reconstructed carrier phase method are included.
89 citations
TL;DR: In this article, it was shown that the restrictions of the functions on a regular boundary surface of an exterior region in Euclidean space ℜ3 (for instance, sphere, ellipsoid, geoid, earth's surface) form a closed system in the spaceC (S), i.e. any functionf, defined and continuous on S, can be approximated uniformly by a linear combination of functions ϕn.
Abstract: Let S be the (regular) boundary-surface of an exterior regionEe in Euclidean space ℜ3 (for instance: sphere, ellipsoid, geoid, earth's surface). Denote by {φn} a countable, linearly independent system of trial functions (e.g., solid spherical harmonics or certain singularity functions) which are harmonic in some domain containingEe ∪ S. It is the purpose of this paper to show that the restrictions {ϕn} of the functions {φn} onS form a closed system in the spaceC (S), i.e. any functionf, defined and continuous onS, can be approximated uniformly by a linear combination of the functions ϕn.
46 citations
TL;DR: In this paper, the authors used a data set of 260 000 gravity anomalies and found that common characteristics for a local covariance function exist in an area as large as Canada excluding the Rocky Mountains.
Abstract: Using a data set of 260 000 gravity anomalies it is shown that common characteristics for a local covariance function exist in an area as large as Canada excluding the Rocky Mountains. After eliminating global features by referencing the data to the GEM-10 satellite solution, the shape of the covariance function is remarkably consistent from one sample area to the next. The determination of the essential parameters and the fitting of the covariance function are discussed in detail.
36 citations
TL;DR: The data centralised by the BIH for computing UT1-UTC and the coordinates of the pole are analysed and the model adopted to represent the errors of astronomical data series is introduced and its validity for comparing them with results from modern techniques is discussed.
Abstract: This description refers to the method which was initiated by the BIH in 1967 and the results of which appear in the Annual Reports and Circular D The computation with this method has been extended to the past until 19620
34 citations
TL;DR: In this paper, a numerically efficient solution strategy is developed for the second-order design of a free distance network, based on the fact that the direct (non-canonical) way has a regular least-squares solution.
Abstract: A numerically efficient solution strategy is developed for the second-order design of a free distance network. It is based on the fact that the direct (non-canonical) way has a regular least-squares solution. A flow chart illustrates the direct construction of the final equations, using a list of point coordinates and a list of projected distances as input. Results are shown for an actual network (11 points, 47 distances), considering different types of criterion matrices: Taylor-Karman structure with homogeneous-isotropic point error ellipses and special Taylor-Karman structure with isotropic relative error ellipses. Finally, the construction of a criterion-matrixQ
x
is briefly discussed in the case that a certain number of quantities shall be derived from the network.
33 citations
TL;DR: In this article, the authors compared GEOS-3 altimeter data with gravimetric geoid computed by various techniques for 30 x 30 deg areas in the Tonga Trench and the Indian Ocean.
Abstract: Geoids computed from GEOS-3 altimeter data are compared with gravimetric geoids computed by various techniques for 30 x 30 deg areas in the Tonga Trench and the Indian Ocean. The gravimetric geoids were calculated using the standard Stokes integration with the Molodenskii truncation procedure, the modified Stokes integration suggested by Ostach (1970) and Meissl (1971) with modified Molodenskii truncation functions, and three sets of potential coefficients including one complete to degree 180. It is found that the modified Stokes procedure with a cap size of 10 deg provides better results when used with a combined altimeter terrestrial anomaly field data set. Excellent agreement at the plus or minus 1 m level is obtained between the altimeter and gravimetric geoid using the combined data set, with the modified Stokes procedure having a greater accuracy. Coefficients derived from the 180 x 180 solution are found to be of an accuracy comparable to that of the modified Stokes method, however to require six times less computational effort.
28 citations
TL;DR: In this paper, a recurrence relation is presented for the smoothing function βn, which is used in geodesy to relate spherical harmonics to their mean values over circular areas (caps).
Abstract: A recurrence relation is presented for the smoothing function, βn, which is used in geodesy to relate spherical harmonics to their mean values over circular areas (caps). The proposed formula does not require the computation of the Legendre's polynomials. Moreover, it is numerically more stable than the formulas ofPellinen (1969) andMeissl (1971).
23 citations
14 citations
13 citations
TL;DR: In this article, a short pulse laser on board an orbiting spacecraft is used to measure the distances between the spacecraft and many laser retroreflectors (targets) deployed on the earth's surface.
Abstract: The 'spaceborne laser ranging system' is a proposed short pulse laser on board an orbiting spacecraft. It measures the distances between the spacecraft and many laser retroreflectors (targets) deployed on the earth's surface. The precision of these range measurements was assumed to be about plus or minus 2 cm. These measurements were then used together with the orbital dynamics of the spacecraft to derive the intersite vector between the laser ground targets. The errors associated with this vector were on the order of 1 to 2 cm. The baseline distances determined range from 25 km to 1200 km. By repeating the measurements of the intersite vector, strain and strain rate errors were estimated. The realizable precision for intersite distance determination was estimated to be on the order of 0.5 cm at 300 km and about 1.5 cm at 1200 km. The corresponding inaccuracies for the intersite distances were larger, than is 1 cm and 3.5 cm respectively. The corresponding precision in the vertical direction was 1 cm and 3 cm.
TL;DR: In this article, the geodetic boundary value problem is formulated which uses as boundary values the differences between the geopotential of points at the surface of the continents and the potential of the geoid.
Abstract: The geodetic boundary value problem is formulated which uses as boundary values the differences between the geopotential of points at the surface of the continents and the potential of the geoid. These differences are computed by gravity measurements and levelling data. In addition, the shape of the geoid over the oceans is assumed to be known from satellite altimetry and the shape of the continents from satellite results together with three-dimensional triangulation. The boundary value problem thus formulated is equivalent to Dirichlet's exterior problem except for the unknown potential of the geoid. This constant is determined by an integral equation for the normal derivative of the gravitational potential which results from the first derivative of Green's fundamental formula. The general solution, which exists, of the integral equation gives besides the potential of the geoid the solution of the geodetic boundary value problem. In addition approximate solutions for a spherical surface of the earth are derived.
TL;DR: In this paper, a finite set of potential coefficients based on satellite measurements of gravity anomalies and gravity disturbances are analyzed. But the authors assume that the inner zone (spherical cap) is sufficiently covered by surface gravity measurements in conjunction with altimetry or by gravity anomaly data.
Abstract: Errors in the outer zone contribution to oceanic undulation differences computed from a finite set of potential coefficients based on satellite measurements of gravity anomalies and gravity disturbances are analyzed. Equations are derived for the truncation errors resulting from the lack of high-degree coefficients and the commission errors arising from errors in the available lower-degree coefficients, and it is assumed that the inner zone (spherical cap) is sufficiently covered by surface gravity measurements in conjunction with altimetry or by gravity anomaly data. Numerical computations of error for various observational conditions reveal undulation difference errors ranging from 13 to 15 cm and from 6 to 36 cm in the cases of gravity anomaly and gravity disturbance data, respectively for a cap radius of 10 deg and mean anomalies accurate to 10 mgal, with a reduction of errors in both cases to less than 10 cm as mean anomaly accuracy is increased to 1 mgal. In the absence of a spherical cap, both cases yield error estimates of 68 cm for an accuracy of 1 mgal and between 93 and 160 cm for the lesser accuracy, which can be reduced to about 110 cm by the introduction of a perfect 30-deg reference field.
TL;DR: The error in the mean earth ellipsoid computer on the basis of Doppler or laser observations of artificial earth satellites or radar altimeter observations of the ocean surface from a satellite depends upon instrument precision, on uncertainties in the specification of the earth's gravity field at both long and short wave lengths, on the origin of the coordinate system, on modeling errors in ionospheric (except laser) and tropospheric refraction, and on oceanographic effects.
Abstract: The error in the mean earth ellipsoid computer on the basis of Doppler or laser observations of artificial earth satellites or radar altimeter observations of the ocean surface from a satellite depends upon instrument precision, on uncertainties in the specification of the earth's gravity field at both long and short wave lengths, on uncertainties in the origin of the coordinate system, on modeling errors in ionospheric (except laser) and tropospheric refraction, and, for altimetry, on oceanographic effects. The magnitude of the uncertainty in the computed ellipsoid will vary depending on the size of these errors and on the number and distribution of observation stations. Review of computations based on various data sets indicates that differences in the computed ellipsoids are consistent with those expected due to the various error sources and that the best fitting ellipsoid has a semi-major axis of6378136±2 m.
TL;DR: In this paper, a combined Doppler and terrestrial net adjustment procedure is proposed, where not only the known systematic discrepancies in scale and orientation between the terrestrial measurements and the terrestrial results are modelled, but also all available informations about the accuracy of these systematic differences are to be taken into account.
Abstract: In a combined Doppler and terrestrial net adjustment not only the known systematic discrepancies in scale and orientation between the Doppler measurements and the terrestrial results must be modelled, but also all available informations about the accuracy of these systematic differences are to be taken into account. Using the Helmert-block method for the combination procedure, no covariance matrices for the terrestrially determined coordinates must be computed, their numerical evaluation being a computational detour. The proposed procedure as applied to real nets, includes all different kinds of geometric or physical models, whereby their specific parameters are eliminated at this level. Two solutions are discussed, a three-dimensional and a two-dimensional one, but “two-dimensional” is not equivalent to “non-spatial” in this context.
TL;DR: In this paper, the principles of three-dimensional geodesy are used in the adjustment of horizontal networks with heights and astronomic coordinates held fixed, which is simpler and faster than any conventional method, as it uses measurements on the terrain without any reductions to a computational surface.
Abstract: The principles of three-dimensional geodesy are used in the adjustment of horizontal networks with heights and astronomic coordinates held fixed. The proposed method is simpler and faster than any conventional method, as it uses measurements on the terrain without any reductions to a computational surface. There are no restrictions on the lengths of the lines.
TL;DR: Doppler tracking of artificial satellites has been applied to determine the pole components through an experiment called MEDOC as mentioned in this paper, which was initiated by the GRGS (Groupe de Recherches de Geodesie Spatiale).
Abstract: Doppler tracking of artificial satellites has been applied to determine the pole components through an experiment called MEDOC In addition to developing scientific aspects dealing with polar motion, it is proposed to promote new observational techniques and to investigate the possibility of operating an international permanent service So far, nearly two years of bi-daily solutions have been derived Each improvement of computational procedures, data processing and station component determination has contributed to better precision in the computed pole positions MEDOC pole coordinate solutions show good agreement with DMA and BIH global solutions corrected for annual terms Differences of the smoothed values are less than one meter for both components The MEDOC experiment was initiated by the GRGS (Groupe de Recherches de Geodesie Spatiale) and took place in 1977 and 1978 The experiment as presently organized will continue up to 1980 Future improvements are still foreseen by increasing the number of observing sites and refinement of the force models, but already international involvement is taking place in the MEDOC experiment
TL;DR: In this article, an attempt is made to obtain the initial values for the Indian geodetic datum in absolute terms on GRS 67 by least-square solution technique, making use of the available astro-geodetic data in India, and the corresponding generalised gravimetric values at the considered astro geodesetic points, as derived from the mean gravity anomalies over 1°×1° squares of latitude and longitude in and around the Indian sub-continent, and over 5° equal area blocks covering the rest of the earth's surface.
Abstract: The Everest spheroid, 1830, in general use in the Survey of India, was finally oriented in an arbitrary manner at the Indian geodetic datum in 1840; while the international spheroid, 1924, in use for scientific purposes; was locally fitted to the Indian geoid in 1927. An attempt is here made to obtain the initial values for the Indian geodetic datum in absolute terms on GRS 67 by least-square solution technique, making use of the available astro-geodetic data in India, and the corresponding generalised gravimetric values at the considered astro-geodetic points, as derived from the mean gravity anomalies over1°×1° squares of latitude and longitude in and around the Indian sub-continent, and over5° equal area blocks covering the rest of the earth’s surface. The values obtained independently by gravimetric method, were also considered before actual finalization of the results of the present determination.
TL;DR: In this article, the coefficients of observation equations for horizontal adjustment in truly height-controlled space were derived and the accuracies compared, and it was concluded that the reduced forms are adequate for practical purposes.
Abstract: The investigation produces correct forms for the coefficients of observation equations for horizontal adjustment in truly height-controlled space. From these, approximate and simple coefficients are derived and the accuracies compared. It is concluded that the reduced forms are adequate for practical purposes.
TL;DR: In this paper, a note on met en evidence l'efficacite et la simplicite de resolution que les coordonnees rectangulaires offrent dans les problemes de lastronomie geodesique.
Abstract: Dans la premiere partie de cette note on met en evidence l’efficacite et la simplicite de resolution que les coordonnees rectangulaires offrent dans les problemes de l’astronomie geodesique.
TL;DR: In this article, the analysis of deformations and reductions of the geodetic networks in general gravity-invariant and potential invariant representations of the actual gravity field of the Earth by normal (theoretical) gravity field has been presented.
Abstract: The analysis of deformations and reductions of the geodetic networks in general gravity-invariant and potential-invariant representations of the actual gravity field of the Earth by normal (theoretical) gravity field has been presented.
TL;DR: In this article, the error caused by using the Honkasalo tidal gravity term in geoid computations with Stokes' formula is discussed and it is pointed out that the relatively large value of the error to a great extent is generated by interaction between the Honkaalo term and the weight function in Stokes's formula.
Abstract: The error caused by using the Honkasalo tidal gravity term in geoid computations with Stokes' formula is discussed. It is pointed out that the relatively large value of the error to a great extent is generated by interaction between the Honkasalo term and the weight function in Stokes' formula.
TL;DR: In this paper, second-order derivatives of a general scalar function of position with respect to the length elements along a family of local Cartesian axes are developed in the spheroidal and spherical coordinate systems.
Abstract: Second-order derivatives of a general scalar function of position (F) with respect to the length elements along a family of local Cartesian axes are developed in the spheroidal and spherical coordinate systems. A link between the two kinds of formulations is established when the results in spherical coordinates are confirmed also indirectly, through a transformation from spheroidal coordinates. IfF becomesW (earth's potential) the six distinct second-order derivatives—which include one vertical and two horizontal gradients of gravity—relate the symmetric Marussi tensor to the curvature parameters of the field. The general formulas for the second-order derivatives ofF are specialized to yield the second-order derivatives ofU (standard potential) and ofT (disturbing potential), which allows the latter to be modeled by a suitable set of parameters. The second-order derivatives ofT in which the property ΔT=0 is explicitly incorporated are also given. According to the required precision, the spherical approximation may or may not be desirable; both kinds of results are presented. The derived formulas can be used for modeling of the second-order derivatives ofW orT at the ground level as well as at higher altitudes. They can be further applied in a rotating or a nonrotating field. The development in this paper is based on the tensor approach to theoretical geodesy, introduced by Marussi [1951] and further elaborated by Hotine [1969], which can lead to significantly shorter demonstrations when compared to conventional approaches.
TL;DR: In this paper, the authors examined computer roundoff error accumulation in the least square adjustment of horizontal geodetic networks containing positions of very poor geometry and showed that roundoff errors accumulate at the weak unknowns but do not disturb the solution of well-determined positions.
Abstract: This paper examines computer roundoff error accumulation in the least-squares adjustment of horizontal geodetic networks containing positions of very poor geometry. Roundoff error accumulates at the weak unknowns but does not disturb the solution of well-determined positions. Numerical results are given.
TL;DR: In this article, the GPS range and Doppler observations were used for the estimation of geodetic coordinates, but the instability of the receiver atomic oscillator limited the usefulness of these observations in providing first-order baseline determination.
Abstract: Geodetic positioning accuracies obtained from range, integrated Doppler and double differenced interferometric phase observations from a constellation of twenty-four Global Positioning System satellites are presented. It is demonstrated that GPS range and Doppler observations will provide sufficient accuracy for the estimation of geodetic coordinates. However the instability of the receiver atomic oscillator will limit the usefulness of these observations in providing rapid first-order baseline determination. Interferometric phase measurements twice differenced to eliminate clock error appear as an alternate procedure for providing such accuracies.
TL;DR: The conclusion is that the fill-in scheme is a viable method for geodetic networks and, in some cases, it needs less computer storage than the profile method.
Abstract: A minimum fill-in scheme, published by Yale University and not previously discussed in the geodetic literature, has been tested on four typical triangulation networks. Its computer storage requirement has been compared with that of the profile method using Snay's station reordering algorithm. Tests have been carried out for terrestrial and mixed terrestrial/satellite networks.
TL;DR: In this article, a simple method for finding the common point of intersection of two planes and a sphere is proposed, which is the same for all the problems of intersection, lateration, and direct problem.
Abstract: Solutions are given for intersection, lateration, and the direct problem by a simple method which finds the common point of intersection of two planes and a sphere. The ways of determining a plane may vary, but the general procedure is the same for all cases. An alternative solution is given for the direct problem.