Conventional terrestrial system by VLBI a kinematic approach

The paper examines the potential ofVLBI time delay observables for the establishment and maintenance of a Conventional Terrestrial System (CTS). TheCTS is defined in2-D by the standard epoch positions and velocities of a network of control points located on a spherical reference surface. VLBI time delay observables are sensitive to the rotational motion of theCTS control points with respect to a Conventional Inertial System (CIS) which is represented by a network of radio sources. The motion of a control point with respect to theCIS is partitioned into global and regional components. The global components represent the rotational motion of the sphere with respect to theCIS, while the regional components represent the motion of theCTS points with respect to the sphere.     

Determination of the earth rotation parameters from optical astrometry observations, 1962.0–1982.0

The optical astrometric data of the years 1962–1982 have been reduced once again at the Bureau International de l’Heure (BIH) in order to redetermine the Earth Rotation Parameters (ERP). This new reduction is based on serie largely revised by the stations since their use in the operational work of theBIH, and on some series which were not available previously. A total of 113 stations is considered, totaling nearly 500,000 measurements of time or latitude. TheERP are determined at five-day intervals. A new approach is developed: the catalog and local errors are analysed and corrected as group unknowns, which values are adjusted together with the main unknowns. The results obtained in the new reduction are compared to other series obtained by astrometry and space geodesy.     

Further considerations on combining earth rotation observations from different space geodetic systems

Additional results are presented concerning a study that consider improvements over present Earth Rotation Parameter (ERP) determination methods by directly combining observations from various space geodetic systems in one adjustment. Earlier results are extended, showing that in addition to slight improvements in accuracy substantial (a factor of three or more) improvements in precision and significant reductions in correlations between various parameters can be obtained (by combining Lunar Laser Ranging (LLR), Satellite Laser Ranging (SLR) to Lageos, and Very Long Baseline Interferometry (VLBI) data in one adjustment) as compared to results from individual systems. Smaller improvements are also seen over the weighted means of the individual system results. Although data transmission would not be significantly reduced, negligible additional computer time would be required if (standardized) normal equations were available from individual solutions. Suggestions for future work and implications for the new International Earth Rotation Service (IERS) are also presented.     

The North American datum of 1983: Project methodology and execution

A new adjustment of the geodetic control networks in North America has been completed, resulting in a new continental datum—the North American Datum of 1983 (NAD 83). The establishment ofNAD 83 was the result of an international project involving the National Geodetic Survey of the United States, the Geodetic Survey of Canada, and the Danish Geodetic Institute (responsible for surveying in Greenland). The geodetic data in Mexico and Central America were collected by the Inter American Geodetic Survey and validated by the Defense Mapping Agency Hydrographic/Topographic Center. The fundamental task ofNAD 83 was a simultaneous least squares adjustment involving 266,436 stations in the United States, Canada, Mexico, and Central America. The networks in Greenland, Hawaii, and the Caribbean islands were connected to the datum through Doppler satellite and Very Long Baseline Interferometry (VLBI) observations. The computations were performed with respect to the ellipsoid of the Geodetic Reference System of 1980. The ellipsoid is positioned in such a way as to be geocentric, and its axes are oriented by the Bureau International de l'Heure Terrestrial System of 1984. The mathematical model for theNAD readjustment was the height-controlled three-dimensional system. The least squares adjustment involved 1,785,772 observations and 928,735 unknowns. The formation and solution of the normal equations were carried out according to the Helmert block method. [Authors' note:This article is a condensation of the final report of the NAD 83 project. The full report (Schwarz,1989) contains a more complete discussion of all the topics.]     

A demonstration of 1–2 parts in 107 accuracy using GPS

By interferometric analysis ofGPS phase observations made at Owens Valley, Mojave, and Mammoth Lakes, California, we determined the coordinate components of the71–245–313 km triangle of baselines connecting these sites. A separate determination was made on each of four days, April 1–4, 1985. The satellite ephemerides used in these determinations had been derived from observations on other baselines. Therms scatters of the four daily determinations of baseline vector components about their respective means ranged from a minimum of6 mm for the north component of the71-km baseline to a maximum of34 mm for the vertical component of the245-km baseline. To test accuracy, we compared the mean of ourGPS determinations of the245-km baseline between Owens Valley and Mojave with independent determinations by others using very-long-baseline interferometry(VLBI) and satellite laser ranging(SLR). TheGPS-VLBI difference was within 2 parts in10 ⁷ for every vector component. TheGPS-SLR difference was within6 parts in10 ⁸ in the horizontal coordinates, but83 mm in height.     

Determination of high frequency variations in earth's rotation from Doppler satellite observations

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.     

GPS inferred geocentric reference frame for satellite positioning and navigation

Accurate geocentric three dimensional positioning is of great importance for various geodetic and oceanographic applications. While relative positioning accuracy of a few centimeters has become a reality using Very Long Baseline Interferometry (VLBI), the uncertainty in the offset of the adopted coordinate system origin from the geocenter is still believed to be of the order of one meter. Satellite Laser Ranging (SLR) is capable of determining this offset to better than10 cm, though, because of the limited number of satellites, this requires a long arc of data. The Global Positioning System (GPS) measurements provide a powerful alternative for an accurate determination of this origin offset in relatively short period of time. Two strategies are discussed, the first utilizes the precise relative positions predetermined byVLBI, where as the second establishes a reference frame by holding only one of the tracking sites longitude fixed. Covariance analysis studies indicate that geocentric positioning to an accuracy of a few centimeters can be achieved with just one day of preciseGPS pseudorange and carrier phase data.     

Baseline estimation with semidynamic and geometric satellite methods

Accurate relative positioning via dynamic satellite methods is a complicated process. In an attempt to simplify this process a semidynamic method has been investigated in a real data environment. In this method quasi-simultaneous observations from pairs of stations are transformed to Simultaneous Range Differences(SRD's). With this transformation it is anticipated to reduce the effects of orbital and observational residual biases and, therefore, to obtain baselines the accuracy of which is less sensitive to the overall orbital accuracy and yet compatible to that of the observations. Using laser range observations to Lageos collected during theMERIT Main Campaign, baselines have been estimated via both theSRD and the geometric methods. Baselines estimated via the geometric method are independent of orbital errors and any inconsistencies affecting the implementation of the Terrestrial Reference Frame, and therefore they have been used in the present study as standards of comparison. From this comparison it was concluded that for baselines of regional extent, theSRD method is very efficient and at least as accurate as the more complex dynamic methods.     

On comparison of the Earth orientation parameters obtained from different VLBI networks and observing programs

In this paper, a new geometry index of very long baseline interferometry (VLBI) observing networks, the volume of network V, is examined as an indicator of the errors in the Earth orientation parameters (EOP) obtained from VLBI observations. It has been shown that both EOP precision and accuracy can be well described by the power law σ = aV ^c in a wide range of the network size from domestic to global VLBI networks. In other words, as the network volume grows, the EOP errors become smaller following a power law. This should be taken into account for a proper comparison of EOP estimates obtained from different VLBI networks. Thus, performing correct EOP comparison allows us to investigate accurately finer factors affecting the EOP errors. In particular, it was found that the dependence of the EOP precision and accuracy on the recording data rate can also be described by a power law. One important conclusion is that the EOP accuracy depends primarily on the network geometry and to lesser extent on other factors, such as recording mode and data rate and scheduling parameters, whereas these factors have a stronger impact on the EOP precision.     

Improvement of the GPS time comparisons by simultaneous relative positioning of the receiver antennas

The Global Positioning System,GPS, is widely used for time comparisons between distant laboratories. Over distances of the order of 1000km or less, the system has the capability of 1 to 2ns accuracy. However this requires a relative positioning with errors lower than 30cm. We show that this positioning can be derived from theGPS time comparisons themselves. An example for European laboratories is given.     

Determination of GPS orbits using double difference carrier phase observations from regional networks

Summary Carrier phase measurements are potentially the most precise observations available from theGPS satellite system, the formal precision being of the order of one centimeter per observation. If the so called double differences are used as the basic observable, the analysis is relatively simple, since satellite- and receiver-clocks may be represented by basic models. We investigate the feasibility of double difference phase observations for orbit determination using the material of the 1985 High Precision Baseline Test, where the coordinates of the so called fiducial points (Haystack, Ft. Davis Richmond and Mojave) are held fixed.TI-4100 andAFGL-receiver observations were used in the same orbit determination process. Although no surface weather data had been available to us, the orbit quality seems to be of the order of0.1 ppm. When we use these orbits to estimate the coordinates of the five “non-fiducial points” Owens Valley, Hat Creek Mammoth Lake, Austin and Dahlgren we get a repeatability of the order of5 cm for latitude and longitude and10 cm for height, if the observations of the first four days of the campaign are compared to those of the second four days. If we use our orbits estimated withTI andAFGL observations to process the Mojave—Owens Valley baseline (length245 km) measured by the twoSERIES-X receivers, we obtain day to day repeatabilities of1.6 cm (0.06 ppm) in length,2 cm (0.08 ppm) in latitude,4 cm (0.16 ppm) in longitude and7 cm (0.29 ppm) in height. Since there are indications that regional networks will be realized in the near future, the results presented here should encourage the realization of regional high precision orbit determination services.     

Use of phase data for accurate differential GPS kinematic positioning

DifferentialGPS land kinematic positioning tests conducted at velocities of20 to100 km/h over a baseline of1,000 km using a combination of pseudo-range and phase measurements are described. An algorithm designed for high reliability and accuracy of1 to2 m in real time field operational mode was utilized. The relatively long baseline used for the tests provided valuable information on the effects of broadcast ephemeris errors on the differential results. The tests were conducted with two Texas InstrumentsTI4100 receivers using both theP andC/A codes to assess the effect of both code measurement noise, and ionospheric irregularities on differential positioning over such a baseline. The use of cesium clocks to constrain time was also tested. Accuracies (in terms of repeatabilities) of the order of1 to3 ppm, i.e.,1 to3 m, were obtained.     

Accuracy analysis for the NAD 83 geodetic reference system

The North American Datum of 1983 (NAD 83) provides horizontal coordinates for more than 250,000 geodetic stations. These coordinates were derived by a least squares adjustment of existing terrestrial and space-based geodetic data. For pairs of first order stations with interstation distances between 10km and 100km, therms discrepancy between distances derived fromNAD 83 coordinates and distances derived from independentGPS data may be suitably approximated by the empirical rulee=0.008 K^0.7 where e denotes therms discrepancy in meters and K denotes interstation distance in kilometers. For the same station pairs, therms discrepancy in azimuth may be approximated by the empirical rule e=0.020 K^0.5. Similar formulas characterize therms discrepancies for pairs involving second and third order stations. Distance and orientation accuracies, moreover, are well within adopted standards. While these expressions indicate that the magnitudes of relative positional accuracies depend on station order, absolute positional accuracies are similar in magnitude for first, second, and third order stations. Adjustment residuals reveal a few local problems with theNAD 83 coordinates and with the weights assigned to certain classes of observations.     

A graph-theoretical algorithm for detecting configuration defects in triangular geodetic networks

Summary The problem to detect configurational defects in geodetic networks is solved by a graph-theoretical algorithm, here applied to triangular geodetic networks and being presented as a computer program in the Appendix. Based on an analysis of the incidence matrix the algorithm detects, for instance, missing vertical directions which cause two types of deficiencies. In case of only vertical direction measurements from one point to another, but no counter vertical direction measurements backwards, the rank deficiency of the first type is identified. Furtheron if there are “bare” points with no vertical direction measurements at all, the rank deficiency of the second type is found. The algorithm has proved a rank deficiency of 4+13=17 in theSW Finland triangular network which before has been found as the surprizing rank defect ofTAGNET 3d-operational adjustment.     

Demonstration of sub-meter GPS orbit determination and 1.5 parts in 108 three-dimensional baseline accuracy

Differential tracking of theGPS satellites in high-earth orbit provides a powerful relative positioning capability, even when a relatively small continental U.S. fiducial tracking network is used with less than one-third of the fullGPS constellation. To demonstrate this capability, we have determined baselines of up to2000 km in North America by estimating high-accuracyGPS orbits and ground receiver positions simultaneously. The2000 km baselines agree with very long baseline interferometry(VLBI) solutions at the level of1.5 parts in10 ⁸ and showrms daily repeatability of0.3–2 parts in10 ⁸. The orbits determined for the most thoroughly trackedGPS satellites are accurate to better than1 m. GPS orbit accuracy was assessed from orbit predictions, comparisons with independent data sets, and the accuracy of the continental baselines determined along with the orbits. The bestGPS orbit strategies included data arcs of at least one week, process noise models for tropospheric fluctuations, estimation ofGPS solar pressure coefficients, and combined processing ofGPS carrier phase and pseudorange data. For data arcs of two weeks, constrained process noise models forGPS dynamic parameters significantly improved the solutions.     

First direct geodetic link between Europe,Africa and South America with a multi station VLBI array

The first geodetic experiment tying Europe, Africa and South-America was realized in July 1985 by Very Long Baseline Interferometry with a network of 5 radiotelescopes. TheVLBI technique and data analysis are presented, with special emphasis on the ionosphere modeling because of its importance in this particular experiment. Comparisons of the results with other geodetic information confirm the achievement of decimetric accuracy.     

Local geoid computation from gravity using the fast fourier transform technique

Model computations were performed for the study of numerical errors which are interjected into local geoid computations byFFT. The gravity field model was generated through the attractions of granitic prisms derived from actual geology. Changes in sampling interval introduced only0.3 cm variation in geoid heights. Although zero padding alone provided an improvement of more than5 cm in theFFT generated geoid, the combination of spectral windowing (tapering) and padding further reduced numerical errors. For theGPS survey of Franklin County, Ohio, the parameters selected as a result of model computations, allow large reduction in local data requirements while still retaining the centimeter accuracy when tapering and padding is applied.     

The oblique Mercator projection of the ellipsoid of revolution IE a 2 ,b

While the standardMercator projection / transverse Mercator projecton maps the equator / the transverse metaequator equivalent to the meridian of referenceequidistantly, theoblique Mercator projection aims at aconformal mapping of the ellipsoid of revolution constraint to anequidistant mapping of an oblique metaequator. Obliqueness is determined by the extension of the area to be mapped, e.g. determined by the inclination of satellite orbits: Satellite cameras map the area just under the orbit geometry. Here we derive themapping equations of theoblique Mercator projection being characterized to beconformal andequidistant on the oblique metaequator extending results ofM. Hotine (1946, 1947).     

Robust estimation of deformation from observation differences for free control networks

Deformation measurements have a repeatable nature. This means that deformation measurements are performed often with the same equipment, methods, geometric conditions and in a similar environment in epochs 1 and 2 (e.g., a fully automated, continuous control measurements). It is, therefore, reasonable to assume that the results of deformation measurements can be distorted by both random errors and by some non-random errors, which are constant in both epochs. In other words, there is a high probability that the difference in the accuracy and precision of measurement of the same geometric element of the network in both epochs has a constant value and sign. The constant errors are understood, but the manifestation of these errors is difficult to determine in practice. For free control networks (the group of potential reference points in absolute control networks or the group of potential stable points in relative networks), the results of deformation measurements are most often processed using robust methods. Classical robust methods do not completely eliminate the effect of constant errors. This paper proposes a new robust alternative method called REDOD. The performed tests showed that if the results of deformation measurements were additionally distorted by constant errors, the REDOD method completely eliminated their effect from deformation analysis results. If the results of deformation measurements are only distorted by random errors, the REDOD method yields very similar deformation analysis results as the classical IWST method. The numerical tests were preceded by a theoretical part. The theoretical part describes the algorithm of classical robust methods. Particular attention was paid to the IWST method. In relation to classical robust methods, the optimization problem of the new REDOD method was formulated and the algorithm for its solution was derived.