Geodetic Parameters Research Articles

The GLONASS-M satellite yaw-attitude model

The proper modeling of the satellites’ yaw-attitude is a prerequisite for high-precision Global Navigation Satellite System (GNSS) positioning and poses a particular challenge during periods when the satellite orbital planes are partially eclipsed. Whereas a lot of effort has been put in to examine the yaw-attitude control of GPS satellites that are in eclipsing orbits, hardly anything is known about the yaw-attitude behavior of eclipsing GLONASS-M satellites. However, systematic variations of the carrier phase observation residuals in the vicinity of the orbit’s noon and midnight points of up to ±27 cm indicate significant attitude-related modeling issues. In order to explore the GLONASS-M attitude laws during eclipse seasons, we have studied the evolution of the horizontal satellite antenna offset estimates during orbit noon and orbit midnight using a technique that we refer to as “reverse kinematic precise point positioning”. In this approach, we keep all relevant global geodetic parameters fixed and estimate the satellite clock and antenna phase center positions epoch-by-epoch using 30-second observation and clock data from a global multi-GNSS ground station network. The estimated horizontal antenna phase center offsets implicitly provide the spacecraft’s yaw-attitude. The insights gained from studying the yaw angle behavior have led to the development of the very first yaw-attitude model for eclipsing GLONASS-M satellites. The derived yaw-attitude model proves to be much better than the nominal yaw-attitude model commonly being used by today’s GLONASS-capable GNSS software packages as it reduces the observation residuals of eclipsing satellites down to the normal level of non-eclipsing satellites and thereby prevents a multitude of measurements from being incorrectly identified as outliers. It facilitates continuous satellite clock estimation during eclipse and improves in particular the results of kinematic precise point positioning of ground-based receivers.

Triaxial ellipsoid models of the Moon based on the laser altimetry data of Chang’E-1

Lunar geodetic parameters, which play an important role in lunar exploration, can be calculated from the gravity and topography data. With the CE-1 altimetry data and LP gravity model, we calculate such geodetic parameters as the principle moment of inertia, the principle inertia axes, equatorial radius, polar radius, mean radius, flattening and offset between center of mass and center of figure (DCOM-COF). According to the CE-1 altimetry data and the above geodetic parameters, a tri-axial ellipsoid (CE-1-LAM-GEO) and a tri-axial level ellipsoid (CE-1-LAM-LEVEL) are calculated individually, providing mass center and figure center offset (DCOM-COF) and parameters more reliable in direction and magnitude.

A model of recent vertical movements of the earth's surface in Lithuania: integration of geodetic levelling data and geological parameters

A model of recent vertical movements of the earth's surface in Lithuania: integration of geodetic levelling data and geological parameters

Second‐order ionospheric term in GPS: Implementation and impact on geodetic estimates

In this paper, different aspects of the application of the second‐order ionospheric term (abbreviated as I2) and its impact on geodetic estimates are studied. A method to correct the GPS observations from this effect is proposed. This method provides a more accurate correction to the GPS measurements (in some cases, it can even be 50% better) with respect to other ways of computing such effect. Moreover, this method can be applied routinely to estimate geodetic parameters. Applying the I2 correction to subdaily differential positioning, several relationships between the deviation of the parameter estimates and the I2 term are derived in the context of a new global approach to the problem. In particular, it is shown that the effect in receiver position mainly depends on the differential value of this term between GPS receivers, while the satellite clocks are directly affected by the undifferenced values. Data from the International GNSS Service (IGS) global network of receivers have been gathered over a period of 21 months. These data have been used to study the I2 effect on the geodetic estimates, such as receiver positions, satellite clocks, and orbits. The most important effect appears for the satellite clocks, and it can be greater than 1 cm depending on the geographical location, comparable to the IGS nominal accuracies. The effect on orbits consists of a global contribution of several millimeters (which confirms the geocenter displacement detected by other authors) plus a subdaily contribution, also of several millimeters, that is geographically dependent, also comparable to the IGS nominal accuracies. As for the position of receivers, the obtained shifts are, in general, at submillimeter level and are directed southward for low‐latitude receivers and northward for high‐latitude receivers. These results will be explained in detail since they are not completely in agreement with the ones presented in previous works.

SIMILARITIES BETWEEN CLASSICAL TIME-LIKE GEODESICS IN A NAKED REISSNER–NORDSTRÖM SINGULARITY BACKGROUND AND THE BEHAVIOR OF ELECTRONS IN QUANTUM THEORY

A study of classical time-like geodesics in a naked Reissner–Nordström singularity background is presented. Regarding the electron as naked a singularity, the size of the clothed singularity turns out to be classical electro-magnetic radius of the electron, to an observer falling freely from infinity, initially at rest. The size shrinks for an observer falling freely from infinity, with a positive initial velocity. For geodetic parameters corresponding to negative energy there are trapped geodesics. The similarity of this picture with that arising in quantum theory is discussed.

Reprocessing of a global GPS network

During the 10 years since the official start of the International GNSS Service (IGS) in 1994 considerable improvements in the processing strategies and modeling of global GPS solutions were achieved. Owing to changes at the individual IGS Analysis Centers during these years the resulting time series of global geodetic parameters are very inhomogeneous and inconsistent. A geophysical interpretation of these long series and the realization of a high‐accuracy global reference frame are therefore difficult and questionable. In view of these deficiencies, the Technical Universities of Munich and Dresden decided to perform a reprocessing of a global GPS network over the last decade in a joint effort. First results of the reprocessing of 11 years of data show significant improvements in the quality and homogeneity of the estimated parameters and will allow for new geodynamic and geophysical interpretations. In the early years an improvement of the coordinate repeatability by a factor of more than 2 could be achieved. The formal errors of subdaily Earth rotation parameters could be reduced by 30%. Advanced modeling approaches like a mapping function based on numerical weather models, consideration of second‐ and third‐order ionospheric corrections and absolute antenna phase center corrections for receivers and satellites were tested to achieve further improvements.

On the impossibility of measuring the general relativistic part of the terrestrial acceleration of gravity with superconducting gravimeters

In this paper we very preliminarily investigate the possibility of measuring the post-Newtonian general relativistic gravitoelectric and gravitomagnetic components of the acceleration of gravity on the Earth, in continuous regime, with two absolute measurements at the equator and the south pole with superconducting gravimeters. The magnitudes of such relativistic effects are 10^-10 m s^-2 and 10^-11 m s^-2, respectively. Unfortunately, the present-day uncertainties in the Earth's geodetic parameters which enter the classical Newtonian terms induce systematic errors 1-2 orders of magnitude larger than the relativistic ones. Moreover, a \sim 1 ngal sensitivity can be reached by the currently available superconducting gravimeters, but only for relative measurements.

Effect of gravitational consistency and mass conservation on seasonal surface mass loading models

Increasingly, models of surface mass loads are used either to correct geodetic time coordinates by removing seasonal and other “noise”, or for comparison with other geodetic parameters. However, models of surface loading obtained by simply combining the mass redistribution due to individual phenomena will not in general be self‐consistent, in that (i) the implied global water budget will not be mass‐conserving, and (ii) the modelled sea level will not be an equipotential surface of Earth's total gravity field. We force closure of the global water budget by allowing the “passive” ocean to change in mass. This medium‐term passive ocean response will not be a uniform change in non‐steric ocean surface height, but must necessarily be spatially variable to keep the “passive” ocean surface on an equipotential. Using existing load models, we demonstrate the effects of our consistency theory. Geocenter motion is amplified significantly, by up to 43%.

Microarcsecond astrometry using the SKA

The sensitivity and versatility of SKA will provide microarcsec astrometric precision and high quality milliarcsec-resolution images by simultaneously detecting calibrator sources near the target source. To reach these goals, we suggest that the long-baseline component of SKA contains at least 25% of the total collecting area in a region between 1000 and 5000 km from the core SKA. We also suggest a minimum of 60 elements in the long-baseline component of SKA to provide the necessary ( u– v) coverage. For simultaneous all-sky observations, which provide absolute astrometric and geodetic parameters, we suggest using 10 independent subarrays each composed of at least six long-baseline elements correlated with the core SKA. We discuss many anticipated SKA long-baseline astrometric experiments: determination of distance, proper motion and orbital motion of thousands of stellar objects; planetary motion detections; mass determination of degenerate stars using their kinetics; calibration of the universal distance scale from 10 to 10 7 pc; the core and inner-jet interactions of AGN. With an increase by a factor of 10 in absolute astrometric accuracy using simultaneous all sky observations, the fundamental quasar reference frame can be defined to <10 μas and tied to the solar-system dynamic frame to this accuracy. Parameters associated with the earth rotation and orientation, nutation, and geophysical parameters, can be accurately monitored. Tests of fundamental physics include: solar and Jovian deflection experiments, the sky frame accuracy needed to interpret the gravity wave/pulsar-timing experiment, accurate monitoring of spacecraft orbits that impact solar system dynamics.

Numerical simulations of a Mars geodesy network experiment: Effect of orbiter angular momentum desaturation on Mars' rotation estimation

The scientific objectives of a geodetic experiment based on a network of landers, such as NEIGE (NEtlander Ionosphere and Geodesy Experiment) are to improve the current knowledge of Mars' interior and atmosphere dynamics. Such a network science experiment allows monitoring the motions of the Martian rotation axis with a precision of a few centimeters (or milli-arc-seconds (mas)) over annual and sub-annual periods. Thereto, besides radio tracking of a Mars orbiter from the Earth, radio Doppler shifts between this orbiter and several landers at the planet's surface will be performed. From the analysis of these radio Doppler data, it is possible to reconstruct the orbiter motion and Mars' orientation in space. The errors on the orbit determination (position and velocity of the orbiter) have an impact on the geodetic parameters determination from the Doppler shifts and must be removed from the signal in order to achieve a high enough accuracy. In this paper, we perform numerical simulations of the two Doppler signals involved in such an experiment to estimate the impact of the spacecraft angular momentum desaturations on the determination of Mars' orientation variations. The attitude control of the orbiter needs such desaturation maneuvers regularly repeated. They produce velocity variations that must be taken into account when determining the orbit. For our simulations, we use a priori models of the Martian rotation and introduce the spacecraft velocity variations induced by each desaturation event. By a least-squares adjustment of the simulated Doppler signals, we then estimate the orbiter velocity variations and the parameters of the Mars' rotation model. We show that these velocity variations are ill resolved when the spacecraft is not tracked, therefore requiring a near-continuous tracking from the Earth to accurately determine the orbit. In such conditions we show that only 15– 20 min of lander–orbiter tracking per week allows recovering Mars' orientation parameters with a precision of a few mas over a period of 1 Martian year.

The influence on GPS estimates of NWP-derived mapping functions

When estimating zenith total delays (ZTD) from global positioning system (GPS) signals it is assumed that the atmosphere is symmetric in the horizontal plane and that delays in the signal from one of the GPS satellites to a receiver can be mapped onto the zenith direction through a known mapping function. The generally used mapping function has only a dependence on the day of the year and the latitude of the receiver. The fact that these mapping functions do not depend on the actual weather may introduce errors in estimates of the location parameters and the estimate of the ZTD. In this paper mapping functions from numerical weather prediction (NWP) models are derived and the influence on the accuracy of location parameters and ZTD estimates is investigated during a cold front passage in the Netherlands on the 30th of October 2000. The hydrostatic mapping function computed from NWP was smaller than the Niell mapping function (0.02 at 5° elevation). The differences for the wet mapping function were much larger, and of opposite sign. However, since the hydrostatic delay is larger than the wet delay, we found that the geodetic parameters are mainly influenced by errors in the hydrostatic mapping function. Using an elevation cut-off error of 10°, we observed systematic errors in the estimated ZTD of −2.1 to −3.1 mm, in the clock error of 6.5–9.2 mm and in the height of 4.8–6.5 mm.

National height datum, the Gauss-Listing geoid level value w 0 and its time variation 0 (Baltic Sea Level Project: epochs 1990.8, 1993.8, 1997.4)

A methodology for precise determination of the fundamental geodetic parameter w 0, the potential value of the Gauss–Listing geoid, as well as its time derivative 0, is presented. The method is based on: (1) ellipsoidal harmonic expansion of the external gravitational field of the Earth to degree/order 360/360 (130 321 coefficients; http://www.uni-stuttgard.de/gi/research/ index.html projects) with respect to the International Reference Ellipsoid WGD2000, at the GPS positioned stations; and (2) ellipsoidal free-air gravity reduction of degree/order 360/360, based on orthometric heights of the GPS-positioned stations. The method has been numerically tested for the data of three GPS campaigns of the Baltic Sea Level project (epochs 1990.8,1993.4 and 1997.4). New w 0 and 0 values (w 0=62 636 855.75 ± 0.21 m2/s2, 0=−0.0099±0.00079 m2/s2 per year, w 0/&γmacr;=6 379 781.502 m,0/&γmacr;=1.0 mm/year, and &γmacr;= −9.81802523 m2/s2) for the test region (Baltic Sea) were obtained. As by-products of the main study, the following were also determined: (1) the high-resolution sea surface topography map for the Baltic Sea; (2) the most accurate regional geoid amongst four different regional Gauss–Listing geoids currently proposed for the Baltic Sea; and (3) the difference between the national height datums of countries around the Baltic Sea.

Hardy's multiquadric-biharmonic method for gravity field predictions II

The biharmonic equivalent of Poisson's equation is defined here as follows. The biharmonic operator on potential at a point density is double the right-hand side of Poisson's equation for the same point density. The mathematical proof of this and other matters are provided in the body of this presentation. This relationship has brought about the replacement of the point mass model with a point density model as the first step of the procedure. The point density model avoids the difficulties associated with point masses. Point masses produce impulse responses at zero distances. Point densities produce null responses at zero distances. Our point density model works extremely well for interpolating scattered geodetic surface data. The unknowns in our system of equations are interpretable as point density anomalies. It is customary to place the point density anomalies at shallow or near zero depths in the vicinity of the surface data. This cannot be done with points masses. We have not been concerned with the possible usefulness of the geodetically estimated point densities for other purposes. They simply provide the basis for smooth interpolation of several geodetic parameters, which fit data values exactly. In any case, we are not competing with seismologists who in a sense are measuring densities, instead of estimating them. In fact, we believe that geodetic interpolation could be improved with the use of seismic density data. That is why we are proposing a joint venture in seismic/geodetic subsurface analysis.

Determination of Geopotential Differences between Local Vertical Datums and Realization of a World Height System

The methodology developed for connecting Local Vertical Datums (LVD) was applied to the Australian Height Datum (AHD) and the North American Vertical Datum (NAVD88). The geopotential values at AHD and NAVD88 were computed and the corresponding vertical offset of 974 mm with rms 51 mm was obtained between the zero reference surfaces defined by AHD and NAVD88. The solution is based on the four primary geodetic parameters, the GPS/levelling sites and the geopotential model EGM96. The Global Height System (or the Major Vertical Datum) can be defined by a geoidal geopotential value used in the solution as the reference value, or by the geopotential value of the LVD, e.g. NAVD88.

Comparison of tropospheric gradients determined by VLBI and GPS

The estimation of geodetic parameters from GPS and VLBI requires the modeling of tropospheric refraction in order to account for the path delays of radio signals being emitted by extragalactic radio sources and satellites, respectively. Precise models consider the deviation from the azimuthal symmetry by introducing horizontal tropospheric gradients. While estimation of gradients had been included in the GPS software package GIPSY several years ago it was implemented in the BERNESE GPS software package (version 4.2) and in the VLBI software OCCAM (modified version 4.0) quite recently. We present a comparison of tropospheric gradient estimates derived with the three software packages mentioned above. The parameters have been estimated for the fundamental station Wettzell (Germany) for four VLBI experiments in the first half of 1999 (Euro48, Euro50, Iris 136, Iris 139) and for simultaneous GPS observations. The gradients obtained by the different software packages show a similar behaviour although offsets between the solutions can be as large as two millimeters. Astonishingly there is no better agreement between the two gradient estimates derived by GPS (BERNESE compared with GIPSY) than between gradients from the different techniques (OCCAM compared with GIPSY or BERNESE). This is probably due to the application of different estimation strategies by the GPS solutions.

Report of Special Commission 3 of IAG

AbstractSince the last presentation of SC-3 on numerical values of fundamental geodetic parameters at the IAU General Assembly at Kyoto in 1997 there were some conceptual as well as fundamental numerical changes. The four basic parameters of geodetic (ellipsoidal) reference systems (GRS) can no longer be considered as constant with time:J2,a, ω, and GM have to be replaced by clearly (±10−8or better) specified mean values or have to be associated with a specific epoch or, in case of GM, with specific reference frames (a= semi-major axis of Earth ellipsoid,J2= second degree zonal harmonic of geopotential,ω= spin of Earth rotation). In case of (a, J2....) associated tidal reductions must be specifically defined in view of particular applications and significant differences between different tidal reduction types. Or we may replace “a” by a quantity which is independent of tides like the geopotential at the geoid, W0, where, however, also temporal changes are now discussed. The official geodetic reference systems such as GRS 80 and WGS 84 (revised in 97-form) are also no longer truly representing reality; a new system GRS 2000 is desired. We are, meanwhile, able to define and determine tidal and non-tidal (secular, periodic, aperiodic) variatipns of some fundamental geodetic parameters. Others are under investigation. New precession and/or nutation formulas to be adopted by IAU in 2000 or later would imply, again, changes in geodetic parameters such asH= hydrostatic flattening. Those and related other consequences are considered.

Boundary-value problems in the complex world of geodetic measurements

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.

Atmospheric modelling in GPS analysis and its effect on the estimated geodetic parameters

Permanently operating Global Positioning System (GPS) receivers are used today, for example, in precise positioning and determination of atmospheric water vapour content. The GPS signals are delayed by various gases when traversing the atmosphere. The delay due to water vapour, the wet delay, is difficult to model using ground surface data and is thus often estimated from the GPS data. In order to obtain the most accurate results from the GPS processing, a modelling of the horizontal distribution of the wet delay may be necessary. Through simulations, three such models are evaluated, one of which is developed in this paper. In the first model the water vapour is assumed to be horizontally stratified, thus the wet delay can be described by only one zenith parameter. The second model gives the wet delay with one zenith and two horizontal gradient parameters. The third model uses the correlation between the wet-delay values in different directions. It is found that for large gradients and strong turbulence the two latter models yield lower errors in the estimated vertical coordinate and wet-delay parameters. For large gradients this improvement is up to 7 mm in the zenith wet-delay parameter, from 9 mm down to 2 and 4 mm for the second and third models, respectively.

AN EVALUATION OF SOME ROBUST ESTIMATION TECHNIQUES IN THE ESTIMATION OF GEODETIC PARAMETERS

Four robust estimation techniques are evaluated in respect of their efficiency and effectivenes through the estimation of geodetic parameters within the framework of a geodetic network. A theoretical geodetic network in which gross errors have been simulated is adopted for the study. Using each of the robust estimation techniques in turns, two versions of the network contaminated with gross errors are adjusted and the results compared with the case without gross errors. The results indicate that the robust estimation techniques have been able to cope quite effectively with the gross errors introduced into the observations. The different levels of effectiveness for the individual techniques are also indicated.

A Study Of Internal Structure Models And Dynamical Parameters Of Ganymede

Jupiter's satellite Ganymede is the largest natural satellite in the Solar System. As a result of the close encounter of Ganymede by the Galileo spacecraft in June and September 1996, the second zonal J2 and the second sectorial C22 Stokes parameters are now well determined (Anderson et al., 1996). Using the updated geodetic parameters, we have constructed a group of models for the internal structure of Ganymede, and have estimated some dynamical parameters for these models. A comparison with the Moon is made. The conclusion that can be drawn from this study is that, whereas Ganymede at present is in a state of hydrostatic equilibrium, this is certainly not the case for the Moon.