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A Terrestrial Reference Frame realised on the observation level using a GPS-LEO satellite constellation
Abstract
Applying a one-step integrated process, i.e. by simultaneously processing all data and determining all satellite orbits involved, a Terrestrial Reference Frame (TRF) consisting of a geometric as well as a dynamic part has been determined at the observation level using the EPOS-OC software of Deutsches GeoForschungsZentrum. The satellite systems involved comprise the Global Positioning System (GPS) as well as the twin GRACE spacecrafts. Applying a novel approach, the inherent datum defect has been overcome empirically. In order not to rely on theoretical assumptions this is done by carrying out the TRF estimation based on simulated observations and using the associated satellite orbits as background truth. The datum defect is identified here as the total of all three translations as well as the rotation about the z-axis of the ground station network leading to a rank-deficient estimation problem. To rectify this singularity, datum constraints comprising no-net translation (NNT) conditions in x, y, and z as well as a no-net rotation (NNR) condition about the z-axis are imposed. Thus minimally constrained, the TRF solution covers a time span of roughly a year with daily resolution. For the geometric part the focus is put on Helmert transformations between the a priori and the estimated sets of ground station positions, and the dynamic part is represented by gravity field coefficients of degree one and two. The results of a reference solution reveal the TRF parameters to be estimated reliably with high precision. Moreover, carrying out a comparable two-step approach using the same data and models leads to parameters and observational residuals of worse quality. A validation w.r.t. external sources shows the dynamic origin to coincide at a level of 5 mm or better in x and y, and mostly better than 15 mm in z. Comparing the derived GPS orbits to IGS final orbits as well as analysing the SLR residuals for the GRACE satellites reveals an orbit quality on the few cm level. Additional TRF test solutions demonstrate that K-Band Range-Rate observations between both GRACE spacecrafts are crucial for accurately estimating the dynamic frame’s orientation, and reveal the importance of the NNT- and NNR-conditions imposed for estimating the components of the dynamic geocenter.
... Our solution strategy also enables unified estimates for both geometric parameters (such as station coordinates) and dynamical parameters that describe the motion of satellites (cf. Haines et al., 2015Haines et al., , 2017Koenig, 2018). In this spirit, we have taken important steps toward a more unified solution for the TRF and the gravity field, taking advantage of the inextricable link between the two. ...
... Central to our TRF strategy is a rigorous combination of techniques at the observation level, rather than the station coordinate level (e.g., Diamantidis et al., 2021;Gambis et al., 2009;Haines et al., 2022;Koenig, 2018). This approach enables us to assess the solution from the perspective of the fundamental satellite tracking (GPS/SLR) and astronomical (VLBI) observations. ...
We describe the development and assessment of a new terrestrial reference frame (TRF) based on a combination of geodetic techniques at the observation level over the period 2010–2022. Included in the solution are observations from the Global Positioning System (GPS), Satellite Laser Ranging (SLR) and Very Long Baseline Interferometry (VLBI). A key feature of our solution strategy is the use of space ties in low‐Earth orbit to connect SLR to GPS. Though the resulting TRF solution is based on only 12.6 years of data, it is competitive with the international (ITRF2020) standard in terms of fundamental frame parameters (origin and scale) and their temporal evolution, both linear and seasonal. The relative rates of origin (3D) and scale (at Earth's surface) are 0.2 mm yr−1 and 0.1 mm yr−1 respectively. Absolute scale and 3D origin (at epoch 2015.0) both differ by 2–3 mm. In addition to station positions and velocities, our combined solution includes Earth orientation parameters (EOP), low‐degree zonal coefficients (J2 and J3) of the geopotential and precise orbit solutions for all participating satellites (GPS, GRACE and GRACE Follow‐on tandems, Jason 2 and 3, and LAGEOS 1 and 2). We discuss potential benefits of our solution strategy and characterize the impacts of our new TRF on estimates of geocenter motion and sea level change from satellite altimetry.
... The global terrestrial reference system (ITRS) is a dynamic system. It defines not only the coordinates of the stations at a certain epoch, but also their temporal variations, namely their velocities (Koenig 2018). In the 80's, accurate positioning through satellite measurements became increasingly popular due to precise accuracy and cost-effectiveness. ...
Increasing mobility of people and goods, as well as the rapid growth of users of mobile devices with positioning services expands constantly the need for geospatial information. Today, the challenge for suppliers and users or sellers and buyers is how to use this information to identify and accelerate profitable measures in public and private affairs like security, environment, resource, disaster and transportation or risk assessment for industry and insurers. In this context, georeferencing of geoinformation is the key instrument to visualise the location of events of interest. This paper deals with the background of spatial reference for precise positioning on the dynamic Earth and focuses on the ETRS89 regarding applications in real-estate cadaster and similar services provided by the official authorities.
... The realization of terrestrial reference frames based on active LEO was previously studied by, e.g., Haines Männel and Rothacher (2017), Koenig (2018), who focused on selected missions and the possibility of deriving origin, scale, and the orientation of the reference frames using LEO. SLR measurements to single active LEO satellites were used by Guo et al. (2018) together with the GPS-based kinematic orbits of GRACE-A for the determination of SLR station coordinates in 2012. ...
The number of satellites equipped with retroreflectors dedicated to Satellite Laser Ranging (SLR) increases simultaneously with the development and invention of the spherical geodetic satellites, low Earth orbiters (LEOs), Galileo and other components of the Global Navigational Satellite System (GNSS). SLR and GNSS techniques onboard LEO and GNSS satellites create the possibility of widening the use of SLR observations for deriving SLR station coordinates, which up to now have been typically based on spherical geodetic satellites. We determine SLR station coordinates based on integrated SLR observations to LEOs, spherical geodetic, and GNSS satellites orbiting the Earth at different altitudes, from 330 to 26,210 km. The combination of eight LEOs, LAGEOS-1/2, LARES, and 13 Galileo satellites increased the number of 7-day SLR solutions from 10-20% to even 50%. We discuss the issues of handling of range biases in multi-satellite combinations and the proper solution constraining and weighting. Weighted combination is characterized by a reduction of formal error medians of estimated station coordinates up to 50%, and the reduction of station coordinate residuals. The combination of all satellites with optimum weighting increases the consistency of station coordinates in terms of interquartile ranges by 10% of horizontal components for non-core stations w.r.t LAGEOS-only solutions.
... A large number of GNSS observations can be obtained from the massive number of stations among the many CORS networks, and these data can be used to establish reference frames (Koenig 2018), provide positioning services in urban canyons (Amir et al. 2018;Geng et al. 2019), and perform crustal monitoring (Milyukov et al. 2010). Obviously, scientific research on any of these topics depends significantly on high-accuracy and large-scale CORS network solutions. ...
The Global Navigation Satellite System (GNSS) has been an indispensable tool for geodetic surveying and geodynamics research and has rapidly developed over the past few years with abundant ground networks, modern constellations and multiple signal frequencies. However, due to increasing numbers of stations and satellites, the data processing burden has increased significantly. In this contribution, an improved parallel computing method is proposed for processing large GNSS network datasets. First, a parallelization strategy is introduced for the traditional GNSS processing model by analyzing the practicability of parallel integrated processing for GNSS network data. In addition, to maximize the advantages of modern microprocessors and local area network environments, we present the multi-core parallel computing of traditional GNSS data processing methods; then, the product is released as a service-oriented architecture that can be found and invoked through multiple nodes in the Internet. Obviously, this method combines the advantages of multi-core parallelism and network parallelism. Experiments show that the efficiency of the proposed method can be further increased with the accumulation of GNSS data and additional nodes. For example, in a network with 2000 stations, the efficiency of the parallel scheme with four quad-core nodes is at least 8 times faster than that of the traditional serial scheme. All the results demonstrate that the proposed strategy is an efficient and promising approach for processing large GNSS network datasets.
... There are also some studies on the integrated processing of ground-and space-based observations, mainly focusing on the estimation of Earth parameters, including gravity field parameters , the geocenter (Kuang et al. 2015;Männel and Rothacher 2017), and the terrestrial reference frame (König 2018). The integrated POD of GPS satellites and LEOs was also performed by several studies. ...
The precise orbit determination (POD) of Global Navigation Satellite System (GNSS) satellites and low Earth orbiters (LEOs) are usually performed independently. It is a potential way to improve the GNSS orbits by integrating LEOs onboard observations into the processing, especially for the developing GNSS, e.g., Galileo with a sparse sensor station network and Beidou with a regional distributed operating network. In recent years, few studies combined the processing of ground- and space-based GNSS observations. The integrated POD of GPS satellites and seven LEOs, including GRACE-A/B, OSTM/Jason-2, Jason-3 and, Swarm-A/B/C, is discussed in this study. GPS code and phase observations obtained by onboard GPS receivers of LEOs and ground-based receivers of the International GNSS Service (IGS) tracking network are used together in one least-squares adjustment. The POD solutions of the integrated processing with different subsets of LEOs and ground stations are analyzed in detail. The derived GPS satellite orbits are validated by comparing with the official IGS products and internal comparison based on the differences of overlapping orbits and satellite positions at the day-boundary epoch. The differences between the GPS satellite orbits derived based on a 26-station network and the official IGS products decrease from 37.5 to 23.9 mm (34% improvement) in 1D-mean RMS when adding seven LEOs. Both the number of the space-based observations and the LEO orbit geometry affect the GPS satellite orbits derived in the integrated processing. In this study, the latter one is proved to be more critical. By including three LEOs in three different orbital planes, the GPS satellite orbits improve more than from adding seven well-selected additional stations to the network. Experiments with a ten-station and regional network show an improvement of the GPS satellite orbits from about 25 cm to less than five centimeters in 1D-mean RMS after integrating the seven LEOs.
... Aufgrund der im Vergleich zu den anderen Beobachtungsverfahren der Weltraumgeodäsie (VLBI, GNSS, DORIS) geringen Störeinflüsse auf den Messprozess sowie die Bahnen der Kugelsatelliten liefert SLR einen enorm wichtigen Beitrag zur Bestimmung des Maßstabes. Außerdem sind insbesondere die zwei LAGEOS-Satelliten wegen ihrer niedrigen Umlaufbahn besonders sensitiv für das Massenzentrum der Erde und damit sehr wichtig für die Bestimmung des Ursprungs eines ITRF (siehe König, 2018). ...
The importance of global satellite navigation systems for everyday life and for numerous surveying tasks is well known to every user. Wherever positioning or navigation tasks are involved, GNSS devices for the use of GPS, GLONASS, Galileo or Beidou are used, which provide coordinates in a reference frame of a global geodetic reference system. What is less known is the elementary activities of the Federal Agency for Cartography and Geodesy (BKG) in global geodesy. The activities are integrated into international cooperation projects, which are primarily coordinated by the International Association of Geodesy (IAG) and its components. - Published in: VDV-Magazin : Geodäsie und Geoinformatik (ISSN 1863-1320) (2020) No. 5, p. 378-388. Online version: https://www.bkg.bund.de/SharedDocs/Downloads/BKG/DE/Downloads-Wettzell/Artikel-2020.html
... satellites, i.e., simultaneous orbit determination and parameter adjustment at the observation level, is beneficial for the determination of the terrestrial reference frame (TRF). However, the dynamic part of the TRF in König [20] is limited to the SH gravity field coefficients of degrees one and two and all parameters have been estimated daily. When expanding the parameter space of the gravity field to a maximum degree and order (d/o) of 90 or higher, typically for monthly GRACE gravity field solutions, which requires that daily NEQs need to be stacked to obtain a monthly solution, such an integrated approach becomes quite demanding in terms of computational efficiency and proper separation of daily and monthly Earth system and other parameters. ...
Time-variable gravity field models derived from observations of the Gravity Recovery and Climate Experiment (GRACE) mission, whose science operations phase ended in June 2017 after more than 15 years, enabled a multitude of studies of Earth’s surface mass transport processes and climate change. The German Research Centre for Geosciences (GFZ), routinely processing such monthly gravity fields as part of the GRACE Science Data System, has reprocessed the complete GRACE mission and released an improved GFZ GRACE RL06 monthly gravity field time series. This study provides an insight into the processing strategy of GFZ RL06 which has been considerably changed with respect to previous GFZ GRACE releases, and modifications relative to the precursor GFZ RL05a are described. The quality of the RL06 gravity field models is analyzed and discussed both in the spectral and spatial domain in comparison to the RL05a time series. All results indicate significant improvements of about 40% in terms of reduced noise. It is also shown that the GFZ RL06 time series is a step forward in terms of consistency, and that errors of the gravity field coefficients are more realistic. These findings are confirmed as well by independent validation of the monthly GRACE models, as done in this work by means of ocean bottom pressure in situ observations and orbit tests with the GOCE satellite. Thus, the GFZ GRACE RL06 time series allows for a better quantification of mass changes in the Earth system.
... The established GEO-based SBAS systems worldwide include the US wide area augmentation system (WAAS), the European geostationary navigation overlay service (EGNOS), the Japan multifunctional satellite augmentation system (MSAS), and the Indian global positioning system (GPS)-aided geo augmented navigation (GAGAN). Recently, LEObased SBAS has also driven much attention, and various missions have been launched, 7 such as Oneweb, Starlink, and China's Hongyan satellite constellation communication system. GBAS is developed on the basis of differential technique to improve positioning accuracy. ...
Global navigation satellite system signals are easily distorted by the interferences or disturbances, and global navigation satellite system receivers cannot offer continuous effective navigation results in challenging environments. As a representative regional augmentation technology, pseudolite has the potential to provide accurate positioning service to satisfy specific performance requirements in various applications. In this article, we developed a dynamic localization network based on pseudolite technology for regional augmentation navigation purpose. First, the collaborative positioning algorithm is given, and the architecture of localization system is proposed. Then the error sources of localization system are analyzed for performance evaluation. Finally, the proposed system is verified by experiments conducted in both static and kinenatic scenarios. The experiment results demonstrate that the positioning accuracy of the proposed localization system is nearly 10 m, which is close to the global navigation satellite system single-point positioning accuracy. Therefore, it can be used for emergency dynamic positioning of critical areas under the global navigation satellite system denial environments.
Geocenter motion between the center-of-mass of the Earth system (CM) and the center-of-figure of the solid Earth surface is a critical signature of degree-1 components of global surface mass transport process that includes sea level rise, ice mass imbalance, and continental-scale hydrological change. To complement GRACE data for complete-spectrum mass transport monitoring, geocenter motion needs to be measured accurately. However, current methods of geodetic translational approach and global inversions of various combinations of geodetic deformation, simulated ocean bottom pressure, and GRACE data contain substantial biases and systematic errors. Here, we demonstrate a new and more reliable unified approach to geocenter motion determination using a recently formed satellite laser ranging based geocentric displacement time series of an expanded geodetic network of all four space geodetic techniques and GRACE gravity data. The unified approach exploits both translational and deformational signatures of the displacement data, while the addition of GRACE’s near global coverage significantly reduces biases found in the translational approach and spectral aliasing errors in the inversion.
The Earth’s center of mass (CM) is defined in the satellite orbit dynamics as the center of mass of the entire Earth system, including the solid earth, oceans, cryosphere and atmosphere. Satellite Laser Ranging (SLR) provides accurate and unambiguous range measurements to geodetic satellites to determine variations in the vector from the origin of the ITRF to the CM. Estimates of the Global mass redistribution induced geocenter variations at seasonal scales from SLR are in good agreement with the results from the global inversion from the displacements of the dense network of GPS sites and from ocean bottom pressure model and GRACE-derived geoid changes.
We use a series of simulated scenarios to characterize the observability of geocenter location with GPS tracking data. We examine in particular the improvement realized when a GPS receiver in low Earth orbit (LEO) augments the ground network. Various orbital configurations for the LEO are considered and the observability of geocenter location based on GPS tracking is compared to that based on satellite laser ranging (SLR). The distance between a satellite and a ground tracking-site is the primary measurement, and Earth rotation plays important role in determining the geocenter location. Compared to SLR, which directly and unambiguously measures this distance, terrestrial GPS observations provide a weaker (relative) measurement for geocenter location determination. The estimation of GPS transmitter and receiver clock errors, which is equivalent to double differencing four simultaneous range measurements, removes much of this absolute distance information. We show that when ground GPS tracking data are augmented with precise measurements from a GPS receiver onboard a LEO satellite, the sensitivity of the data to geocenter location increases by more than a factor of two for Z-component. The geometric diversity underlying the varying baselines between the LEO and ground stations promotes improved global observability, and renders the GPS technique comparable to SLR in terms of information content for geocenter location determination. We assess a variety of LEO orbital configurations, including the proposed orbit for the geodetic reference antenna in space mission concept. The results suggest that a retrograde LEO with altitude near 3,000 km is favorable for geocenter determination.
The final publication is available at
https://link.springer.com/content/pdf/10.1007%2Fs00190-015-0792-6.pdf
The geocenter variations reflect the global scale mass redistribution and the interaction between the solid Earth and the mass load. Determination of the geocenter variations due to surface mass load from various geophysical sources places constraints on the variations of the origin of terrestrial reference frame, and provides the expected range of variations for space-geodesy. Our results suggest that on the time scale from 30 days to 10 years the primary variability of geocenter variations from atmosphere, ocean and surface ground water occurs on the annual and semiannual scales. The lumped sum of these surface mass load induced geocenter variations is within 1 cm level.
The GRACE mission is designed to track changes in the Earth's gravity
field for a period of five years. Launched in March 2002, the two GRACE
satellites have collected nearly two years of data. A span of data
available during the Commissioning Phase was used to obtain initial
gravity models. The gravity models developed with this data are more
than an order of magnitude better at the long and mid wavelengths than
previous models. The error estimates indicate a 2-cm accuracy uniformly
over the land and ocean regions, a consequence of the highly accurate,
global and homogenous nature of the GRACE data. These early results are
a strong affirmation of the GRACE mission concept.
ITRF2008 is a refined version of the International Terrestrial Reference Frame based on reprocessed solutions of the four
space geodetic techniques: VLBI, SLR, GPS and DORIS, spanning 29, 26, 12.5 and 16years of observations, respectively. The
input data used in its elaboration are time series (weekly from satellite techniques and 24-h session-wise from VLBI) of station
positions and daily Earth Orientation Parameters (EOPs). The ITRF2008 origin is defined in such a way that it has zero translations
and translation rates with respect to the mean Earth center of mass, averaged by the SLR time series. Its scale is defined
by nullifying the scale factor and its rate with respect to the mean of VLBI and SLR long-term solutions as obtained by stacking
their respective time series. The scale agreement between these two technique solutions is estimated to be 1.05 ± 0.13 ppb
at epoch 2005.0 and 0.049 ± 0.010ppb/yr. The ITRF2008 orientation (at epoch 2005.0) and its rate are aligned to the ITRF2005
using 179 stations of high geodetic quality. An estimate of the origin components from ITRF2008 to ITRF2005 (both origins
are defined by SLR) indicates differences at epoch 2005.0, namely: −0.5, −0.9 and −4.7mm along X, Y and Z-axis, respectively. The translation rate differences between the two frames are zero for Y and Z, while we observe an X-translation rate of 0.3mm/yr. The estimated formal errors of these parameters are 0.2mm and 0.2mm/yr, respectively. The
high level of origin agreement between ITRF2008 and ITRF2005 is an indication of an imprecise ITRF2000 origin that exhibits
a Z-translation drift of 1.8mm/yr with respect to ITRF2005. An evaluation of the ITRF2008 origin accuracy based on the level
of its agreement with ITRF2005 is believed to be at the level of 1cm over the time-span of the SLR observations. Considering
the level of scale consistency between VLBI and SLR, the ITRF2008 scale accuracy is evaluated to be at the level of 1.2ppb
(8mm at the equator) over the common time-span of the observations of both techniques. Although the performance of the ITRF2008
is demonstrated to be higher than ITRF2005, future ITRF improvement resides in improving the consistency between local ties
in co-location sites and space geodesy estimates.
KeywordsReference systems–Reference frames–ITRF–Earth rotation
Two 4.5-year sets of daily geocenter variations have been derived from GPS-LEO (Low-Earth Orbiter) tracking of the GRACE (Gravity
Recovery And Climate Experiment) satellites. The twin GRACE satellites, launched in March 2002, are each equipped with a BlackJack
global positioning system (GPS) receiver for precise orbit determination and gravity recovery. Since launch, there have been
significant improvements in the background force models used for satellite orbit determination, most notably the model for
the geopotential, which has resulted in significant improvements to the orbit determination accuracy. The purpose of this
paper is to investigate the potential for determining seasonal (annual and semiannual) geocenter variations using GPS-LEO
tracking data from the GRACE twin satellites. Internal comparison between the GRACE-A and GRACE-B derived geocenter variations
shows good agreement. In addition, the annual and semiannual variations of geocenter motions determined from this study have
been compared with other space geodetic solutions and predictions from geophysical models. The comparisons show good agreement
except for the phase of the z-translation component.
The development and numerical values of the new absolute phase-center correction model for GPS receiver and satellite antennas,
as adopted by the International GNSS (global navigation satellite systems) Service, are presented. Fixing absolute receiver
antenna phase-center corrections to robot-based calibrations, the GeoForschungsZentrum Potsdam (GFZ) and the Technische Universität
München reprocessed more than 10years of GPS data in order to generate a consistent set of nadir-dependent phase-center variations
(PCVs) and offsets in the z-direction pointing toward the Earth for all GPS satellites in orbit during that period. The agreement between the two solutions
estimated by independent software packages is better than 1mm for the PCVs and about 4cm for the z-offsets. In addition, the long time-series facilitates the study of correlations of the satellite antenna corrections with
several other parameters such as the global terrestrial scale or the orientation of the orbital planes with respect to the
Sun. Finally, completely reprocessed GPS solutions using different phase-center correction models demonstrate the benefits
from switching from relative to absolute antenna phase-center corrections. For example, tropospheric zenith delay biases between
GPS and very long baseline interferometry (VLBI), as well as the drift of the terrestrial scale, are reduced and the GPS orbit
consistency is improved.
The International GNSS Service (IGS) is an international activity involving more than 200 participating organisations in over
80 countries with a track record of one and a half decades of successful operations. The IGS is a service of the International
Association of Geodesy (IAG). It primarily supports scientific research based on highly precise and accurate Earth observations
using the technologies of Global Navigation Satellite Systems (GNSS), primarily the US Global Positioning System (GPS). The
mission of the IGS is “to provide the highest-quality GNSS data and products in support of the terrestrial reference frame,
Earth rotation, Earth observation and research, positioning, navigation and timing and other applications that benefit society”.
The IGS will continue to support the IAG’s initiative to coordinate cross-technique global geodesy for the next decade, via
the development of the Global Geodetic Observing System (GGOS), which focuses on the needs of global geodesy at the mm-level.
IGS activities are fundamental to scientific disciplines related to climate, weather, sea level change, and space weather.
The IGS also supports many other applications, including precise navigation, machine automation, and surveying and mapping.
This article discusses the IGS Strategic Plan and future directions of the globally-coordinated ~400 station IGS network,
tracking data and information products, and outlines the scope of a few of its numerous working groups and pilot projects
as the world anticipates a truly multi-system GNSS in the coming decade.
The International GNSS Service (IGS) contributes to the construction of the International Terrestrial Reference Frame (ITRF)
by submitting time series of station positions and Earth Rotation Parameters (ERP). For the first time, its submission to
the ITRF2008 construction is based on a combination of entirely reprocessed GPS solutions delivered by 11 Analysis Centers
(ACs). We analyze the IGS submission and four of the individual AC contributions in terms of the GNSS frame origin and scale,
station position repeatability and time series seasonal variations. We show here that the GPS Terrestrial Reference Frame
(TRF) origin is consistent with Satellite laser Ranging (SLR) at the centimeter level with a drift lower than 1mm/year. Although
the scale drift compared to Very Long baseline Interferometry (VLBI) and SLR mean scale is smaller than 0.4mm/year, we think
that it would be premature to use that information in the ITRF scale definition due to its strong dependence on the GPS satellite
and ground antenna phase center variations. The new position time series also show a better repeatability compared to past
IGS combined products and their annual variations are shown to be more consistent with loading models. The comparison of GPS
station positions and velocities to those of VLBI via local ties in co-located sites demonstrates that the IGS reprocessed
solution submitted to the ITRF2008 is more reliable and precise than any of the past submissions. However, we show that some
of the remaining inconsistencies between GPS and VLBI positioning may be caused by uncalibrated GNSS radomes.
KeywordsGNSS–Terrestrial reference frames–Loading–Geocenter motion–Systematic errors
The International Laser Ranging Service (ILRS) was established in September 1998 to support programs in geodetic, geophysical, and lunar research activities and to provide the International Earth Rotation Service (IERS) with products important to the maintenance of an accurate International Terrestrial Reference Frame (ITRF). Now in operation for nearly two years, the ILRS develops (1) the standards and specifications necessary for product consistency, and (2) the priorities and tracking strategies required to maximize network efficiency. The Service collects, merges, analyzes, archives and distributes satellite and lunar laser ranging data to satisfy a variety of scientific, engineering, and operational needs and encourages the application of new technologies to enhance the quality, quantity, and cost effectiveness of its data products. The ILRS works with (1) new satellite missions in the design and building of retroreflector targets to maximize data quality and quantity, and (2) science programs to optimize scientific data yield. The ILRS is organized into permanent components: (1) a Governing Board, (2) a Central Bureau, (3) Tracking Stations and Subnetworks, (4) Operations Centers, (5) Global and Regional Data Centers, and (6) Analysis, Lunar Analysis, and Associate Analysis Centers. The Governing Board, with broad representation from the international Satellite Laser Ranging (SLR) and Lunar Laser Ranging (LLR) community, provides overall guidance and defines service policies, while the Central Bureau oversees and coordinates the daily service activities, maintains scientific and technological data bases, and facilitates communications. Active Working Groups in (1) Missions, (2) Networks and Engineering, (3) Data Formats and Procedures, (4) Analysis, and (5) Signal Processing provide key operational and technical expertise to better exploit current capabilities and to challenge the ILRS participants to keep pace with evolving user needs. The ILRS currently includes more than 40 SLR stations, routinely tracking about 20 retroreflector-equipped satellites and the Moon in support of user needs.
When creating camera‐ready figures, most scientists are familiar with the sequence of raw data → processing → final illustration and with the spending of large sums of money to finalize papers for submission to scientific journals, prepare proposals, and create overheads and slides for various presentations. This process can be tedious and is often done manually, since available commercial or in‐house software usually can do only part of the job.
To expedite this process, we introduce the Generic Mapping Tools (GMT), which is a free, public domain software package that can be used to manipulate columns of tabular data, time series, and gridded data sets and to display these data in a variety of forms ranging from simple x‐y plots to maps and color, perspective, and shaded‐relief illustrations. GMT uses the PostScript page description language, which can create arbitrarily complex images in gray tones or 24‐bit true color by superimposing multiple plot files. Line drawings, bitmapped images, and text can be easily combined in one illustration. PostScript plot files are device‐independent, meaning the same file can be printed at 300 dots per inch (dpi) on an ordinary laserwriter or at 2470 dpi on a phototypesetter when ultimate quality is needed. GMT software is written as a set of UNIX tools and is totally self contained and fully documented. The system is offered free of charge to federal agencies and nonprofit educational organizations worldwide and is distributed over the computer network Internet.
For the first time in the International Terrestrial Reference Frame (ITRF) history, the ITRF2014 is generated with an enhanced modeling of non-linear station motions, including seasonal (annual and semi-annual) signals of station positions and post-seismic deformation for sites that were subject to major earthquakes. Using the full observation history of the four space geodetic techniques (VLBI, SLR, GNSS, DORIS), the corresponding international services provided reprocessed time series (weekly from SLR and DORIS, daily from GNSS and 24-hour session-wise from VLBI) of station positions and daily Earth Orientation Parameters (EOPs). ITRF2014 is demonstrated to be superior to past ITRF releases, as it precisely models the actual station trajectories leading to a more robust secular frame and site velocities. The ITRF2014 long-term origin coincides with the Earth system center of mass as sensed by SLR observations collected on the two LAGEOS satellites over the time-span between 1993.0 and 2015.0. The estimated accuracy of the ITRF2014 origin, as reflected by the level of agreement with the ITRF2008 (both origins are defined by SLR) is at the level of less than 3 mm at epoch 2010.0 and less than 0.2 mm/yr in time evolution. The ITRF2014 scale is defined by the arithmetic average of the implicit scales of SLR and VLBI solutions as obtained by the stacking of their respective time series. The resulting scale and scale rate differences between the two solutions are 1.37 (± 0.10) ppb at epoch 2010.0 and 0.02 (± 0.02) ppb/yr. While the post-seismic deformation models were estimated using GNSS/GPS data, the resulting parametric models at earthquake co-location sites were applied to the station position time series of the three other techniques, showing a very high level of consistency which enforces more the link between techniques within the ITRF2014 frame. The users should be aware that the post-seismic deformation models are part of the ITRF2014 products, unlike the annual and semi-annual signals, which were estimated internally with the only purpose of enhancing the velocity field estimation of the secular frame.
Satellite laser ranging (SLR) has monitored for a long time the continuous redistribution of mass within the Earth system through concomitant changes in the Stokes’ coefficients of the terrestrial gravity field. JCET’s latest analysis of the 1993-present SLR data set from LAGEOS and LAGEOS 2 data for the IERS (International Earth Rotation Service) Terrestrial Reference Frame (ITRF) includes the weekly monitoring of such compound changes in the low degree and order harmonics. Along with the static parameters of the TRF we have determined a time series of variations of its origin with respect to the center of mass of the Earth system (geocenter). These estimates provide a measure of the total motion due to all unaccounted sources of mass transport within the Earth system and can be used to either complement the estimates from the future missions or to validate them through comparisons with their estimates for the same quantities. The data were reduced using NASA Goddard’s GEODYN and SOLVE II software, resulting to a final RMS error of ~8 mm.
CHAMP is a German small satellite mission aiming at the simultaneous precise observation of both the gravity and magnetic field from a low altitude orbit. Thanks to the dedicated orbit design, an unprecedented low altitude in a near polar orbit, its continuous undisturbed observation of the magnetic field vector through scalar and vector magnetometers and its continuous GPS satellite-to-satellite tracking capability together with a direct on-board measurement of the nongravitational orbit perturbations, a dramatic improvement in the global modeling of the magnetic field and also an order of magnitude improvement for the broad to mesoscale structures of the gravity field can be expected. In addition, due to the designed 5 years mission duration, temporal changes in both fields will be detectable with a higher signal/noise ratio and at increased spatial resolution as it is possible now. CHAMP was successfully launched on 15 July 2000.
We describe a terrestrial reference frame (TRF) realization based on Global Positioning System (GPS) data alone. Our approach rests on a highly dynamic, long-arc (9-d) estimation strategy and on GPS satellite antenna calibrations derived from GRACE and TOPEX/Poseidon low-Earth orbit (LEO) receiver GPS data. Based on nearly 17 years of data (1997–2013), our solution for scale rate agrees with ITRF2008 to 0.03 ppb yr-1 and our solution for 3D-origin rate agrees with ITRF2008 to 0.4 mm yr-1. Absolute scale differs by 1.1 ppb (7 mm at the Earth's surface) and 3D origin by 8 mm. These differences lie within estimated error levels for the contemporary TRF.
The long wavelength part of the Earth’s gravity field can be determined, with varying accuracy, from satellite laser ranging (SLR). In this study, we investigate the combination of up to ten geodetic SLR satellites using iterative variance component estimation. SLR observations to different satellites are combined in order to identify the impact of each satellite on the estimated Stokes coefficients. The combination of satellite-specific weekly or monthly arcs allows to reduce parameter correlations of the single-satellite solutions and leads to alternative estimates of the second-degree Stokes coefficients. This alternative time series might be helpful for assessing the uncertainty in the impact of the low-degree Stokes coefficients on geophysical investigations. In order to validate the obtained time series of second-degree Stokes coefficients, a comparison with the SLR RL05 time series of the Center of Space Research (CSR) is done. This investigation shows that all time series are comparable to the CSR time series. The precision of the weekly/monthly C21 and S21 coefficients is analyzed by comparing mass-related equatorial excitation functions χmass1,2 with geophysical model results and reduced geodetic excitation functions. In case of χmass1 , the annual amplitude and phase of the DGFI solution agrees better with three of four geophysical model combinations than other time series. In case of χmass2 , all time series agree very well to each other. The impact of C20 on the ice mass trend estimates for Antarctica are compared based on CSR GRACE RL05 solutions, in which different monthly C20 time series are used for replacing. We found differences in the long-term Antarctic ice loss of 12.3 Gt/year between the GRACE solutions induced by the different C20 SLR time series of CSR and DGFI, which is about 13 % of the total ice loss of Antarctica. This result shows that Antarctic ice mass loss quantifications must be carefully interpreted.
The problem of observing geocenter motion from global navigation satellite system (GNSS) solutions through the network shift approach is addressed from the perspective of collinearity (or multicollinearity) among the parameters of a least-squares regression. A collinearity diagnosis, based on the notion of variance inflation factor, is therefore developed and allows handling several peculiarities of the GNSS geocenter determination problem. Its application reveals that the determination of all three components of geocenter motion with GNSS suffers from serious collinearity issues, with a comparable level as in the problem of determining the terrestrial scale simultaneously with the GNSS satellite phase center offsets. The inability of current GNSS, as opposed to satellite laser ranging, to properly sense geocenter motion is mostly explained by the estimation, in the GNSS case, of epoch-wise station and satellite clock offsets simultaneously with tropospheric parameters. The empirical satellite accelerations, as estimated by most Analysis Centers of the International GNSS Service, slightly amplify the collinearity of the geocenter coordinate, but their role remains secondary.
Satellite Laser Ranging (SLR) data to LAGEOS, ETALON and to Global Navigation Satellite Systems (GNSS) were combined with GNSS microwave data for 5 years. Including SLR data to GNSS satellites and estimating common orbit parameters allows it to connect both space-geodetic techniques using satellite instead of station co-location. We show that only SLR data to the spherical satellites can improve the geocenter estimates, whereas SLR data to the GNSS satellites suffer from the same GNSS orbit modelling deficiencies as in the analysis of microwave data.
The horizontal transport of water in Earth's surface layer, including
sea level change, deglaciation, and surface runoff, is a manifestation
of many geophysical processes. These processes entail ocean and
atmosphere circulation and tidal attraction, global climate change, and
the hydrological cycle, all having a broad range of spatiotemporal
scales. The largest atmospheric mass variations occur mostly at synoptic
wavelengths and at seasonal time scales. The longest wavelength
component of surface mass transport, the spherical harmonic degree-1,
involves the exchange of mass between the northern and southern
hemispheres. These degree-1 mass loads deform the solid Earth, including
its surface, and induce geocenter motion between the center-of-mass of
the total Earth system (CM) and the center-of-figure (CF) of the solid
Earth surface. Because geocenter motion also depends on the mechanical
properties of the solid Earth, monitoring geocenter motion thus provides
an additional opportunity to probe deep into Earth's interior. Most
modern geodetic measurement systems rely on tracking data between ground
stations and satellites that orbit around CM. Consequently, geocenter
motion is intimately related to the realization of the International
Terrestrial Reference Frame (ITRF) origin, and, in various ways, affects
many of our measurement objectives for global change monitoring. In the
last 15 years, there have been vast improvements in geophysical fluid
modeling and in the global coverage, densification, and accuracy of
geodetic observations. As a result of these developments, tremendous
progress has been made in the study of geocenter motion over the same
period. This paper reviews both the theoretical and measurement aspects
of geocenter motion and its implications.
Time series of geocenter coordinates were determined with data of two global navigation satellite systems (GNSSs), namely the U.S. GPS (Global Positioning System) and the Russian GLONASS (Global’naya Nawigatsionnaya Sputnikowaya Sistema). The data was recorded in the years 2008–2011 by a global network of 92 permanently observing GPS/GLONASS receivers. Two types of daily solutions were generated independently for each GNSS, one including the estimation of geocenter coordinates and one without these parameters.
High-resolution global gravity field models play a fundamental role in geodesy and Earth sciences, ranging from practical purposes, like precise orbit determination, to scientific applications, like investigations of the density structure of the Earth's interior. We report on the latest combined EIGEN-model (EIGEN = European Improved Gravity model of the Earth by New techniques), which is complete to degree and order 720 and was jointly elaborated by GFZ Potsdam and CNES/GRGS Toulouse. It is the first EIGEN model inferred from a combination of GRACE and GOCE data (2 months, November-December 2009), enhanced with the DNSC08 surface gravity data. The combination of GRACE and GOCE data allows the construction of an accurate satellite-only model to degree and order 240, the gradiometer data of the latter contributing only to degrees upwards of 100. This is achieved through filtering of the GOCE observation equations, which is necessary because of the degraded gradiometer performance outside the measurement bandwidth. Analyses of gradiometer residuals calculated with ITG10S, EIGEN-5C and EGM2008 as background models revealed considerable model errors in current combined gravity field models caused by the inclusion low-quality and/or low resolution surface data in particular over South America, Africa, the Himalayas and New Guinea. Therefore, the combination procedure of satellite and surface data was revisited in order to mitigate this error source. In particular, the surface data normal equations are combined with satellite normal equations at a higher degree than presently applied (for instance at degree 70 in EIGEN-5C). The comparison of test results (orbit computation, GPS leveling) of this latest EIGEN model with a GOCE-only model, EGM08 and ITG10S demonstrates the gain in accuracy at high degrees, while its performance is identical to a GRACE-only model for the low degrees.
Crustal motion can be described as a vector displacement field, which depends on both the physical deformation and the reference frame. Self-consistent descriptions of surface kinematics must account for the dynamic relationship between the Earth's surface and the frame origin at some defined center of the Earth, which is governed by the Earth's response to the degree-one spherical harmonic component of surface loads. Terrestrial reference frames are defined here as “isomorphic” if the computed surface displacements functionally accord with load Love number theory. Isomorphic frames are shown to move relative to each other along the direction of the load's center of mass. The following frames are isomorphic: center of mass of the solid Earth, center of mass of the entire Earth system, no-net translation of the surface, no-net horizontal translation of the surface, and no-net vertical translation of the surface. The theory predicts different degree-one load Love numbers and geocenter motion for specific isomorphic frames. Under a change in center of mass of surface load in any isomorphic frame, the total surface displacement field consists not only of a geocenter translation in inertial space, but must also be accompanied by surface deformation. Therefore estimation of geocenter displacement should account for this deformation. Even very long baseline interferometry (VLBI) is sensitive to geocenter displacement, as the accompanying deformation changes baseline lengths. The choice of specific isomorphic frame can facilitate scientific interpretation; the theory presented here clarifies how coordinate displacements and horizontal versus vertical motion are critically tied to this choice.
In the analyses of geodetic very long baseline interferometry (VLBI) and GPS data the analytic form used for mapping of the atmosphere delay from zenith to the line of site is most often a three-parameter continued fraction in 1/sin(elevation). Using the 40 years reanalysis (ERA-40) data of the European Centre for Medium-Range Weather Forecasts for the year 2001, the b and c coefficients of the continued fraction form for the hydrostatic mapping functions have been redetermined. Unlike previous mapping functions based on data from numerical weather models (isobaric mapping functions (Niell, 2000) and Vienna mapping functions (VMF) (Boehm and Schuh, 2004)), the new c coefficients are dependent on the day of the year, and unlike the Niell mapping functions (Niell, 1996) they are no longer symmetric with respect to the equator (apart from the opposite phase for the two hemispheres). Compared to VMF, this causes an effect on the VLBI or GPS station heights that is constant and as large as 2 mm at the equator and that varies seasonally between 4 mm and 0 mm at the poles. The updated VMF, based on these new coefficients and called VMF1 hereinafter, yields slightly better baseline length repeatabilities for VLBI data. The hydrostatic and wet mapping functions are applied in various combinations with different kinds of a priori zenith delays in the analyses of all VLBI International VLBI Service for Geodesy and Astrometry (IVS)-R1 and IVS-R4 24-hour sessions of 2002 and 2003; the investigations concentrate on baseline length repeatabilities, as well as on absolute changes of station heights.
Review of the 4th edition "... The growing society of GPS users and designers could be very grateful for the efforts of both the authors and the publisher resulting in the fourth, revised edition of this splendid reference book within six years ... The continous updating and revising make this book an excellent standard reference on GPS for theoreticians and practicians in the future. Acta Geodaetica, Geophysica et Montanistica Hungarica
Weekly surface loading variations are estimated from a joint least squares inversion of load-induced GPS site displacements, GRACE gravimetry and simulated ocean bottom pressure (OBP) from the finite element sea-ice ocean model (FESOM).
In this study, we directly use normal equations derived from reprocessed GPS observations, where station and satellite positions are estimated simultaneously. The OBP weight of the model in the inversion is based on a new error model, obtained from 2 FESOM runs forced with different atmospheric data sets.
Our findings indicate that the geocenter motion derived from the inversion is smooth, with non-seasonal RMS values of 1.4, 0.9 and 1.9 mm for the X, Y and Z directions, respectively. The absolute magnitude of the seasonal geocenter motion varies annually between 2 and 4.5 mm. Important hydrological regions such as the Amazon, Australia, South-East Asia and Europe are mostly affected by the geocenter motion, with magnitudes of up to 2 cm, when expressed in equivalent water height.
The chosen solar radiation pressure model, used in the GPS processing, has only a marginal effect on the joint inversion results. Using the empirical CODE model slightly increases the annual amplitude of the Z component of the geocenter by 0.8 mm. However, in case of a GPS-only inversion, notable larger differences are found for the annual amplitude and phase estimates when applying the older physical ROCK models. Regardless of the used radiation pressure model the GPS network still exhibits maximum radial expansions in the order of 3 mm (0.45 ppb in terms of scale), which are most likely caused by remaining GPS technique errors.
In an additional experiment, we have used the joint inversion solution as a background loading model in the GPS normal equations. The reduced time series, compared to those without a priori loading model, show a consistent decrease in RMS. In terms of the annual height component, 151 of the 189 stations show a reduction of at least 10% in seasonal amplitude.
On the ocean floor, we find a positive overall correlation (0.51) of the inversion solution with time series from globally distributed independent bottom pressure recorders.
Even after removing a seasonal fit we still find a correlation of 0.45. Furthermore, the geocenter motion has a significant effect on ocean bottom pressure as neglecting it causes the correlation to drop to 0.42.
A key geodetic contribution to both the three Global Observing Systems and initiatives like the European Global Monitoring for Environment and Security is an accurate, long-term stable, and easily accessible reference frame as the backbone. Many emerging scientific as well as non-scientific high-accuracy applications require access to an unique, technique-independent reference frame decontaminated for short-term fluctuations due to global Earth system processes. Such a reference frame can only be maintained and made available through an observing system such as the Global Geodetic Observing System (GGOS), which is currently implemented and expected to provide sufficient information on changes in the Earth figure, its rotation and its gravity field. Based on a number of examples from monitoring of infrastructure, point positioning, maintenance of national references frames to global changes studies, likely future accuracy requirements for a global terrestrial reference frame are set up as function of time scales. Expected accuracy requirements for a large range of high-accuracy applications are less than 5 mm for diurnal and sub-diurnal time scales, 2–3 mm on monthly to seasonal time scales, better than 1 mm/year on decadal to 50 years time scales. Based on these requirements, specifications for a geodetic observing system meeting the accuracy requirements can be derived.
Satellite Laser Ranging (SLR) observations to Global Navigation Satellite System (GNSS) satellites may be used for several
purposes. On one hand, the range measurement may be used as an independent validation for satellite orbits derived solely
from GNSS microwave observations. On the other hand, both observation types may be analyzed together to generate a combined
orbit. The latter procedure implies that one common set of orbit parameters is estimated from GNSS and SLR data. We performed
such a combined processing of GNSS and SLR using the data of the year 2008. During this period, two GPS and four GLONASS satellites
could be used as satellite co-locations. We focus on the general procedure for this type of combined processing and the impact
on the terrestrial reference frame (including scale and geocenter), the GNSS satellite antenna offsets (SAO) and the SLR range
biases. We show that the combination using only satellite co-locations as connection between GNSS and SLR is possible and
allows the estimation of SLR station coordinates at the level of 1–2cm. The SLR observations to GNSS satellites provide the
scale allowing the estimation of GNSS SAO without relying on the scale of any a priori terrestrial reference frame. We show
that the necessity to estimate SLR range biases does not prohibit the estimation of GNSS SAO. A good distribution of SLR observations
allows a common estimation of the two parameter types. The estimated corrections for the GNSS SAO are 119mm and −13mm on
average for the GPS and GLONASS satellites, respectively. The resulting SLR range biases suggest that it might be sufficient
to estimate one parameter per station representing a range bias common to all GNSS satellites. The estimated biases are in
the range of a few centimeters up to 5cm. Scale differences of 0.9ppb are seen between GNSS and SLR.
KeywordsInter-technique combination–Satellite co-locations–Terrestrial reference frame–GNSS satellite antenna offset–SLR range bias
In this article we highlight the advances in gravity field recovery with CHAMP and GRACE, leading to the new GFZ release 04
(RL04) EIGEN (European Improved Gravity field of the Earth by New techniques) models. RL04 consists of time series of monthly
CHAMP and GRACE gravity models, pure weekly GRACE solutions and combined static fields from satellite-only and terrestrial
data. Additionally a new mean CHAMP-only gravity field model has been generated. It becomes obvious that the improvements
in the RL04 background modelling, processing standards and strategies have led to significant improvements in the reprocessed
gravity field models. These new RL04 EIGEN models, available for nearly the whole CHAMP and GRACE mission periods, provide
an important data base to monitor mass transport and mass distribution phenomena in the system Earth, such as the continental
hydrological cycle, ice mass loss in Antarctica and Greenland, ocean mass changes or the ocean surface topography.
KeywordsEIGEN-gravity models-Global gravity field modelling-Mass distribution-Mass transport
Various types of observations, such as space-borne Global positioning system (GPS) code and phase data, accelerometer data, K-band range and range-rate data, and ground-based satellite laser ranging data of the CHAllenging Minisatellite Payload (CHAMP) and GRAvity Climate Experiment (GRACE) satellite missions, are used together with ground-based GPS code and phase data in a rigorous adjustment to eventually solve for the ephemerides of the CHAMP, GRACE, and GPS satellites, geocenter variations, and low-degree gravity field parameters. It turns out that this integrated adjustment considerably improves the accuracy of the ephemerides for the high and low satellites, geocenter variations, and gravity field parameters, compared to the case when the adjustment is carried out stepwise or in individual satellite solutions.
With the advent of Space geodesy techniques in early eighties, global terrestrial reference frames became available whose precision is still improving parallel to measuring and modeling advances.As a global reference, the realization of the International Terrestrial Reference System (ITRS), known as the International Terrestrial Reference Frame (ITRF), maintained by the International Earth Rotation Service, has sustained substantial improvement and enhancement. One of the major new trends is the 2000 ITRS realization, to be considered as a standard solution for a wide user community (geodesy, geophysics, astronomy, etc.). The ITRF2000 comprises on one hand primary core stations observed by VLBI, LLR, GPS, SLR and DORIS techniques and, on the other hand, significant extension provided by regional GPS networks for densifications as well as other useful geodetic markers tied to space geodetic ones.The ITRF2000 combination and implementation strategy are described in this paper. Important results in terms of datum definition as well as quality assessment of the ITRF2000 are presented.
Possibilities and limits for estimating a dynamic and a geometric reference frame origin by the integrated approach applied to the CHAMP-GRACE-GPS constellation
- D Koenig
- R König
IERS conventions 2010 Verlag des Bundesamts für Kartographie und Geodäsie, Frankfurt am Main, IERS technical note 36
- G Petit
- B Luzum
Global geodetic observing system-meeting requirements of a global geodetic society on a changing planet in 2020
Geodesy, third completely revised and extended edition. de Gruyter
- W Torge
Verlag des Bundesamts für Kartographie und Geodäsie
- G Petit
- B Luzum