In this work we analyze the integrity properties of an affine-constrained estimator applied to arrays of GNSS antennas. GNSS pseudorange and carrier phase measurements from multiple antennas whose relative positions are known are cast in a linearly-constrained observation model. The linear constraints are inherent to an affine transformation that is applied to the baseline coordinates. The affine transformation yields enhanced redundancy, thus improving the model integrity properties with respect to the unconstrained model. The extent of the improvement is measured in terms of internal and external reliability.

The transformation between European Center for Medium-range Weather Forecast (ECMWF) model level assimilations and the refractivity at any given point of the neutral atmosphere has been investigated. We first present the IFS interpolations and extrapolations of each physical parameter done in operations at ECMWF. These formulae are used to compute, for example, pressure levels from model levels at ECMWF. We use this formulation to compute the pressure levels, the large majority of which are found similar to the pressure levels provided by ECMWF with an appropriate accuracy for ray-tracing. The IFS-based scheme (IFS-BS) is then presented. It is an adaptation of the interpolations and extrapolations done at ECMWF for troposphere delay computation by ray-tracing. This scheme ensures the coherence with the ECMWF meteorological model and is used in our software Horizon designed to compute the Adaptive Mapping Functions (AMF). In the IFS-BS, vertical interpolations are adapted for each thermodynamic parameter necessary to precisely rebuild the refractivity along the ray path according to the physical laws. In order to take into account the atmospheric part between the lowest model level and the Earth’s topography during the ray-tracing, extrapolation of physical parameters below the lowest model level are included. The proposed scheme is expected to be relevant for applications where accuracy of refractivity is important as troposphere delay modelling for high-accuracy geodesy.

Surface mass transfer produces changes in the terrestrial geometric reference frame that are clearly detectable by GNSS techniques. These deformations are mainly observed in the vertical coordinate component and show periodic behavior with seasonal cycles. Therefore, the assumption that the kinematics of the reference frame has a linear behavior is no longer sufficient.

This study focuses on a model of crustal vertical deformations caused by surface loading variations in the South American region. Thirty-four locations were analyzed in order to adjust a parametric exponential function that relates height changes with mass pressure variations.

This parametric function depends on regional rheological properties. Crustal deformations were characterized using multi-annual GPS time series provided by SIRGAS and the surface loading information was derived from GRACE spherical harmonic coefficients provided by GRGS (Release 2). The proposed parametric model was able to properly reproduce inter-annual variations observed in vertical displacement in a 9-year time-span (2003–2012). This study will contribute to a better understanding the kinematics of the reference frame and the elastic parameters on a regional scale.

This study investigates seasonal to interannual changes in regional sea level caused by the recent replacement of the geopotential model EIGEN-GL04S_annual by the model EIGEN-6S for the precise orbit determination of satellite altimeters. We have analysed the radial orbit components for the Envisat, ERS-2 and TOPEX missions originating from two orbit solutions processed at the GeoForschungsZentrum (GFZ). These orbits were computed almost identically except for the use of the two different geopotential models mentioned above. An alternative orbit solution for Envisat provided by the European Space Operations Centre based on the model EIGEN-6C has been analysed as well. Empirical Orthogonal Functions (EOF) of the detrended radial orbit differences have been applied to study the typical spatio-temporal scales. The dominant EOF modes for all orbit differences exhibit large-scale bipolar patterns with opposite phase suggestive of apparent shifts of the origins of the different orbit solutions. In case the geopotential model is replaced the detrended radial orbit differences for all three missions are dominated by annual oscillations. The spatial patterns of these annual oscillations are similar for all three missions, with the TOPEX patterns and the ERS-2/Envisat patterns being out of phase. The annual amplitude reaches 5 mm at its maxima which corresponds to up to ∼10% of the annual sea level signal itself for some locations. In addition, it accounts for annual changes of the height gradient between the two maxima of the first EOF-patterns of up to 1 cm with inverse changes for TOPEX and ERS-2/Envisat.

Several high resolution global geopotential models have been published in recent years. Two of them are EGM2008 and EIGEN-6C2, which have accuracies on the order of 3–20 cm in Europe and Australia. However, part of this accuracy is related to the high number of gravity observations available in these areas. In Africa there are still many regions without terrestrial gravity observations such as north Mozambique. Using the results of a recent terrestrial gravity campaign in north-west Mozambique we conclude that the error of the EGM2008 and EIGEN-6C2 here is still on the order of ± 60 cm, which strongly limits their use for many scientific and technical applications.

We present a Kalman filter for combining dUT1 from the VLBI Intensive sessions with GNSS results for rapid estimation of dUT1. In order to be able to also combine polar motion, pre-reduced normal equations for the Intensive sessions are used in the Kalman filter. We validate our results by comparing with dUT1 estimates from standard global 24-h VLBI sessions. It is found that the Kalman filter is able to use the polar motion measured by GNSS to properly correct the errors in dUT1 caused by inaccurate a priori polar motion. Furthermore, we investigate how the coordinates of the Tsukuba VLBI station can be handled in the analysis after the Tōhoku (Japan) Earthquake in 2011.

In general, any national or regional height reference system is related to an individual vertical datum, defined by one or several tide gauges. The discrepancies of these local vertical datums cause height datum offsets in a range of about ±1–2 m at a global scale. For the purpose of height system unification, global geopotential models derived from homogeneous satellite data provide an important contribution. However, to achieve a unification of high precision, the use of local terrestrial gravity data in the framework of a Geodetic Boundary Value Problem (GBVP) is required. By solving the GBVP at GNSS/leveling benchmarks, the unknown height datum offsets can be estimated in a least squares adjustment. In contrast to previous studies, related to the scalar free GBVP based on gravity anomalies, this paper discusses the alternative use and benefit of the fixed GBVP. This modern formulation of the GBVP is related to gravity disturbances, using the surface of the Earth as boundary surface. In contrast to gravity anomalies, gravity disturbances are not affected by the discrepancies of the local height datum. Therefore, in comparison to a scalar free GBVP approach, the proposed method is not affected by indirect bias terms, which will simplify a height system unification. In this paper, the theory of the fixed GBVP approach is developed and formulas in spherical approximation are derived. Moreover, the method is validated using a closed loop simulation based on the global geopotential model EGM2008, showing mm-accuracy of the estimated height datum offsets.

This paper investigates the capability of observing tropical cyclones using satellite radar altimetry. Two representative cyclones Yasi (February 2011) and Larry (March 2006) in the northeast Australian coastal area are selected based also on available tide gauge sea level measurements. It is shown that altimetry data can capture high water levels induced by Larry and Yasi through a careful re-processing and re-editing of the data. About 18 years of data from multi-satellite altimetry missions including TOPEX/Poseidon, Jason-1 and Jason-2, and seven tide gauges around the northern Australian coast are integrated using a multivariate regression approach. The results reveal that the multi-regression model can, in general, explain >60 % of sea level variances in the study area. The model is then validated using independent data from tide gauge in Townsville. The comparison results indicate that the high sea levels predicted by the model taken into account of both altimetry and tide-gauge data agree well with those observed at Townsville during cyclone Larry.

Earth Orientation Parameters (EOP) provide the rotation of the International Terrestrial Reference System (ITRS) to the Geocentric Celestial Reference System (GCRS) as a function of time. When estimating a Celestial Reference Frame (CRF) usually a number of radio sources with a long history of observations and stable positions are included in the datum used to define the orientation of the frame. How many and which radio sources are taken into account for the datum definition has a significant effect on the estimated EOP. In this study we analyze the effects of different options for the celestial datum definition on the precision of the EOP and on the agreement w.r.t the last realization of the International Celestial Reference Frame (ICRF2; Fey et al., The second realization of the international celestial reference frame by very long baseline interferometry, IERS Technical Note No. 35, 2009). The resulting EOP of the special VLBI session IYA09 are compared to the C04 08 EOP series (Bizouard and Gambis, The combined solution C04 for Earth orientation parameters consistent with international terrestrial reference frame 2008, IERS Notice 2011, 2011). The analysis shows that the smallest uncertainties for EOP are achieved when the maximum number of defining sources is chosen for the datum. Comparing with a typical VLBI session, the precision of the EOP and the agreement of the axes w.r.t. ICRF2 could be improved if more defining sources, especially in the southern hemisphere, were considered.

Real-time monitoring of crustal deformation is important in achieving rapid understanding of earthquake magnitude and fault model. Recently, an algorithm called Real-time Automatic detection method for Permanent Displacement (“

RAPiD

”) has been developed to detect/estimate static ground displacements due to earthquake faulting from real-time kinematic (RTK)-GPS time series. We applied this algorithm to the 2011 off Ibaraki earthquake (M

w

7.7), which occurred only 30 min after the 2011 Tohoku-Oki earthquake (M

w

9.0). The

RAPiD

algorithm worked well with the long baseline RTK-GPS time series for quasi real-time coseismic displacement detection and estimation. A quasi real-time fault determination was also attempted with an automatic detection/estimation displacement field. We found that the estimated moment release reached M

w

7.7 60 s after the origin time, almost the same as the actual seismic moment for this earthquake. We also assessed the long-term stability of the RTK-GPS time series under a 200-km baseline condition. We found the time series precision degraded slightly in summer compared with winter. However, the total stability is good for monitoring crustal deformation. These results suggest clearly that using real-time GPS data in conjunction with the

RAPiD

algorithm can provide rapid coseismic fault determination, even for consecutive large earthquakes.

Over the last few years numerous GPS networks in Italy have been installed and managed, mainly by local authorities and institutions. Therefore the GPS stations have been constructed with a variety of different monument types according to their needs and have been operated in fairly different environmental conditions, such as in towns or industrial regions, in the open country or mountainous regions. In this work we aim to assess the reliability and repeatability of the station positions and to study the noise property of different categories of GPS monument types. We analyze over 500 continuous GPS time series in Italy with a mean temporal length of 5.6 years. All the GPS observations were processed with the Bernese v5.0 software using a loose constraints approach. We include 45 sites in central Europe that are used as fiducial stations in the regional reference frame realization. After fitting a linear drift, offsets and annual sinusoids and after filtering a common mode movement of the whole network, the residual GPS time series represents the noise of each GPS station. We analyze the residuals using different power spectrum estimation schemes and estimate a power law noise model for each time series. The average noise characteristics are compatible with outcomes from earlier studies but we were not able to isolate distinct noise behaviors between different GPS monument types nor to ascertain a preferred monumentation, as far as noise amplitude and spectral indexes are concerned.

Precise point positioning is attractive for numerous applications as it does not require the exchange of raw measurements between reference stations. In this paper, a Kalman filter is used to perform precise point positioning with dual-frequency code and carrier phase measurements, to estimate the receiver position, clock offset, tropospheric zenith delay, ionospheric slant delays and the absolute ambiguities. One improvement is to avoid the correlation between the height component and the tropospheric state by estimating the latter state with intervals. Additionally, a joint estimation of the ambiguity subset and their integer ambiguities is presented. The method differs from conventional partial fixing schemes by taking the stability of the float solution into account. The proposed method is tested with real GPS measurements, and a positioning accuracy in the order of a few centimeters is achieved.

In this paper, a methodology for automatic scheduling of Very Long Baseline Interferometry (VLBI) observations of satellites is presented and first scheduling approaches are investigated. For this investigation the orbit of a geostationary satellite has been chosen, but, the methodology has also been successfully applied to an orbit of a Global Navigation Satellite Systems satellite. A scheduling procedure based on covariance optimization is developed and observations are simulated. In contrast to other simulation studies for a dedicated VLBI satellite mission, we are performing a scheduling process where observations of quasars and satellites are considered being equally important. Thus, the satellites are consistently included into a VLBI experiment. To validate the individual schedules, simplistic daily constant orbit shifts are estimated and analyzed. In this way, the necessary time between two subsequent satellite observations and the geometry of the observing network are investigated. Taking into account all circumstances, large global networks are the best option for estimating orbit shifts. Such a configuration leads to a large number of observations and a good observing geometry for the orbit. For a geostationary satellite, it is sufficient to carry out only one observation per hour or even longer. However, the presented results are only valid for the estimation of orbit shifts. Various improvements of these initial investigations are imaginable, e.g., considering orbit parameters within the scheduling process or estimating realistic orbit parameters.

The Geological Survey of Japan (GSJ), which is a section of the National Institute of Advanced Industrial Science and Technology (AIST), has conducted gravity surveys throughout Japan. The GSJ launched the online gravity database known as “GALILEO” on the GSJ website. The GALILEO source data are included in the Gravity CD-ROM/DVD of Japan from the GSJ. GALILEO supports three main functions: (1) browsing and downloading of raster data (with or without accompanying descriptions) or vector data (e.g., KMZ files), (2) comparisons of gravity maps with geological or topographic maps of the same area (using a JAVA applet), and (3) on-demand mapping using Generic Mapping Tools, which enables GALILEO users to visualize Bouguer anomaly maps on different assumed densities of the surface rocks. These quick views of the gravity anomaly maps through GALILEO are useful for users accessing the database. Gravity data compiled by the GSJ have contributed towards a better understanding of various aspects of the geology of Japan, especially as related to disaster prediction and response.

We constructed a buoy system for real-time observations of tsunamis and crustal deformation in collaboration with the Japan Agency for Marine-Earth Science and Technology, Tohoku University, and the Japan Aerospace Exploration Agency. The most important characteristics of our system are resistance to the strong sea currents in the large-earthquake rupture zone around Japan (e.g., the Kuroshio maximum speed > 5 knots), and the capability to transmit data in real-time. Our system has four units: (1) a buoy station with a GPS/Acoustic station serving as a central base, (2) a wire-end station (WES) 1,000 m below the sea surface that serves as a staging base, (3) a pressure seafloor unit (PSU) comprising a pressure sensor, and (4) six GPS/Acoustic transponders to measure crustal deformation. The pressure data used to detect tsunamis and the vertical component of crustal deformation are sent to the land station via the wire-end and buoy stations at intervals of 1 h in normal mode and 15 s in tsunami mode. The data measured between the buoy and six transponders are also sent to the land station at 1-week intervals. The Iridium satellite is used for data transmission of all data to land station. The dynamic range for pressure observations is + ∕− 8 m with a fine resolution of 2 mm, and the accuracy of the crustal deformation measurements is less than 1 m. We tuned the system for an observation period of 5 months and carried out a sea trial. The length of the observation period influences the total system due to the weight of the battery. We rearranged the geometry of the total system to new one with heavier weight and a lot of batteries on the buoy considering long period observation and decided upon a slack ratio of 1.6. In addition, it is important for a long observation period to minimize electrical consumption. We used double pulses for acoustic data transmission between the PSU and WES. The time difference between two pulses indicates the observed pressure value. For the PSU, we designed a tsunami mode on the basis of data from the tsunami generated by the 2011 earthquake off Tohoku, which were recorded by cabled network system data and offline bottom pressure data. The results confirmed that a tsunami can be detected even if the first tsunami signals include strong-motion signals. In this case, the tsunami was detected 10–20 s after the first seismic arrival. During sea trials, we successfully tested the tsunami mode we designed. We succeeded real-time observation of pressure and crustal deformation using buoy system in strong sea current speed area for 5 months. However, there are some issues to be resolved at this moment. For acoustic data transmission, 1 ms step difference of the detection of acoustic signals at the WES, wrong detection of the multiple phases are issues to be resolved. We will consider assigned mapping of transmitted data to the time difference of the double pulses and take measures on the PSU and WES. In addition, we consider strategy to reduce slack ratio in the future. For data transmission from the WES to the buoy station, we experienced electrical unhealthy of the wire rope due to damages by the fisheries activities and the torsion brought by rotation of the buoy. We consider the countermeasure to reduce the rotation.

Vertical gravity gradient plays an important role in the research of the Earth’s gravity field. However, the measurement of the vertical gravity gradient is a hard work. With the fast development of the Earth’s gravity field modeling technique, it is possible to accurately approximate the vertical gravity gradient with the aid of the gravity field model as well as increasing gravity anomalies and rich terrain data. In the paper, a theoretical analysis was made on the computation of the vertical gravity gradient firstly, and then three methods, the gravity potential model method, the remove-restore method, and the point mass method, were used to accurately approximate the anomaly of the vertical gravity gradient. Tests of the three methods were made using some actual measurements of vertical gravity gradient over some area in China, and analyses were also made. Comparisons among the three methods show that the point mass method has the highest accuracy in approximation. At the end of the paper, some issues on the vertical gravity gradient to be further investigated were proposed.

Recent surface movements in the Upper Rhine Graben (URG) area are investigated with geodetic techniques. Line of sight (LOS) displacement rates from SAR interferometry (InSAR), horizontal and vertical rates from coordinate time series of permanent GNSS sites and vertical rates from precise levelling measurements are estimated with high accuracy. We show that the data sets are capable of providing detailed insight into the current movements in the URG area, which is required for a better understanding of geodynamic processes as well as for a reasonable exploitation of geopotentials in the URG. This paper focusses on a comparison of results from InSAR and levelling on a regional and on a local scale. A case study highlights temporal differences in the deformation characteristics of an oil extraction area detected from ERS-1/2 and Envisat data as well as from levelling measurements in multiple epochs. In order to benefit from the advantages of each technique, our work aims on a proper combination to consistently link the different observation methods in a rigorous multi-technique approach.

GNSS antenna changes are in particular critical for the long-term stability of the coordinate time series and the reference systems realized with these stations. Depending on the antenna types and the available antenna calibrations, discontinuities of up to several centimeters can be introduced. Therefore, a monitoring of the antenna changes is important to verify the continuity of the time series.In order to add Galileo tracking capability the GNSS equipment at the Icelandic IGS stations Reykjavik and Hoefn had to be replaced. Temporary GNSS sites were set up in the vicinity of both sites. These short baselines are analyzed with different observables. In addition, the temporary sites were included in the routine processing of the Center for Orbit Determination in Europe analysis center of the IGS. The equipment changes introduced discontinuities of up to 1.5 cm in the coordinates derived from the global solution. Depending on the analysis strategy and observables used, the results of the short baselines differ by up to 2.5 cm.

Real-time orbit and clock corrections to GPS broadcast ephemeris, in short broadcast corrections (BCs), have become available as International GNSS Service (IGS) products through the IGS Real-time Service (RTS) in 2013. The BCs are distributed via the Network Transport of RTCM by Internet Protocol (NTRIP) according to RTCM State Space Representation standards. When applying the BCs in real-time Precise Point Positioning (PPP), user positions with sub-decimetre precision after convergence can be obtained. The IGS BCs refer to the International Terrestrial Reference Frame 2008 (ITRF2008). BCs in regional reference frames (RBCs) are available through regional NTRIP broadcasters in Europe, North-America, South-America and Australia. The IGS RTS website states that:

Applying orbit and clock corrections from regional product streams in a real-time PPP solution automatically leads to regional coordinates. The PPP client would not need to transform coordinates because that is already done on the server side.

However, in contrast to the PPP-approach that uses BCs in ITRF2008 followed by a transformation to the local datum, the approach based on RBCs causes a bias in the PPP solution due to the scale factor between regional and global reference frames. This scale induced bias is satellite geometry dependent when the conventional 14-parameter transformation from the global to the regional reference frame is applied to the satellite position vectors in ITRF2008, to derive the RBCs from the IGS BCs. The size of the scale induced bias is significant. The bias is up to 8 cm for the Australian GDA94 and up to 0.5 cm for the North American NAD83. Currently an additional satellite position dependent value is added to the satellite clock correction to deal with the scale induced biases of three RBCs, resulting in a transformed clock correction (Weber, BKG Ntrip Client (BNC) Version 2.9 – Manual, 2013). Applying these transformed clocks results in a remaining scale induced bias of less then 10 mm for each RBC of ETRF2000, NAD83 and SIRGAS2000. For GDA94 the remaining scale induced bias is maximum 30 m, this is caused by the large scale factor of GDA94 compared to other regional reference frames. This contribution will show that the remaining bias in the PPP solution is practically independent from satellite geometry and depends mainly on the user position; hence the remaining bias can be predicted and corrected for at any location.

Satellite positioning is evolving rapidly, with the deployment of Galileo and BeiDou systems, in addition to the modernisation programmes for GPS and GLONASS. At the time of writing, the BeiDou constellation consists of 5 Geostationary Orbit (GEO), 5 Geosynchronous Orbit (IGSO) and 4 Medium-Earth Orbit (MEO) satellites. The constellation design is particularly interesting as it allows visibility of a sufficient number of BeiDou satellites over Asia for autonomous positioning. In this paper, possibilities for real-time precise point positioning (PPP) using BeiDou are explored. For real-time generation of orbit and clock products, observation data from Fugro’s proprietary station network are used, together with data from the IGS Multi-GNSS Experiment (MGEX). In order to perform orbit estimation, the NAPEOS (Navigation Package for Earth Orbiting Satellites) software has been extended for processing BeiDou data. Satellite orbits are generated every hour and include a predicted part which can be used for real-time positioning. In order to estimate the accuracy of the real-time orbit, a validation with post-processed products is presented. A Kalman filter has been extended to process BeiDou observation data, in order to estimate satellite clock biases in real-time. For precise point positioning, Fugro’s kinematic PPP engine is used. The engine is fed with real-time orbits and clocks, as well as observation data from test receivers. Kinematic PPP results are presented, in real-time and post-processing, including BeiDou standalone and in combination with GPS.