Station Coordinates Research Articles

Present-day surface deformation of the Alpine region inferred from geodetic techniques

Abstract. We provide a present-day surface-kinematics model for the Alpine region and surroundings based on a high-level data analysis of about 300 geodetic stations continuously operating over more than 12 years. This model includes a deformation model, a continuous surface-kinematic (velocity) field, and a strain field consistently assessed for the entire Alpine mountain belt. Special care is given to the use of the newest Global Navigation Satellite Systems (GNSS) processing standards to determine high-precision 3-D station coordinates. The coordinate solution refers to the reference frame IGb08, epoch 2010.0. The mean precision of the station positions at the reference epoch is ±1.1 mm in N and E and ±2.3 mm in height. The mean precision of the station velocities is ±0.2 mm a−1 in N and E and ±0.4 mm a−1 in height. The deformation model is derived from the point-wise station velocities using a geodetic least-squares collocation (LSC) approach with empirically determined covariance functions. According to our results, no significant horizontal deformation is detected in the Western Alps, while across the Southern and Eastern Alps the deformation vectors describe a progressive eastward rotation towards Pannonia. This kinematic pattern also makes evident an increasing magnitude of the deformation from 0.1 mm a−1 in the western part of Switzerland up to about 1.3 mm a−1 in the Austrian Alps. The largest shortening is observed along the southern front of the Eastern Alps (in the northern area of the Venetian-Friuli Basin) and in the northern part of the Apennine Peninsula, where rates reach 2 and 3 mm a−1, respectively. The average accuracy of the horizontal deformation model is ±0.2 mm a−1. Regarding the vertical kinematics, our results clearly show an ongoing average uplift rate of 1.8 mm a−1 of the entire mountain chain, with the exception of the southern part of the Western Alps, where no significant uplift (less than 0.5 mm a−1) is detected. The fastest uplift rates (more than 2 mm a−1) occur in the central area of the Western Alps, in the Swiss Alps, and in the Southern Alps in the boundary region between Switzerland, Austria, and Italy. The general uplift observed across the Alpine mountain chain decreases towards the outer regions to stable values between 0.0 and 0.5 mm a−1 and, in some cases, to subsidence like in the Liguro-Provençal and Vienna basins, where vertical rates of −0.8 and −0.3 mm a−1 are observed, respectively. In the surrounding region, three regional subsidence regimes are identified: the Rhône-Bresse Graben with −0.8 mm a−1, the Rhine Graben with −1.3 mm a−1, and the Venetian-Friuli Basin with −1.5 mm a−1. The estimated uncertainty of our vertical motion model across the Alpine mountain belt is about ±0.3 mm a−1. The strain field inferred from the deformation model shows two main contrasting strain regimes: (i) shortening across the south-eastern front of the Alps and the northern part of the Dinarides and (ii) extension in the Apennines. The pattern of the principal strain axes indicates that the compression directions are more or less perpendicular to the thrust belt fronts, reaching maximum values of 20×10-9 a−1 in the Venetian-Friuli and Po basins. Across the Alpine mountain belt, we observe a slight dilatation regime in the Western Alps, which smoothly changes to a contraction regime in western Austria and southern Germany, reaching maximum shortening values of 6×10-9 a−1 in north-eastern Austria. The numerical results of this study are available at https://doi.pangaea.de/10.1594/PANGAEA.886889.

The IERS EOP 14C04 solution for Earth orientation parameters consistent with ITRF 2014

The Earth Orientation Center of the International Earth Rotation and Reference Systems Service (IERS) has the task to provide the scientific community with the international reference time series of Earth orientation parameters (EOP), referred to as IERS EOP C04 or C04. These series result from a combination of operational EOP series derived from VLBI, GNSS, SLR, and DORIS. The C04 series were updated to provide EOP series consistent with the set of station coordinates of the ITRF 2014. The new C04, referred to as IERS EOP 14C04, is aligned onto the most recent versions of the conventional reference frames (ITRF 2014 and ICRF2). Additionally, the combination algorithm was revised to include an improved weighting of the intra-technique solutions. Over the period 2010–2015, differences to the IVS combination exhibit standard deviations of 40 $$\upmu $$ as for nutation and 10 $$\upmu $$ s for UT1. Differences to the IGS combination reveal a standard deviation of 30 $$\upmu $$ as for polar motion. The IERS EOP 14C04 was adopted by the IERS directing board as the IERS reference series by February 1, 2017.

Approach for GPS precise time transfer using an augmentation information and zero‐differenced PPP model

This study proposes an approach for global positioning system (GPS) precise time transfer using the augmentation information and zero-differenced precise point positioning (PPP) models. The augmentation information can be real-time generated by constraining the coordinates of the reference stations, it is the difference between the observed distance and the real distance from the satellite to the receiver after considering the modelling errors. As the augmentation information contains the ionosphere delay, troposphere delay, receiver clock, phase ambiguities, ephemeris residuals and the other un-modelling errors, thus some common errors are eliminated and/or reduced after used the augmentation information, then the zero-differenced PPP model can be used for data solution and precise time transfer service. Two pairs of datasets were used to validate the feasibility and effectiveness of the proposed approach. The results show that the accuracy and stability of time transfer are greatly improved by the new approach, especially for the zero baseline. Compared with the traditional PPP time transfer approach, which relies on the precise ephemeris, the new approach used the augmentation correction which contains the ephemeris residuals, thus it can be operated by both precise ephemeris and broadcast ephemeris, and is hence more effective for real-time operation.

Study of Soligorsk Salt Tailings Piles while Using Up-To-Date Geodetic Technologies

. Intensive development of the Starobinsk deposit is related with formation of salt tailings piles which are annually increasing and they have already reached the height of 120–150 m, their volume constitutes 1.5 billion tons and their area is equal up to »3000 ha. Such situation leads to activation of geodynamic processes, salting of soil and underground water. For this reason study of salt tailings piles with the help of up-to-date geodetic technologies is considered as the most efficient methods for environmental protection. Geodetic innovation technologies for study of salt tailings relief include the following: creation of plan and height control along relief perimeter and route of equipment motion within salt tailings pile with the help GPS-system; experimental study of salt tailings relief while using an electronic tacheometer with reflectorless regime; import of total station coordinates in software package LISCAD Plus where simulation of salt tailings is formed; study of digital salt tailings simulation and its interpretation. More accurate study of salt tailings is carried out by laser scanning while using scanner Leica ScanStation C10. Operations from several stations are executed with the purpose to obtain data on salt tailings and these operations provide their complete survey. Results of the survey are loaded into a computer; the data is compiled together and so a digital simulation of salt tailings is obtained. An advantage of laser scanning is complete automation and due to this accuracy is increased significantly and time required for the survey is reduced. Such approach makes it possible to increase efficiency in various measures directed on improvement of environmental conditions.

Consistent estimation of geodetic parameters from SLR satellite constellation measurements

In this paper, we consistently estimate geodetic parameters such as weekly 3-D station coordinates, Earth orientation parameters (EOP) including daily x/y-pole coordinates and the excess length of day $$\Delta \hbox {LOD}$$ , and selected weekly Earth’s gravitational field (Stokes) coefficients up to degree and order 6 from Satellite Laser Ranging measurements to up to 11 geodetic satellites. The SLR constellation consists of LAGEOS-1/2, Etalon-1/2, Stella, Starlette, Ajisai, Larets, LARES, BLITS and WESTPAC, and its observations cover a time span of 38 years ranging from February 16, 1979, to April 30, 2017. If multiple satellites with various altitudes and orbit inclinations are combined, correlations between estimated parameters are significantly reduced. This allows us (i) to investigate the ability of satellite constellations to reduce existing correlations and (ii) to estimate reliable parameters with higher precision compared to the standard 4-satellite constellation (LAGEOS-1/2, Etalon-1/2) which is currently used by the International Laser Ranging Service for the determination of the Terrestrial Reference Frame (TRF) and EOP products. In particular, the Stokes coefficients, EOP and TRF datum parameters (three translations, three rotations, one scale factor), which are highly correlated with satellite-specific orbit parameters, are improved. From our investigations, we found for an 11-satellite solution compared to the above-mentioned 4-satellite solution a decrease in the scatter of the TRF datum parameters of up to 37%, the transformation residuals are decreased by up to 22%, the scatter of the EOP is decreased by up to 22%, and their mean values are decreased by up to 84% w.r.t. the reference solutions. The largest improvement is obtained for the Stokes coefficients which significantly benefit from a combination of multiple satellites (inclinations and orbit altitudes). In total, single coefficients are improved by up to 93% and the overall improvement is up to 74%. Moreover, it could be clearly identified that Ajisai significantly disturbs the TRF solution due to an erroneous center-of-mass correction. We further quantify the impact of specific satellites on the determination of different geodetic parameters and finally evaluate the potential of the existing SLR-tracked spherical satellite constellation to support the goals of GGOS.

On Base Station Coordination in Cache- and Energy Harvesting-Enabled HetNets: A Stochastic Geometry Study

In this paper, we study the performance of base station (BS) coordination in heterogeneous networks (HetNets) with cache-enabled and renewable energy-powered small cell BSs (SBSs). Macrocell base stations (MBSs) provide basic coverage, while the SBSs, powered by harvested energy, conduct content-aware coordinated transmission to provide high data rate and further improve the network coverage. Specifically, a joint transmission strategy is performed based on the knowledge of the energy states and the cached contents of SBSs, along with the awareness of the availability of channel resources and the average received signal strength (RSS) of the corresponding link. Stochastic geometry is applied to characterize the statistics of the cell load at MBSs and SBSs, as well as the aggregated information and interference signal strength. Then, the average user capacity for the joint transmission is obtained. Additionally, the coverage probability is derived with gamma approximation for the aggregated information and interference signal strength. Analytical results reveal that the average user capacity and coverage probability can be maximized with optimal cache size, energy harvesting rate and cooperative RSS threshold. Finally, extensive numerical and simulation results are provided.

On the long-term stability of terrestrial reference frame solutions based on Kalman filtering

The Global Geodetic Observing System requirement for the long-term stability of the International Terrestrial Reference Frame is 0.1 mm/year, motivated by rigorous sea level studies. Furthermore, high-quality station velocities are of great importance for the prediction of future station coordinates, which are fundamental for several geodetic applications. In this study, we investigate the performance of predictions from very long baseline interferometry (VLBI) terrestrial reference frames (TRFs) based on Kalman filtering. The predictions are computed by extrapolating the deterministic part of the coordinate model. As observational data, we used over 4000 VLBI sessions between 1980 and the middle of 2016. In order to study the predictions, we computed VLBI TRF solutions only from the data until the end of 2013. The period of 2014 until 2016.5 was used to validate the predictions of the TRF solutions against the measured VLBI station coordinates. To assess the quality, we computed average WRMS values from the coordinate differences as well as from estimated Helmert transformation parameters, in particular, the scale. We found that the results significantly depend on the level of process noise used in the filter. While larger values of process noise allow the TRF station coordinates to more closely follow the input data (decrease in WRMS of about 45%), the TRF predictions exhibit larger deviations from the VLBI station coordinates after 2014 (WRMS increase of about 15%). On the other hand, lower levels of process noise improve the predictions, making them more similar to those of solutions without process noise. Furthermore, our investigations show that additionally estimating annual signals in the coordinates does not significantly impact the results. Finally, we computed TRF solutions mimicking a potential real-time TRF and found significant improvements over the other investigated solutions, all of which rely on extrapolating the coordinate model for their predictions, with WRMS reductions of almost 50%.

An approach for real-time fast point positioning of the BeiDou Navigation Satellite System using augmentation information

This study proposes an approach to facilitate real-time fast point positioning of the BeiDou Navigation Satellite System (BDS) based on regional augmentation information. We term this as the precise positioning based on augmentation information (BPP) approach. The coordinates of the reference stations were highly constrained to extract the augmentation information, which contained not only the satellite orbit clock error correlated with the satellite running state, but also included the atmosphere error and unmodeled error, which are correlated with the spatial and temporal states. Based on these mixed augmentation corrections, a precise point positioning (PPP) model could be used for the coordinates estimation of the user stations, and the float ambiguity could be easily fixed for the single-difference between satellites. Thus, this technique provided a quick and high-precision positioning service. Three different datasets with small, medium, and large baselines (0.6 km, 30 km and 136 km) were used to validate the feasibility and effectiveness of the proposed BPP method. The validations showed that using the BPP model, 1–2 cm positioning service can be provided in a 100 km wide area after just 2 s of initialization. Thus, as the proposed approach not only capitalized on both PPP and RTK but also provided consistent application, it can be used for area augmentation positioning.

Satellite laser ranging as a tool for the recovery of tropospheric gradients

Space geodetic techniques, such as Global Navigation Satellite Systems (GNSS) and Very Long Baseline Interferometry (VLBI) have been extensively used for the recovery of the tropospheric parameters. Both techniques employ microwave observations, for which the troposphere is a non-dispersive medium and which are very sensitive to the water vapor content. Satellite laser ranging (SLR) is the only space geodetic technique used for the definition of the terrestrial reference frames which employs optical – laser observations. The SLR sensitivity to the hydrostatic part of the troposphere delay is similar to that of microwave observations, whereas the sensitivity of laser observations to non-hydrostatic part of the delay is about two orders of magnitude smaller than in the case of microwave observations. Troposphere is a dispersive medium for optical wavelengths, which means that the SLR tropospheric delay depends on the laser wavelength. This paper presents the sensitivity and capability of the SLR observations for the recovery of azimuthal asymmetry over the SLR stations, which can be described as horizontal gradients of the troposphere delay. For the first time, the horizontal gradients are estimated, together with other parameters typically estimated from the SLR observations to spherical LAGEOS satellites, i.e., station coordinates, earth rotation parameters, and satellite orbits. Most of the SLR stations are co-located with GNSS receivers, thus, a cross-correlation between both techniques is possible. We compare our SLR horizontal gradients to GNSS results and to the horizontal gradients derived from the numerical weather models (NWM). Due to a small number of the SLR observations, SLR is not capable of reconstructing short-period phenomena occurring in the atmosphere. However, the long-term analysis allows for the recovery of the atmosphere asymmetry using SLR. As a result, the mean offsets of the SLR-derived horizontal gradients agree to the level of 47%, 74%, 54% with GNSS, hydrostatic delay, and total delay from NWM, respectively. SLR can be thus employed as a tool for the recovery of the atmospheric parameters with a major sensitivity to the hydrostatic part of the delay.

A new global grid model for the determination of atmospheric weighted mean temperature in GPS precipitable water vapor

In ground-based global positioning system (GPS) meteorology, atmospheric weighted mean temperature, $$T_\mathrm{m}$$ , plays a very important role in the progress of retrieving precipitable water vapor (PWV) from the zenith wet delay of the GPS. Generally, most of the existing $$T_\mathrm{m} $$ models only take either latitude or altitude into account in modeling. However, a great number of studies have shown that $$T_\mathrm{m} $$ is highly correlated with both latitude and altitude. In this study, a new global grid empirical $$T_\mathrm{m} $$ model, named as GGTm, was established by a sliding window algorithm using global gridded $$T_\mathrm{m} $$ data over an 8-year period from 2007 to 2014 provided by TU Vienna, where both latitude and altitude variations are considered in modeling. And the performance of GGTm was assessed by comparing with the Bevis formula and the GPT2w model, where the high-precision global gridded $$T_\mathrm{m} $$ data as provided by TU Vienna and the radiosonde data from 2015 are used as reference values. The results show the significant performance of the new GGTm model against other models when compared with gridded $$T_\mathrm{m} $$ data and radiosonde data, especially in the areas with great undulating terrain. Additionally, GGTm has the global mean $$\hbox {RMS}_{\mathrm{PWV}} $$ and $$\hbox {RMS}_{\mathrm{PWV}} /\hbox {PWV}$$ values of 0.26 mm and 1.28%, respectively. The GGTm model, fed only by the day of the year and the station coordinates, could provide a reliable and accurate $$T_\mathrm{m} $$ value, which shows the possible potential application in real-time GPS meteorology, especially for the application of low-latitude areas and western China.

THE FOUNDATION GPS WATER VAPOR INVERSION AND ITS APPLICATION RESEARCH

Abstract. Using GPS technology to retrieve atmospheric water vapor is a new water vapor detection method, which can effectively compensate for the shortcomings of conventional water vapor detection methods, to provide high-precision, large-capacity, near real-time water vapor information. In-depth study of ground-based GPS detection of atmospheric water vapor technology aims to further improve the accuracy and practicability of GPS inversion of water vapor and to explore its ability to detect atmospheric water vapor information to better serve the meteorological services. In this paper, the influence of the setting parameters of initial station coordinates, satellite ephemeris and solution observation on the total delay accuracy of the tropospheric zenith is discussed based on the observed data. In this paper, the observations obtained from the observation network consisting of 8 IGS stations in China in June 2013 are used to inverse the water vapor data of the 8 stations. The data of Wuhan station is further selected and compared with the data of Nanhu Sounding Station in Wuhan The error between the two data was between -6mm-6mm, and the trend of the two was almost the same, the correlation reached 95.8 %. The experimental results also verify the reliability of ground-based GPS inversion of water vapor technology.

Satellite laser ranging to low Earth orbiters: orbit and network validation

Satellite laser ranging (SLR) to low Earth orbiters (LEOs) provides optical distance measurements with mm-to-cm-level precision. SLR residuals, i.e., differences between measured and modeled ranges, serve as a common figure of merit for the quality assessment of orbits derived by radiometric tracking techniques. We discuss relevant processing standards for the modeling of SLR observations and highlight the importance of line-of-sight-dependent range corrections for the various types of laser retroreflector arrays. A 1–3 cm consistency of SLR observations and GPS-based precise orbits is demonstrated for a wide range of past and present LEO missions supported by the International Laser Ranging Service (ILRS). A parameter estimation approach is presented to investigate systematic orbit errors and it is shown that SLR validation of LEO satellites is not only able to detect radial but also along-track and cross-track offsets. SLR residual statistics clearly depend on the employed precise orbit determination technique (kinematic vs. reduced-dynamic, float vs. fixed ambiguities) but also reveal pronounced differences in the ILRS station performance. Using the residual-based parameter estimation approach, corrections to ILRS station coordinates, range biases, and timing offsets are derived. As a result, root-mean-square residuals of 5–10 mm have been achieved over a 1-year data arc in 2016 using observations from a subset of high-performance stations and ambiguity-fixed orbits of four LEO missions. As a final contribution, we demonstrate that SLR can not only validate single-satellite orbit solutions but also precise baseline solutions of formation flying missions such as GRACE, TanDEM-X, and Swarm.

Decoupling 5G Network Control: Centralised Coordination and Distributed Adaptation

Fifth generation mobile networks (5G) will be featured by miniaturised cells and massive dense deployment. Traditional centralised network control cannot adapt to high signalling delay, and is therefore not scalable for future 5G networks.To address this issue, we adopt the software-defined networking (SDN) approach of decoupled network control and data transmission. In particular, delay-sensitive interference suppression for data transmission is decoupled from delay-tolerant topology control and base station coordination. This substantially alleviates the requirement of network control on delay and complexity, hence simplifying 5G control plane design, reducing signalling overhead, and enhancing network scalability. Case studies show that our decoupled network control is effective for timely interference mitigation and reliable topology management. The stability and scalability of our approach are also demonstrated.

Estimates of Environmental Exposure to Radiofrequency Electromagnetic Fields and Risk of Lymphoma Subtypes.

We investigated the association between environmental exposure to radiofrequency electromagnetic fields (RF-EMF) and risk of lymphoma subtypes in a case-control study comprised of 322 patients and 444 individuals serving as controls in Sardinia, Italy in 1998-2004. Questionnaire information included the self-reported distance of the three longest held residential addresses from fixed radio-television transmitters and mobile phone base stations. We georeferenced the residential addresses of all study subjects and obtained the spatial coordinates of mobile phone base stations. For each address within a 500-meter radius from a mobile phone base station, we estimated the RF-EMF intensity using predictions from spatial models, and we performed RF-EMF measurements at the door in the subset of the longest held addresses within a 250-meter radius. We calculated risk of lymphoma and its major subtypes associated with the RF-EMF exposure metrics with unconditional logistic regression, adjusting by age, gender and years of education. In the analysis of self-reported data, risk associated with residence in proximity (within 50 meters) to fixed radio-television transmitters was likewise elevated for lymphoma overall [odds ratio = 2.7, 95% confidence interval = 1.5-4.6], and for the major lymphoma subtypes. With reference to mobile phone base stations, we did not observe an association with either the self-reported, or the geocoded distance from mobile phone base stations. RF-EMF measurements did not vary by case-control status. By comparing the self-reports to the geocoded data, we discovered that the cases tended to underestimate the distance from mobile phone base stations differentially from the controls ( P = 0.073). The interpretation of our findings is compromised by the limited study size, particularly in the analysis of the individual lymphoma subtypes, and the unavailability of the spatial coordinates of radio-television transmitters. Nonetheless, our results do not support the hypothesis of a link between environmental exposure to RF-EMF from mobile phone base stations and risk of lymphoma subtypes.

Contribution of Multi‐GNSS Constellation to SLR‐Derived Terrestrial Reference Frame

AbstractAll satellites of new Global Navigation Satellite Systems (GNSS) are equipped with laser retroreflectors dedicated to Satellite Laser Ranging (SLR). This paper demonstrates the contribution of SLR tracking of multi‐GNSS constellations to the improved SLR‐derived reference frame and scientific products. We show a solution strategy with estimating satellite orbits, SLR station coordinates, geocenter coordinates, and Earth rotation parameters using SLR observations to 2 Laser Geodynamics Satellites (LAGEOS) and 55 GNSS satellites: 1 GPS, 31 Globalnaya Navigatsionnaya Sputnikovaya Sistema, 18 Galileo, 3 BeiDou Inclined Geosynchronous Orbit, 1 BeiDou Medium Earth Orbit, and 1 Quasi‐Zenith Satellite System satellite for the period 2014.0–2017.4. Due to a substantial number of GNSS observations, the number of weekly solutions for some SLR stations, for example, Arkhyz, Komsomolsk, Altay, and Brasilia, is larger up to 41% in the combined LAGEOS + GNSS solution when compared to the LAGEOS‐only solution. The SLR observations to GNSS can transfer the orientation of the reference frame from GNSS to SLR solutions. As a result, the SLR‐derived pole coordinates and length‐of‐day estimates become more consistent with GNSS microwave‐based results. The root‐mean‐square errors of length‐of‐day are reduced from 122.5 μs/d to 43.0 μs/d, whereas mean offsets are reduced from −81.6 μs/d to 0.5 μs/d in LAGEOS only and in the combined LAGEOS + GNSS solutions, respectively.

Consistent realization of Celestial and Terrestrial Reference Frames

The Celestial Reference System (CRS) is currently realized only by Very Long Baseline Interferometry (VLBI) because it is the space geodetic technique that enables observations in that frame. In contrast, the Terrestrial Reference System (TRS) is realized by means of the combination of four space geodetic techniques: Global Navigation Satellite System (GNSS), VLBI, Satellite Laser Ranging (SLR), and Doppler Orbitography and Radiopositioning Integrated by Satellite. The Earth orientation parameters (EOP) are the link between the two types of systems, CRS and TRS. The EOP series of the International Earth Rotation and Reference Systems Service were combined of specifically selected series from various analysis centers. Other EOP series were generated by a simultaneous estimation together with the TRF while the CRF was fixed. Those computation approaches entail inherent inconsistencies between TRF, EOP, and CRF, also because the input data sets are different. A combined normal equation (NEQ) system, which consists of all the parameters, i.e., TRF, EOP, and CRF, would overcome such an inconsistency. In this paper, we simultaneously estimate TRF, EOP, and CRF from an inter-technique combined NEQ using the latest GNSS, VLBI, and SLR data (2005–2015). The results show that the selection of local ties is most critical to the TRF. The combination of pole coordinates is beneficial for the CRF, whereas the combination of $$\varDelta \hbox {UT1}$$ results in clear rotations of the estimated CRF. However, the standard deviations of the EOP and the CRF improve by the inter-technique combination which indicates the benefits of a common estimation of all parameters. It became evident that the common determination of TRF, EOP, and CRF systematically influences future ICRF computations at the level of several $$\upmu $$ as. Moreover, the CRF is influenced by up to $$50~\upmu $$ as if the station coordinates and EOP are dominated by the satellite techniques.

Application of time-variable process noise in terrestrial reference frames determined from VLBI data

In recent years, Kalman filtering has emerged as a suitable technique to determine terrestrial reference frames (TRFs), a prime example being JTRF2014. The time series approach allows variations of station coordinates that are neither reduced by observational corrections nor considered in the functional model to be taken into account. These variations are primarily due to non-tidal geophysical loading effects that are not reduced according to the current IERS Conventions (2010). It is standard practice that the process noise models applied in Kalman filter TRF solutions are derived from time series of loading displacements and account for station dependent differences. So far, it has been assumed that the parameters of these process noise models are constant over time. However, due to the presence of seasonal and irregular variations, this assumption does not truly reflect reality. In this study, we derive a station coordinate process noise model allowing for such temporal variations. This process noise model and one that is a parameterized version of the former are applied in the computation of TRF solutions based on very long baseline interferometry data. In comparison with a solution based on a constant process noise model, we find that the station coordinates are affected at the millimeter level.

Contributions to reference systems from Lunar Laser Ranging using the IfE analysis model

Lunar Laser Ranging (LLR) provides various quantities related to reference frames like Earth orientation parameters, coordinates and velocities of ground stations in the Earth-fixed frame and selenocentric coordinates of the lunar retro-reflectors. This paper presents the recent results from LLR data analysis at the Institut fur Erdmessung, Leibniz Universitat Hannover, based on all LLR data up to the end of 2016. The estimates of long-periodic nutation coefficients with periods between 13.6 days and 18.6 years are obtained with an accuracy in the order of 0.05–0.7 milliarcseconds (mas). Estimations of the Earth rotation phase $$\Delta $$ UT are accurate at the level of 0.032 ms if more than 14 normal points per night are included. The tie between the dynamical ephemeris frame to the kinematic celestial frame is estimated from pure LLR observations by two angles and their rates with an accuracy of 0.25 and 0.02 mas per year. The estimated station coordinates and velocities are compared to the ITRF2014 solution and the geometry of the retro-reflector network with the DE430 solution. The given accuracies represent 3 times formal errors of the parameter fit. The accuracy for $$\Delta $$ UT is based on the standard deviation of the estimates with respect to the reference C04 solution.

Precise point positioning for ground-based navigation systems without accurate time synchronization

Despite the broad range of navigation, positioning, and timing services offered by the global navigation satellite system (GNSS), its signals are vulnerable to blockage and interference, leading to a degraded performance or even unavailability. In contrast to GNSS, ground-based navigation systems exhibit better layout flexibility and more efficient terrain adaptability in shaded areas, with their additional advantages of accurate station coordinates and the absence of ionospheric delay effects enabling precise point positioning. However, accurate inter-station time synchronization is thought to be necessary for the ground-based precise point positioning. Locata utilizes a proprietary TimeLoc technology for tight time synchronization, allowing the clock difference in the carrier phase measurement equation to be ignored. However, for other ground-based navigation systems, accurate time synchronization requires accurate calibration of equipment delays and thus significantly increases the difficulty of engineering implementation. Herein, we propose a new precise point positioning method that does not rely on accurate inter-station time synchronization. According to this method, the uncalibrated clock difference and the integer carrier phase ambiguity are combined into a new ambiguity parameter, with the ambiguity and position coordinates subsequently solved in two steps. Further, in order to overcome the limitations of the Locata on-the-fly algorithm and the conventional “known-point initialization” method, a new “dynamic key point initialization” method is proposed. Finally, a simulation test and an indoor field trial are conducted, demonstrating that precise point positioning can be achieved by sharing a single clock source without relying on accurate inter-station time synchronization. An atomic clock is not needed and an inexpensive crystal oscillator is sufficient to act as the shared clock. The results of indoor positioning tests reveal real-time centimeter-level accuracy.

Assessment of local GNSS baselines at co-location sites

As one of the major contributors to the realisation of the International Terrestrial Reference System (ITRS), the Global Navigation Satellite Systems (GNSS) are prone to suffer from irregularities and discontinuities in time series. While often associated with hardware/software changes and the influence of the local environment, these discrepancies constitute a major threat for ITRS realisations. Co-located GNSS at fundamental sites, with two or more available instruments, provide the opportunity to mitigate their influence while improving the accuracy of estimated positions by examining data breaks, local biases, deformations, time-dependent variations and the comparison of GNSS baselines with existing local tie measurements. With the use of co-located GNSS data from a subset sites of the International GNSS Service network, this paper discusses a global multi-year analysis with the aim of delivering homogeneous time series of coordinates to analyse system-specific error sources in the local baselines. Results based on the comparison of different GNSS-based solutions with the local survey ties show discrepancies of up to 10 mm despite GNSS coordinate repeatabilities at the sub-mm level. The discrepancies are especially large for the solutions using the ionosphere-free linear combination and estimating tropospheric zenith delays, thus corresponding to the processing strategy used for global solutions. Snow on the antennas causes further problems and seasonal variations of the station coordinates. These demonstrate the need for a permanent high-quality monitoring of the effects present in the short GNSS baselines at fundamental sites.