Ocean-Surface Wave Measurements Using Scintillation Theories on Seaborne Software-Defined GPS and SBAS Reflectometry Observations.

In this study, a low-cost, software-defined Global Positioning System (GPS) and Satellite-Based Augmentation System (SBAS) Reflectometry (GPS&SBAS-R) system has been built and proposed to measure ocean-surface wave parameters on board the research vessel New Ocean Researcher 1 (R/V NOR-1) of Taiwan. A power-law, ocean-wave spectrum model has been used and applied with the Small Perturbation Method approach to solve the electromagnetic wave scattering problem from rough ocean surface, and compared with experimental seaborne GPS&SBAS-R observations. Meanwhile, the intensity scintillations of high-sampling GPS&SBAS-R signal acquisition data are thought to be caused by the moving of rough surfaces of the targeted ocean. We found that each derived scintillation power spectrum is a Fresnel-filtering result on ocean-surface elevation fluctuations and depends on the First Fresnel Zone (FFZ) distance and the ocean-surface wave velocity. The determined ocean-surface wave speeds have been compared and validated against nearby buoy measurements.

The Short-Term Prediction of Length of Day Using 1D Convolutional Neural Networks (1D CNN).

Accurate Earth orientation parameter (EOP) predictions are needed for many applications, e.g., for the tracking and navigation of interplanetary spacecraft missions. One of the most difficult parameters to forecast is the length of day (LOD), which represents the variation in the Earth's rotation rate since it is primarily affected by the torques associated with changes in atmospheric circulation. In this study, a new-generation time-series prediction algorithm is developed. The one-dimensional convolutional neural network (1D CNN), which is one of the deep learning methods, is introduced to model and predict the LOD using the IERS EOP 14 C04 and axial Z component of the atmospheric angular momentum (AAM), which was taken from the German Research Centre for Geosciences (GFZ) since it is strongly correlated with the LOD changes. The prediction procedure operates as follows: first, we detrend the LOD and Z-component series using the LS method, then, we obtain the residual series of each one to be used in the 1D CNN prediction algorithm. Finally, we analyze the results before and after introducing the AAM function. The results prove the potential of the proposed method as an optimal algorithm to successfully reconstruct and predict the LOD for up to 7 days.

Inter-Comparison of UT1-UTC from 24-Hour, Intensives, and VGOS Sessions during CONT17.

This work focuses on the assessment of UT1-UTC estimates from various types of sessions during the CONT17 campaign. We chose the CONT17 campaign as it provides 15 days of continuous, high-quality VLBI data from two legacy networks (S/X band), i.e., Legacy-1 (IVS) and Legacy-2 (VLBA) (having different network geometry and are non-overlapping), two types of Intensive sessions, i.e., IVS and Russian Intensives, and five days of new-generation, broadband VGOS sessions. This work also investigates different approaches to optimally compare dUT1 from Intensives with respect to the 24 h sessions given the different parameterization adopted for analyzing Intensives and different session lengths. One approach includes the estimation of dUT1 from pseudo Intensives, which are created from the 24 h sessions having their epochs synchronized with respect to the Intensive sessions. Besides, we assessed the quality of the dUT1 estimated from VGOS sessions at daily and sub-daily resolution. The study suggests that a different approach should be adopted when comparing the dUT1 from the Intensives, i.e., comparison of dUT1 value at the mean epoch of an Intensive session. The initial results regarding the VGOS sessions show that the dUT1 estimated from VGOS shows good agreement with the legacy network despite featuring fewer observations and stations. In the case of sub-daily dUT1 from VGOS sessions, we found that estimating dUT1 with 6 h resolution is superior to other sub-daily resolutions. Moreover, we introduced a new concept of sub-daily dUT1-tie to improve the estimation of dUT1 from the Intensive sessions. We observed an improvement of up to 20% with respect to the dUT1 from the 24 h sessions.

Towards Understanding the Interconnection between Celestial Pole Motion and Earth's Magnetic Field Using Space Geodetic Techniques.

The understanding of forced temporal variations in celestial pole motion (CPM) could bring us significantly closer to meeting the accuracy goals pursued by the Global Geodetic Observing System (GGOS) of the International Association of Geodesy (IAG), i.e., 1 mm accuracy and 0.1 mm/year stability on global scales in terms of the Earth orientation parameters. Besides astronomical forcing, CPM excitation depends on the processes in the fluid core and the core-mantle boundary. The same processes are responsible for the variations in the geomagnetic field (GMF). Several investigations were conducted during the last decade to find a possible interconnection of GMF changes with the length of day (LOD) variations. However, less attention was paid to the interdependence of the GMF changes and the CPM variations. This study uses the celestial pole offsets (CPO) time series obtained from very long baseline interferometry (VLBI) observations and data such as spherical harmonic coefficients, geomagnetic jerk, and magnetic field dipole moment from a state-of-the-art geomagnetic field model to explore the correlation between them. In this study, we use wavelet coherence analysis to compute the correspondence between the two non-stationary time series in the time-frequency domain. Our preliminary results reveal interesting common features in the CPM and GMF variations, which show the potential to improve the understanding of the GMF's contribution to the Earth's rotation. Special attention is given to the corresponding signal between FCN and GMF and potential time lags between geomagnetic jerks and rotational variations.

A new hybrid method to improve the ultra-short-term prediction of LOD.

Accurate, short-term predictions of Earth orientation parameters (EOP) are needed for many real-time applications including precise tracking and navigation of interplanetary spacecraft, climate forecasting, and disaster prevention. Out of the EOP, the LOD (length of day), which represents the changes in the Earth's rotation rate, is the most challenging to predict since it is largely affected by the torques associated with changes in atmospheric circulation. In this study, the combination of Copula-based analysis and singular spectrum analysis (SSA) method is introduced to improve the accuracy of the forecasted LOD. The procedure operates as follows: First, we derive the dependence structure between LOD and the Z component of the effective angular momentum (EAM) arising from atmospheric, hydrologic, and oceanic origins (AAM + HAM + OAM). Based on the fitted theoretical Copula, we then simulate LOD from the Z component of EAM data. Next, the difference between LOD time series and its Copula-based estimation is modeled using SSA. Multiple sets of short-term LOD prediction have been done based on the IERS 05 C04 time series to assess the capability of our hybrid model. The results illustrate that the proposed method can efficiently predict LOD.

Drift of the Earth's Principal Axes of Inertia from GRACE and Satellite Laser Ranging Data.

The location of the Earth's principal axes of inertia is a foundation for all the theories and solutions of its rotation, and thus has a broad effect on many fields, including astronomy, geodesy, and satellite-based positioning and navigation systems. That location is determined by the second-degree Stokes coefficients of the geopotential. Accurate solutions for those coefficients were limited to the stationary case for many years, but the situation improved with the accomplishment of Gravity Recovery and Climate Experiment (GRACE), and nowadays several solutions for the time-varying geopotential have been derived based on gravity and satellite laser ranging data, with time resolutions reaching one month or one week. Although those solutions are already accurate enough to compute the evolution of the Earth's axes of inertia along more than a decade, such an analysis has never been performed. In this paper, we present the first analysis of this problem, taking advantage of previous analytical derivations to simplify the computations and the estimation of the uncertainty of solutions. The results are rather striking, since the axes of inertia do not move around some mean position fixed to a given terrestrial reference frame in this period, but drift away from their initial location in a slow but clear and not negligible manner.

A new method to improve the prediction of the celestial pole offsets.

Knowledge of the Earth's changing rotation is fundamental to positioning objects in space and on the planet. Nowadays, the Earth's orientation in space is expressed by five Earth Orientation Parameters (EOP). Many applications in astronomy, geosciences, and space missions require accurate EOP predictions. Operational predictions are released daily by the Rapid Service/Prediction Centre of the International Earth Rotation and Reference Systems Service (IERS). The prediction procedures and performances differ for the three EOP classes: polar motion, rotation angle (UT1-UTC), and the two celestial pole offsets (CPO), dX and dY. The IERS Annual Report 2016 shows Rapid Service CPO predictions errors with respect to IERS 08 C04 observations in 2016 ranging from 120 to 140 µas in 40 days for dX, and 100-160 µas for dY. We test a new method for the CPO prediction based on the recent availability of sophisticated empirical models for the Free Core Nutation, a main component of the CPO variations. We found it allows predicting both CPO with error estimates for the period 2000-2016 lower than the 2016 Rapid Service products, reaching about 85 µas after 40 days and near 90 µas after a year. These results would represent a 35-40% improvement.

Polar motion prediction using the combination of SSA and Copula-based analysis.

The real-time estimation of polar motion (PM) is needed for the navigation of Earth satellite and interplanetary spacecraft. However, it is impossible to have real-time information due to the complexity of the measurement model and data processing. Various prediction methods have been developed. However, the accuracy of PM prediction is still not satisfactory even for a few days in the future. Therefore, new techniques or a combination of the existing methods need to be investigated for improving the accuracy of the predicted PM. There is a well-introduced method called Copula, and we want to combine it with singular spectrum analysis (SSA) method for PM prediction. In this study, first, we model the predominant trend of PM time series using SSA. Then, the difference between PM time series and its SSA estimation is modeled using Copula-based analysis. Multiple sets of PM predictions which range between 1 and 365 days have been performed based on an IERS 08 C04 time series to assess the capability of our hybrid model. Our results illustrate that the proposed method can efficiently predict PM. The improvement in PM prediction accuracy up to 365 days in the future is found to be around 40% on average and up to 65 and 46% in terms of success rate for the PM x and PM y , respectively.

The Impact of Estimating High-Resolution Tropospheric Gradients on Multi-GNSS Precise Positioning.

Benefits from the modernized US Global Positioning System (GPS), the revitalized Russian GLObal NAvigation Satellite System (GLONASS), and the newly-developed Chinese BeiDou Navigation Satellite System (BDS) and European Galileo, multi-constellation Global Navigation Satellite System (GNSS) has emerged as a powerful tool not only in positioning, navigation, and timing (PNT), but also in remote sensing of the atmosphere and ionosphere. Both precise positioning and the derivation of atmospheric parameters can benefit from multi-GNSS observations. In this contribution, extensive evaluations are conducted with multi-GNSS datasets collected from 134 globally-distributed ground stations of the International GNSS Service (IGS) Multi-GNSS Experiment (MGEX) network in July 2016. The datasets are processed in six different constellation combinations, i.e., GPS-, GLONASS-, BDS-only, GPS + GLONASS, GPS + BDS, and GPS + GLONASS + BDS + Galileo precise point positioning (PPP). Tropospheric gradients are estimated with eight different temporal resolutions, from 1 h to 24 h, to investigate the impact of estimating high-resolution gradients on position estimates. The standard deviation (STD) is used as an indicator of positioning repeatability. The results show that estimating tropospheric gradients with high temporal resolution can achieve better positioning performance than the traditional strategy in which tropospheric gradients are estimated on a daily basis. Moreover, the impact of estimating tropospheric gradients with different temporal resolutions at various elevation cutoff angles (from 3° to 20°) is investigated. It can be observed that with increasing elevation cutoff angles, the improvement in positioning repeatability is decreased.

Improving GLONASS Precise Orbit Determination through Data Connection.

In order to improve the precision of GLONASS orbits, this paper presents a method to connect the data segments of a single station-satellite pair to increase the observation continuity and, consequently, the strength of the precise orbit determination (POD) solution. In this method, for each GLONASS station-satellite pair, the wide-lane ambiguities derived from the Melbourne-Wübbena combination are statistically tested and corrected for phase integer offsets and then the same is carried out for the narrow-lane ambiguities calculated from the POD solution. An experimental validation was carried out using one-month GNSS data of a global network with 175 IGS stations. The result shows that, on average, 27.1% of the GLONASS station-satellite pairs with multiple data segments could be connected to a single long observation arc and, thus, only one ambiguity parameter was estimated. Using the connected data, the GLONASS orbit overlapping RMS at the day boundaries could be reduced by 19.2% in ideal cases with an averaged reduction of about 6.3%.

Tightly coupled integration of ionosphere-constrained precise point positioning and inertial navigation systems.

The continuity and reliability of precise GNSS positioning can be seriously limited by severe user observation environments. The Inertial Navigation System (INS) can overcome such drawbacks, but its performance is clearly restricted by INS sensor errors over time. Accordingly, the tightly coupled integration of GPS and INS can overcome the disadvantages of each individual system and together form a new navigation system with a higher accuracy, reliability and availability. Recently, ionosphere-constrained (IC) precise point positioning (PPP) utilizing raw GPS observations was proven able to improve both the convergence and positioning accuracy of the conventional PPP using ionosphere-free combined observations (LC-PPP). In this paper, a new mode of tightly coupled integration, in which the IC-PPP instead of LC-PPP is employed, is implemented to further improve the performance of the coupled system. We present the detailed mathematical model and the related algorithm of the new integration of IC-PPP and INS. To evaluate the performance of the new tightly coupled integration, data of both airborne and vehicle experiments with a geodetic GPS receiver and tactical grade inertial measurement unit are processed and the results are analyzed. The statistics show that the new approach can further improve the positioning accuracy compared with both IC-PPP and the tightly coupled integration of the conventional PPP and INS.

Precise positioning with current multi-constellation Global Navigation Satellite Systems: GPS, GLONASS, Galileo and BeiDou.

The world of satellite navigation is undergoing dramatic changes with the rapid development of multi-constellation Global Navigation Satellite Systems (GNSSs). At the moment more than 70 satellites are already in view, and about 120 satellites will be available once all four systems (BeiDou + Galileo + GLONASS + GPS) are fully deployed in the next few years. This will bring great opportunities and challenges for both scientific and engineering applications. In this paper we develop a four-system positioning model to make full use of all available observations from different GNSSs. The significant improvement of satellite visibility, spatial geometry, dilution of precision, convergence, accuracy, continuity and reliability that a combining utilization of multi-GNSS brings to precise positioning are carefully analyzed and evaluated, especially in constrained environments.

Efficient high-rate satellite clock estimation for PPP ambiguity resolution using carrier-ranges.

In order to catch up the short-term clock variation of GNSS satellites, clock corrections must be estimated and updated at a high-rate for Precise Point Positioning (PPP). This estimation is already very time-consuming for the GPS constellation only as a great number of ambiguities need to be simultaneously estimated. However, on the one hand better estimates are expected by including more stations, and on the other hand satellites from different GNSS systems must be processed integratively for a reliable multi-GNSS positioning service. To alleviate the heavy computational burden, epoch-differenced observations are always employed where ambiguities are eliminated. As the epoch-differenced method can only derive temporal clock changes which have to be aligned to the absolute clocks but always in a rather complicated way, in this paper, an efficient method for high-rate clock estimation is proposed using the concept of "carrier-range" realized by means of PPP with integer ambiguity resolution. Processing procedures for both post- and real-time processing are developed, respectively. The experimental validation shows that the computation time could be reduced to about one sixth of that of the existing methods for post-processing and less than 1 s for processing a single epoch of a network with about 200 stations in real-time mode after all ambiguities are fixed. This confirms that the proposed processing strategy will enable the high-rate clock estimation for future multi-GNSS networks in post-processing and possibly also in real-time mode.

New VLBI2010 scheduling strategies and implications on the terrestrial reference frames.

In connection with the work for the next generation VLBI2010 Global Observing System (VGOS) of the International VLBI Service for Geodesy and Astrometry, a new scheduling package (Vie_Sched) has been developed at the Vienna University of Technology as a part of the Vienna VLBI Software. In addition to the classical station-based approach it is equipped with a new scheduling strategy based on the radio sources to be observed. We introduce different configurations of source-based scheduling options and investigate the implications on present and future VLBI2010 geodetic schedules. By comparison to existing VLBI schedules of the continuous campaign CONT11, we find that the source-based approach with two sources has a performance similar to the station-based approach in terms of number of observations, sky coverage, and geodetic parameters. For an artificial 16 station VLBI2010 network, the source-based approach with four sources provides an improved distribution of source observations on the celestial sphere. Monte Carlo simulations yield slightly better repeatabilities of station coordinates with the source-based approach with two sources or four sources than the classical strategy. The new VLBI scheduling software with its alternative scheduling strategy offers a promising option with respect to applications of the VGOS.

New approach for earthquake/tsunami monitoring using dense GPS networks.

In recent times increasing numbers of high-rate GPS stations have been installed around the world and set-up to provide data in real-time. These networks provide a great opportunity to quickly capture surface displacements, which makes them important as potential constituents of earthquake/tsunami monitoring and warning systems. The appropriate GPS real-time data analysis with sufficient accuracy for this purpose is a main focus of the current GPS research. In this paper we propose an augmented point positioning method for GPS based hazard monitoring, which can achieve fast or even instantaneous precise positioning without relying on data of a specific reference station. The proposed method overcomes the limitations of the currently mostly used GPS processing approaches of relative positioning and global precise point positioning. The advantages of the proposed approach are demonstrated by using GPS data, which was recorded during the 2011 Tohoku-Oki earthquake in Japan.

Experimental study on the precise orbit determination of the BeiDou navigation satellite system.

The regional service of the Chinese BeiDou satellite navigation system is now in operation with a constellation including five Geostationary Earth Orbit satellites (GEO), five Inclined Geosynchronous Orbit (IGSO) satellites and four Medium Earth Orbit (MEO) satellites. Besides the standard positioning service with positioning accuracy of about 10 m, both precise relative positioning and precise point positioning are already demonstrated. As is well known, precise orbit and clock determination is essential in enhancing precise positioning services. To improve the satellite orbits of the BeiDou regional system, we concentrate on the impact of the tracking geometry and the involvement of MEOs, and on the effect of integer ambiguity resolution as well. About seven weeks of data collected at the BeiDou Experimental Test Service (BETS) network is employed in this experimental study. Several tracking scenarios are defined, various processing schemata are designed and carried out; and then, the estimates are compared and analyzed in detail. The results show that GEO orbits, especially the along-track component, can be significantly improved by extending the tracking network in China along longitude direction, whereas IGSOs gain more improvement if the tracking network extends in latitude. The involvement of MEOs and ambiguity-fixing also make the orbits better.

Tidal Love and Shida numbers estimated by geodetic VLBI.

Frequency-dependent Love and Shida numbers, which characterize the Earth response to the tidal forces, were estimated in a global adjustment of all suitable geodetic Very Long Baseline Interferometry (VLBI) sessions from 1984.0 to 2011.0. Several solutions were carried out to determine the Love and Shida numbers for the tidal constituents at periods in the diurnal band and in the long-period band in addition to values of the Love and Shida numbers common for all tides of degree two. Adding up all twelve diurnal tidal waves that were estimated, the total differences in displacement with respect to the theoretical conventional values of the Love and Shida numbers calculated from an Earth model reach 1.73 ± 0.29 mm in radial direction and 1.15 ± 0.15 mm in the transverse plane. The difference in the radial deformation following from the estimates of the zonal Love numbers is largest for the semi-annual tide Ssa with 1.07 ± 0.19 mm.