Showing papers in "Journal of Geodesy in 2017"

International VLBI Service for Geodesy and Astrometry. Delivering high-quality products and embarking on observations of the next generation

Abstract: The International VLBI Service for Geodesy and Astrometry (IVS) regularly produces high-quality Earth orientation parameters from observing sessions employing extensive networks or individual baselines. The master schedule is designed according to the telescope days committed by the stations and by the need for dense sampling of the Earth orientation parameters (EOP). In the pre-2011 era, the network constellations with their number of telescopes participating were limited by the playback and baseline capabilities of the hardware (Mark4) correlators. This limitation was overcome by the advent of software correlators, which can now accommodate many more playback units in a flexible configuration. In this paper, we describe the current operations of the IVS with special emphasis on the quality of the polar motion results since these are the only EOP components which can be validated against independent benchmarks. The polar motion results provided by the IVS have improved continuously over the years, now providing an agreement with IGS results at the level of 20–25 $$\upmu $$ as in a WRMS sense. At the end of the paper, an outlook is given for the realization of the VLBI Global Observing System.

Initial assessment of the COMPASS/BeiDou-3: new-generation navigation signals

Abstract: The successful launch of five new-generation experimental satellites of the China’s BeiDou Navigation Satellite System, namely BeiDou I1-S, I2-S, M1-S, M2-S, and M3-S, marks a significant step in expanding BeiDou into a navigation system with global coverage. In addition to B1I (1561.098 MHz) and B3I (1269.520 MHz) signals, the new-generation BeiDou-3 experimental satellites are also capable of transmitting several new navigation signals in space, namely B1C at 1575.42 MHz, B2a at 1176.45 MHz, and B2b at 1207.14 MHz. For the first time, we present an initial characterization and performance assessment for these new-generation BeiDou-3 satellites and their signals. The L1/L2/L5 signals from GPS Block IIF satellites, E1/E5a/E5b signals from Galileo satellites, and B1I/B2I/B3I signals from BeiDou-2 satellites are also evaluated for comparison. The characteristics of the B1C, B1I, B2a, B2b, and B3I signals are evaluated in terms of observed carrier-to-noise density ratio, pseudorange multipath and noise, triple-frequency carrier-phase ionosphere-free and geometry-free combination, and double-differenced carrier-phase and code residuals. The results demonstrate that the observational quality of the new-generation BeiDou-3 signals is comparable to that of GPS L1/L2/L5 and Galileo E1/E5a/E5b signals. However, the analysis of code multipath shows that the elevation-dependent code biases, which have been previously identified to exist in the code observations of the BeiDou-2 satellites, seem to be not obvious for all the available signals of the new-generation BeiDou-3 satellites. This will significantly benefit precise applications that resolve wide-lane ambiguity based on Hatch–Melbourne–Wubbena linear combinations and other applications such as single-frequency precise point positioning (PPP) based on the ionosphere-free code–carrier combinations. Furthermore, with regard to the triple-frequency carrier-phase ionosphere-free and geometry-free combination, it is found that different from the BeiDou-2 and GPS Block IIF satellites, no apparent bias variations could be observed in all the new-generation BeiDou-3 experimental satellites, which shows a good consistency of the new-generation BeiDou-3 signals. The absence of such triple-frequency biases simplifies the potential processing of multi-frequency PPP using observations from the new-generation BeiDou-3 satellites. Finally, the precise relative positioning results indicate that the additional observations from the new-generation BeiDou-3 satellites can improve ambiguity resolution performance with respect to BeiDou-2 only positioning, which indicates that observations from the new-generation BeiDou-3 satellites can contribute to precise relative positioning.

CODE’s five-system orbit and clock solution—the challenges of multi-GNSS data analysis

Abstract: This article describes the processing strategy and the validation results of CODE’s MGEX (COM) orbit and satellite clock solution, including the satellite systems GPS, GLONASS, Galileo, BeiDou, and QZSS. The validation with orbit misclosures and SLR residuals shows that the orbits of the new systems Galileo, BeiDou, and QZSS are affected by modelling deficiencies with impact on the orbit scale (e.g., antenna calibration, Earth albedo, and transmitter antenna thrust). Another weakness is the attitude and solar radiation pressure (SRP) modelling of satellites moving in the orbit normal mode—which is not yet correctly considered in the COM solution. Due to these issues, we consider the current state COM solution as preliminary. We, however, use the long-time series of COM products for identifying the challenges and for the assessment of model-improvements. The latter is demonstrated on the example of the solar radiation pressure (SRP) model, which has been replaced by a more generalized model. The SLR validation shows that the new SRP model significantly improves the orbit determination of Galileo and QZSS satellites at times when the satellite’s attitude is maintained by yaw-steering. The impact of this orbit improvement is also visible in the estimated satellite clocks—demonstrating the potential use of the new generation satellite clocks for orbit validation. Finally, we point out further challenges and open issues affecting multi-GNSS data processing that deserves dedicated studies.

Multi-GNSS precise point positioning (MGPPP) using raw observations

Abstract: A joint-processing model for multi-GNSS (GPS, GLONASS, BDS and GALILEO) precise point positioning (PPP) is proposed, in which raw code and phase observations are used. In the proposed model, inter-system biases (ISBs) and GLONASS code inter-frequency biases (IFBs) are carefully considered, among which GLONASS code IFBs are modeled as a linear function of frequency numbers. To get the full rank function model, the unknowns are re-parameterized and the estimable slant ionospheric delays and ISBs/IFBs are derived and estimated simultaneously. One month of data in April, 2015 from 32 stations of the International GNSS Service (IGS) Multi-GNSS Experiment (MGEX) tracking network have been used to validate the proposed model. Preliminary results show that RMS values of the positioning errors (with respect to external double-difference solutions) for static/kinematic solutions (four systems) are 6.2 mm/2.1 cm (north), 6.0 mm/2.2 cm (east) and 9.3 mm/4.9 cm (up). One-day stabilities of the estimated ISBs described by STD values are 0.36 and 0.38 ns, for GLONASS and BDS, respectively. Significant ISB jumps are identified between adjacent days for all stations, which are caused by the different satellite clock datums in different days and for different systems. Unlike ISBs, the estimated GLONASS code IFBs are quite stable for all stations, with an average STD of 0.04 ns over a month. Single-difference experiment of short baseline shows that PPP ionospheric delays are more precise than traditional leveling ionospheric delays.

Methodology and consistency of slant and vertical assessments for ionospheric electron content models

Abstract: A summary of the main concepts on global ionospheric map(s) [hereinafter GIM(s)] of vertical total electron content (VTEC), with special emphasis on their assessment, is presented in this paper. It is based on the experience accumulated during almost two decades of collaborative work in the context of the international global navigation satellite systems (GNSS) service (IGS) ionosphere working group. A representative comparison of the two main assessments of ionospheric electron content models (VTEC-altimeter and difference of Slant TEC, based on independent global positioning system data GPS, dSTEC-GPS) is performed. It is based on 26 GPS receivers worldwide distributed and mostly placed on islands, from the last quarter of 2010 to the end of 2016. The consistency between dSTEC-GPS and VTEC-altimeter assessments for one of the most accurate IGS GIMs (the tomographic-kriging GIM ‘UQRG’ computed by UPC) is shown. Typical error RMS values of 2 TECU for VTEC-altimeter and 0.5 TECU for dSTEC-GPS assessments are found. And, as expected by following a simple random model, there is a significant correlation between both RMS and specially relative errors, mainly evident when large enough number of observations per pass is considered. The authors expect that this manuscript will be useful for new analysis contributor centres and in general for the scientific and technical community interested in simple and truly external ways of validating electron content models of the ionosphere.

Ambiguity resolved precise point positioning with GPS and BeiDou

Abstract: This paper focuses on the contribution of the global positioning system (GPS) and BeiDou navigation satellite system (BDS) observations to precise point positioning (PPP) ambiguity resolution (AR). A GPS + BDS fractional cycle bias (FCB) estimation method and a PPP AR model were developed using integrated GPS and BDS observations. For FCB estimation, the GPS + BDS combined PPP float solutions of the globally distributed IGS MGEX were first performed. When integrating GPS observations, the BDS ambiguities can be precisely estimated with less than four tracked BDS satellites. The FCBs of both GPS and BDS satellites can then be estimated from these precise ambiguities. For the GPS + BDS combined AR, one GPS and one BDS IGSO or MEO satellite were first chosen as the reference satellite for GPS and BDS, respectively, to form inner-system single-differenced ambiguities. The single-differenced GPS and BDS ambiguities were then fused by partial ambiguity resolution to increase the possibility of fixing a subset of decorrelated ambiguities with high confidence. To verify the correctness of the FCB estimation and the effectiveness of the GPS + BDS PPP AR, data recorded from about 75 IGS MGEX stations during the period of DOY 123-151 (May 3 to May 31) in 2015 were used for validation. Data were processed with three strategies: BDS-only AR, GPS-only AR and GPS + BDS AR. Numerous experimental results show that the time to first fix (TTFF) is longer than 6 h for the BDS AR in general and that the fixing rate is usually less than 35 % for both static and kinematic PPP. An average TTFF of 21.7 min and 33.6 min together with a fixing rate of 98.6 and 97.0 % in static and kinematic PPP, respectively, can be achieved for GPS-only ambiguity fixing. For the combined GPS + BDS AR, the average TTFF can be shortened to 16.9 min and 24.6 min and the fixing rate can be increased to 99.5 and 99.0 % in static and kinematic PPP, respectively. Results also show that GPS + BDS PPP AR outperforms single-system PPP AR in terms of convergence time and position accuracy.

The unexpected signal in GRACE estimates of $$C_{20}$$

Abstract: For science applications of the gravity recovery and climate experiment (GRACE) monthly solutions, the GRACE estimates of $$C_{20}$$ (or $$J_{2}$$ ) are typically replaced by the value determined from satellite laser ranging (SLR) due to an unexpectedly strong, clearly non-geophysical, variation at a period of $$\sim $$ 160 days. This signal has sometimes been referred to as a tide-like variation since the period is close to the perturbation period on the GRACE orbits due to the spherical harmonic coefficient pair $$C_{22}/S_{22}$$ of S2 ocean tide. Errors in the S2 tide model used in GRACE data processing could produce a significant perturbation to the GRACE orbits, but it cannot contribute to the $$\sim $$ 160-day signal appearing in $$C_{20}$$ . Since the dominant contribution to the GRACE estimate of $$C_{20}$$ is from the global positioning system tracking data, a time series of 138 monthly solutions up to degree and order 10 ( $$10\times 10$$ ) were derived along with estimates of ocean tide parameters up to degree 6 for eight major tides. The results show that the $$\sim $$ 160-day signal remains in the $$C_{20}$$ time series. Consequently, the anomalous signal in GRACE $$C_{20}$$ cannot be attributed to aliasing from the errors in the S2 tide. A preliminary analysis of the cross-track forces acting on GRACE and the cross-track component of the accelerometer data suggests that a temperature-dependent systematic error in the accelerometer data could be a cause. Because a wide variety of science applications relies on the replacement values for $$C_{20}$$ , it is essential that the SLR estimates are as reliable as possible. An ongoing concern has been the influence of higher degree even zonal terms on the SLR estimates of $$C_{20}$$ , since only $$C_{20}$$ and $$C_{40}$$ are currently estimated. To investigate whether a better separation between $$C_{20}$$ and the higher-degree terms could be achieved, several combinations of additional SLR satellites were investigated. In addition, a series of monthly gravity field solutions ( $$60\times 60$$ ) were estimated from a combination of GRACE and SLR data. The results indicate that the combination of GRACE and SLR data might benefit the resonant orders in the GRACE-derived gravity fields, but it appears to degrade the recovery of the $$C_{20}$$ variations. In fact, the results suggest that the poorer recovery of $$C_{40}$$ by GRACE, where the annual variation is significantly underestimated, may be affecting the estimates of $$C_{20}$$ . Consequently, it appears appropriate to continue using the SLR-based estimates of $$C_{20}$$ , and possibly also $$C_{40}$$ , to augment the existing GRACE mission.

Positive and negative ionospheric responses to the March 2015 geomagnetic storm from BDS observations

Abstract: The most intense geomagnetic storm in solar cycle 24 occurred on March 17, 2015, and the detailed ionospheric storm morphologies are difficultly obtained from traditional observations. In this paper, the Geostationary Earth Orbit (GEO) observations of BeiDou Navigation Satellite System (BDS) are for the first time used to investigate the ionospheric responses to the geomagnetic storm. Using BDS GEO and GIMs TEC series, negative and positive responses to the March 2015 storm are found at local and global scales. During the main phase, positive ionospheric storm is the main response to the geomagnetic storm, while in the recovery phase, negative phases are pronounced at all latitudes. Maximum amplitudes of negative and positive phases appear in the afternoon and post-dusk sectors during both main and recovery phases. Furthermore, dual-peak positive phases in main phase and repeated negative phase during the recovery are found from BDS GEO observations. The geomagnetic latitudes corresponding to the maximum disturbances during the main and recovery phases show large differences, but they are quasi-symmetrical between southern and northern hemispheres. No clear zonal propagation of traveling ionospheric disturbances is detected in the GNSS TEC disturbances at high and low latitudes. The thermospheric composition variations could be the dominant source of the observed ionospheric storm effect from GUVI $$\hbox {[O]/[N}_{2}]$$ ratio data as well as storm-time electric fields. Our study demonstrates that the BDS (especially the GEO) observations are an important data source to observe ionospheric responses to the geomagnetic storm.

Rapid initialization of real-time PPP by resolving undifferenced GPS and GLONASS ambiguities simultaneously

Abstract: Rapid initialization of real-time precise point positioning (PPP) has constantly been a difficult problem. Recent efforts through multi-GNSS and multi-frequency data, though beneficial indeed, have not proved sufficiently effective in reducing the initialization periods to far less than 10 min. Though this goal can be easily reached by introducing ionosphere corrections as accurate as a few centimeters, a dense reference network is required which is impractical for wi de-area applications. Leveraging the latest development of GLONASS PPP ambiguity resolution (PPP-AR) technique, we propose a composite strategy, where simultaneous GPS and GLONASS dual-frequency PPP-AR is carried out, and herein, the reliability of partial AR improves dramatically. We used 14 days of data from a German network and divided them into hourly data to test this strategy. We found that the initialization periods were shortened drastically from over 25 min when only GPS data were processed to about 6 min when GPS and GLONASS PPP-AR were accomplished simultaneously. More encouragingly, over 50% of real-time PPP solutions could be initialized successfully within 5 min through our strategy, in contrast to only 4% when only GPS data were used. We expect that our strategy can provide a promising route to overcoming the difficulty of achieving PPP initializations within a few minutes.

On the short-term temporal variations of GNSS receiver differential phase biases

Abstract: As a first step towards studying the ionosphere with the global navigation satellite system (GNSS), leveling the phase to the code geometry-free observations on an arc-by-arc basis yields the ionospheric observables, interpreted as a combination of slant total electron content along with satellite and receiver differential code biases (DCB). The leveling errors in the ionospheric observables may arise during this procedure, which, according to previous studies by other researchers, are due to the combined effects of the code multipath and the intra-day variability in the receiver DCB. In this paper we further identify the short-term temporal variations of receiver differential phase biases (DPB) as another possible cause of leveling errors. Our investigation starts by the development of a method to epoch-wise estimate between-receiver DPB (BR-DPB) employing (inter-receiver) single-differenced, phase-only GNSS observations collected from a pair of receivers creating a zero or short baseline. The key issue for this method is to get rid of the possible discontinuities in the epoch-wise BR-DPB estimates, occurring when satellite assigned as pivot changes. Our numerical tests, carried out using Global Positioning System (GPS, US GNSS) and BeiDou Navigation Satellite System (BDS, Chinese GNSS) observations sampled every 30 s by a dedicatedly selected set of zero and short baselines, suggest two major findings. First, epoch-wise BR-DPB estimates can exhibit remarkable variability over a rather short period of time (e.g. 6 cm over 3 h), thus significant from a statistical point of view. Second, a dominant factor driving this variability is the changes of ambient temperature, instead of the un-modelled phase multipath.

Precise orbit determination of the Fengyun-3C satellite using onboard GPS and BDS observations

Abstract: The GNSS Occultation Sounder instrument onboard the Chinese meteorological satellite Fengyun-3C (FY-3C) tracks both GPS and BDS signals for orbit determination. One month’s worth of the onboard dual-frequency GPS and BDS data during March 2015 from the FY-3C satellite is analyzed in this study. The onboard BDS and GPS measurement quality is evaluated in terms of data quantity as well as code multipath error. Severe multipath errors for BDS code ranges are observed especially for high elevations for BDS medium earth orbit satellites (MEOs). The code multipath errors are estimated as piecewise linear model in $$2{^{\circ }}\times 2{^{\circ }}$$ grid and applied in precise orbit determination (POD) calculations. POD of FY-3C is firstly performed with GPS data, which shows orbit consistency of approximate 2.7 cm in 3D RMS (root mean square) by overlap comparisons; the estimated orbits are then used as reference orbits for evaluating the orbit precision of GPS and BDS combined POD as well as BDS-based POD. It is indicated that inclusion of BDS geosynchronous orbit satellites (GEOs) could degrade POD precision seriously. The precisions of orbit estimates by combined POD and BDS-based POD are 3.4 and 30.1 cm in 3D RMS when GEOs are involved, respectively. However, if BDS GEOs are excluded, the combined POD can reach similar precision with respect to GPS POD, showing orbit differences about 0.8 cm, while the orbit precision of BDS-based POD can be improved to 8.4 cm. These results indicate that the POD performance with onboard BDS data alone can reach precision better than 10 cm with only five BDS inclined geosynchronous satellite orbit satellites and three MEOs. As the GNOS receiver can only track six BDS satellites for orbit positioning at its maximum channel, it can be expected that the performance of POD with onboard BDS data can be further improved if more observations are generated without such restrictions.

Improving BeiDou real-time precise point positioning with numerical weather models

Abstract: Precise positioning with the current Chinese BeiDou Navigation Satellite System is proven to be of comparable accuracy to the Global Positioning System, which is at centimeter level for the horizontal components and sub-decimeter level for the vertical component. But the BeiDou precise point positioning (PPP) shows its limitation in requiring a relatively long convergence time. In this study, we develop a numerical weather model (NWM) augmented PPP processing algorithm to improve BeiDou precise positioning. Tropospheric delay parameters, i.e., zenith delays, mapping functions, and horizontal delay gradients, derived from short-range forecasts from the Global Forecast System of the National Centers for Environmental Prediction (NCEP) are applied into BeiDou real-time PPP. Observational data from stations that are capable of tracking the BeiDou constellation from the International GNSS Service (IGS) Multi-GNSS Experiments network are processed, with the introduced NWM-augmented PPP and the standard PPP processing. The accuracy of tropospheric delays derived from NCEP is assessed against with the IGS final tropospheric delay products. The positioning results show that an improvement in convergence time up to 60.0 and 66.7% for the east and vertical components, respectively, can be achieved with the NWM-augmented PPP solution compared to the standard PPP solutions, while only slight improvement in the solution convergence can be found for the north component. A positioning accuracy of 5.7 and 5.9 cm for the east component is achieved with the standard PPP that estimates gradients and the one that estimates no gradients, respectively, in comparison to 3.5 cm of the NWM-augmented PPP, showing an improvement of 38.6 and 40.1%. Compared to the accuracy of 3.7 and 4.1 cm for the north component derived from the two standard PPP solutions, the one of the NWM-augmented PPP solution is improved to 2.0 cm, by about 45.9 and 51.2%. The positioning accuracy for the up component improves from 11.4 and 13.2 cm with the two standard PPP solutions to 8.0 cm with the NWM-augmented PPP solution, an improvement of 29.8 and 39.4%, respectively.

ERTK: extra-wide-lane RTK of triple-frequency GNSS signals

Abstract: Triple-frequency signals have thus far been available for all satellites of BeiDou and Galileo systems and for some GPS satellites. The main benefit of triple-frequency signals is their formation of extra-wide-lane (EWL) combinations whose ambiguities can be instantaneously fixed for several 10–100 km baselines. Yet, this benefit has not been fully exploited and only used as a constraint for narrow-lane (NL) ambiguity resolution (AR) in most previous studies. In this study, we comprehensively investigate the real-time kinematic (RTK) capabilities of EWL observations, also referred to as EWL RTK (ERTK). We begin by mathematically expressing the ease of EWL AR and the difficulty of NL AR, respectively, using a numerical demonstration. We then present the mathematical models for ERTK including the ionosphere-ignored, ionosphere-float and ionosphere-smoothed types. The experiments are conducted using a four-station network of real triple-frequency BeiDou data with baseline lengths from 33 to 75 km. The results show that the ionosphere-ignored ERTK achieves real-time solutions with a horizontal accuracy of about 10 cm. Although the ionosphere-float ERTK solutions are very noisy, they can be quickly improved at the centimetre level by further applying the ionosphere-smoothed model. Note that such accurate results are very promising and already satisfy many applications without complicated NL AR. To the best of our knowledge, this is the first comprehensive study to make full use of EWL observations of triple-frequency signals on RTK.

Spatiotemporal filtering for regional GPS network in China using independent component analysis

Abstract: Removal of the common mode error (CME) is a routine procedure in postprocessing regional GPS network observations, which is commonly performed using principal component analysis (PCA). PCA decomposes a network time series into a group of modes, where each mode comprises a common temporal function and corresponding spatial response based on second-order statistics (variance and covariance). However, the probability distribution function of a GPS time series is non-Gaussian; therefore, the largest variances do not correspond to the meaningful axes, and the PCA-derived components may not have an obvious physical meaning. In this study, the CME was assumed statistically independent of other errors, and it was extracted using independent component analysis (ICA), which involves higher-order statistics. First, the ICA performance was tested using a simulated example and compared with PCA and stacking methods. The existence of strong local effects on some stations causes significant large spatial responses and, therefore, a strategy based on median and interquartile range statistics was proposed to identify abnormal sites. After discarding abnormal sites, two indices based on the analysis of the spatial responses of all sites in each independent component (east, north, and vertical) were used to define the CME quantitatively. Continuous GPS coordinate time series spanning $$\sim $$ 4.5 years obtained from 259 stations of the Tectonic and Environmental Observation Network of Mainland China (CMONOC II) were analyzed using both PCA and ICA methods and their results compared. The results suggest that PCA is susceptible to deriving an artificial spatial structure, whereas ICA separates the CME from other errors reliably. Our results demonstrate that the spatial characteristics of the CME for CMONOC II are not uniform for the east, north, and vertical components, but have an obvious north–south or east–west distribution. After discarding 84 abnormal sites and performing spatiotemporal filtering using ICA, an average reduction in scatter of 6.3% was achieved for all three components.

A method for scintillation characterization using geodetic receivers operating at 1 Hz

Abstract: Ionospheric scintillation produces strong disruptive effects on global navigation satellite system (GNSS) signals, ranging from degrading performances to rendering these signals useless for accurate navigation. The current paper presents a novel approach to detect scintillation on the GNSS signals based on its effect on the ionospheric-free combination of carrier phases, i.e. the standard combination of measurements used in precise point positioning (PPP). The method is implemented using actual data, thereby having both its feasibility and its usefulness assessed at the same time. The results identify the main effects of scintillation, which consist of an increased level of noise in the ionospheric-free combination of measurements and the introduction of cycle-slips into the signals. Also discussed is how mis-detected cycle-slips contaminate the rate of change of the total electron content index (ROTI) values, which is especially important for low-latitude receivers. By considering the effect of single jumps in the individual frequencies, the proposed method is able to isolate, over the combined signal, the frequency experiencing the cycle-slip. Moreover, because of the use of the ionospheric-free combination, the method captures the diffractive nature of the scintillation phenomena that, in the end, is the relevant effect on PPP. Finally, a new scintillation index is introduced that is associated with the degradation of the performance in navigation.

Determination of a high spatial resolution geopotential model using atomic clock comparisons

Abstract: Recent technological advances in optical atomic clocks are opening new perspectives for the direct determination of geopotential differences between any two points at a centimeter-level accuracy in geoid height. However, so far detailed quantitative estimates of the possible improvement in geoid determination when adding such clock measurements to existing data are lacking. We present a first step in that direction with the aim and hope of triggering further work and efforts in this emerging field of chronometric geodesy and geophysics. We specifically focus on evaluating the contribution of this new kind of direct measurements in determining the geopotential at high spatial resolution ( $$\approx $$ 10 km). We studied two test areas, both located in France and corresponding to a middle (Massif Central) and high (Alps) mountainous terrain. These regions are interesting because the gravitational field strength varies greatly from place to place at high spatial resolution due to the complex topography. Our method consists in first generating a synthetic high-resolution geopotential map, then drawing synthetic measurement data (gravimetry and clock data) from it, and finally reconstructing the geopotential map from that data using least squares collocation. The quality of the reconstructed map is then assessed by comparing it to the original one used to generate the data. We show that adding only a few clock data points (less than 1% of the gravimetry data) reduces the bias significantly and improves the standard deviation by a factor 3. The effect of the data coverage and data quality on the results is investigated, and the trade-off between the measurement noise level and the number of data points is discussed.

An analytical study on the carrier-phase linear combinations for triple-frequency GNSS

Abstract: The linear combinations of multi-frequency carrier-phase measurements for Global Navigation Satellite System (GNSS) are greatly beneficial to improving the performance of ambiguity resolution (AR), cycle slip correction as well as precise positioning. In this contribution, the existing definitions of the carrier-phase linear combination are reviewed and the integer property of the resulting ambiguity of the phase linear combinations is examined. The general analytical method for solving the optimal integer linear combinations for all triple-frequency GNSS is presented. Three refined triple-frequency integer combinations solely determined by the frequency values are introduced, which are the ionosphere-free (IF) combination that the Sum of its integer coefficients equal to 0 (IFS0), the geometry-free (GF) combination that the Sum of its integer coefficients equal to 0 (GFS0) and the geometry-free and ionosphere-free (GFIF) combination. Besides, the optimal GF, IF, extra-wide lane and ionosphere-reduced integer combinations for GPS and BDS are solved exhaustively by the presented method. Their potential applications in cycle slip detection, AR as well as precise positioning are discussed. At last, a more straightforward GF and IF AR scheme than the existing method is presented based on the GFIF integer combination.

Model improvements and validation of TerraSAR-X precise orbit determination

Abstract: The radar imaging satellite mission TerraSAR-X requires precisely determined satellite orbits for validating geodetic remote sensing techniques. Since the achieved quality of the operationally derived, reduced-dynamic (RD) orbit solutions limits the capabilities of the synthetic aperture radar (SAR) validation, an effort is made to improve the estimated orbit solutions. This paper discusses the benefits of refined dynamical models on orbit accuracy as well as estimated empirical accelerations and compares different dynamic models in a RD orbit determination. Modeling aspects discussed in the paper include the use of a macro-model for drag and radiation pressure computation, the use of high-quality atmospheric density and wind models as well as the benefit of high-fidelity gravity and ocean tide models. The Sun-synchronous dusk–dawn orbit geometry of TerraSAR-X results in a particular high correlation of solar radiation pressure modeling and estimated normal-direction positions. Furthermore, this mission offers a unique suite of independent sensors for orbit validation. Several parameters serve as quality indicators for the estimated satellite orbit solutions. These include the magnitude of the estimated empirical accelerations, satellite laser ranging (SLR) residuals, and SLR-based orbit corrections. Moreover, the radargrammetric distance measurements of the SAR instrument are selected for assessing the quality of the orbit solutions and compared to the SLR analysis. The use of high-fidelity satellite dynamics models in the RD approach is shown to clearly improve the orbit quality compared to simplified models and loosely constrained empirical accelerations. The estimated empirical accelerations are substantially reduced by 30% in tangential direction when working with the refined dynamical models. Likewise the SLR residuals are reduced from $$-3\,\pm \,17$$ to $$2\,\pm \,13$$ mm, and the SLR-derived normal-direction position corrections are reduced from 15 to 6 mm, obtained from the 2012–2014 period. The radar range bias is reduced from $$-10.3$$ to $$-6.1$$ mm with the updated orbit solutions, which coincides with the reduced standard deviation of the SLR residuals. The improvements are mainly driven by the satellite macro-model for the purpose of solar radiation pressure modeling, improved atmospheric density models, and the use of state-of-the-art gravity field models.

Multivariate analysis of GPS position time series of JPL second reprocessing campaign

Abstract: The second reprocessing of all GPS data gathered by the Analysis Centers of IGS was conducted in late 2013 using the latest models and methodologies. Improved models of antenna phase center variations and solar radiation pressure in JPL’s reanalysis are expected to significantly reduce errors. In an earlier work, JPL estimates of position time series, termed first reprocessing campaign, were examined in terms of their spatial and temporal correlation, power spectra, and draconitic signal. Similar analyses are applied to GPS time series at 89 and 66 sites of the second reanalysis with the time span of 7 and 21 years, respectively, to study possible improvements. Our results indicate that the spatial correlations are reduced on average by a factor of 1.25. While the white and flicker noise amplitudes for all components are reduced by 29–56 %, the random walk amplitude is enlarged. The white, flicker, and random walk noise amount to rate errors of, respectively, 0.01, 0.12, and 0.09 mm/yr in the horizontal and 0.04, 0.41 and 0.3 mm/yr in the vertical. Signals reported previously, such as those with periods of 13.63, 14.76, 5.5, and 351.4 / n for $$n=1,2,{\ldots },8$$ days, are identified in multivariate spectra of both data sets. The oscillation of the draconitic signal is reduced by factors of 1.87, 1.87, and 1.68 in the east, north and up components, respectively. Two other signals with Chandlerian period and a period of 380 days can also be detected.

Ionospheric and receiver DCB-constrained multi-GNSS single-frequency PPP integrated with MEMS inertial measurements

Abstract: Single-frequency precise point positioning (SF-PPP) is a potential precise positioning technique due to the advantages of the high accuracy in positioning after convergence and the low cost in operation However, there are still challenges limiting its applications at present, such as the long convergence time, the low reliability, and the poor satellite availability and continuity in kinematic applications In recent years, the achievements in the dual-frequency PPP have confirmed that its performance can be significantly enhanced by employing the slant ionospheric delay and receiver differential code bias (DCB) constraint model, and the multi-constellation Global Navigation Satellite Systems (GNSS) data Accordingly, we introduce the slant ionospheric delay and receiver DCB constraint model, and the multi-GNSS data in SF-PPP modular together In order to further overcome the drawbacks of SF-PPP in terms of reliability, continuity, and accuracy in the signal easily blocking environments, the inertial measurements are also adopted in this paper Finally, we form a new approach to tightly integrate the multi-GNSS single-frequency observations and inertial measurements together to ameliorate the performance of the ionospheric delay and receiver DCB-constrained SF-PPP In such model, the inter-system bias between each two GNSS systems, the inter-frequency bias between each two GLONASS frequencies, the hardware errors of the inertial sensors, the slant ionospheric delays of each user-satellite pair, and the receiver DCB are estimated together with other parameters in a unique Kalman filter To demonstrate its performance, the multi-GNSS and low-cost inertial data from a land-borne experiment are analyzed The results indicate that visible positioning improvements in terms of accuracy, continuity, and reliability can be achieved in both open-sky and complex conditions while using the proposed model in this study compared to the conventional GPS SF-PPP

Combination of multi-mission altimetry data along the Mekong River with spatio-temporal kriging

Abstract: River water-level time series at fixed geographical locations, so-called virtual stations, have been computed from single altimeter crossings for many years. Their temporal resolution is limited by the repeat cycle of the individual altimetry missions. The combination of all altimetry measurements along a river enables computing a water-level time series with improved temporal and spatial resolutions. This study uses the geostatistical method of spatio-temporal ordinary kriging to link multi-mission altimetry data along the Mekong River. The required covariance models reflecting the water flow are estimated based on empirical covariance values between altimetry observations at various locations. In this study, two covariance models are developed and tested in the case of the Mekong River: a stationary and a non-stationary covariance model. The proposed approach predicts water-level time series at different locations along the Mekong River with a temporal resolution of 5 days. Validation is performed against in situ data from four gauging stations, yielding RMS differences between 0.82 and 1.29 m and squared correlation coefficients between 0.89 and 0.94. Both models produce comparable results when used for combining data from Envisat, Jason-1, and SARAL for the time period between 2002 and 2015. The quality of the predicted time series turns out to be robust against a possibly decreasing availability of altimetry mission data. This demonstrates that our method is able to close the data gap between the end of the Envisat and the launch of the SARAL mission with interpolated time series.

Ionospheric error contribution to GNSS single-frequency navigation at the 2014 solar maximum

Abstract: For single-frequency users of the global satellite navigation system (GNSS), one of the main error contributors is the ionospheric delay, which impacts the received signals. As is well-known, GPS and Galileo transmit global models to correct the ionospheric delay, while the international GNSS service (IGS) computes precise post-process global ionospheric maps (GIM) that are considered reference ionospheres. Moreover, accurate ionospheric maps have been recently introduced, which allow for the fast convergence of the real-time precise point position (PPP) globally. Therefore, testing of the ionospheric models is a key issue for code-based single-frequency users, which constitute the main user segment. Therefore, the testing proposed in this paper is straightforward and uses the PPP modeling applied to single- and dual-frequency code observations worldwide for 2014. The usage of PPP modeling allows us to quantify—for dual-frequency users—the degradation of the navigation solutions caused by noise and multipath with respect to the different ionospheric modeling solutions, and allows us, in turn, to obtain an independent assessment of the ionospheric models. Compared to the dual-frequency solutions, the GPS and Galileo ionospheric models present worse global performance, with horizontal root mean square (RMS) differences of 1.04 and 0.49 m and vertical RMS differences of 0.83 and 0.40 m, respectively. While very precise global ionospheric models can improve the dual-frequency solution globally, resulting in a horizontal RMS difference of 0.60 m and a vertical RMS difference of 0.74 m, they exhibit a strong dependence on the geographical location and ionospheric activity.

Ice mass change in Greenland and Antarctica between 1993 and 2013 from satellite gravity measurements

Abstract: We construct long-term time series of Greenland and Antarctic ice sheet mass change from satellite gravity measurements. A statistical reconstruction approach is developed based on a principal component analysis (PCA) to combine high-resolution spatial modes from the Gravity Recovery and Climate Experiment (GRACE) mission with the gravity information from conventional satellite tracking data. Uncertainties of this reconstruction are rigorously assessed; they include temporal limitations for short GRACE measurements, spatial limitations for the low-resolution conventional tracking data measurements, and limitations of the estimated statistical relationships between low- and high-degree potential coefficients reflected in the PCA modes. Trends of mass variations in Greenland and Antarctica are assessed against a number of previous studies. The resulting time series for Greenland show a higher rate of mass loss than other methods before 2000, while the Antarctic ice sheet appears heavily influenced by interannual variations.

Application of ray-traced tropospheric slant delays to geodetic VLBI analysis

Abstract: The correction of tropospheric influences via so-called path delays is critical for the analysis of observations from space geodetic techniques like the very long baseline interferometry (VLBI). In standard VLBI analysis, the a priori slant path delays are determined using the concept of zenith delays, mapping functions and gradients. The a priori use of ray-traced delays, i.e., tropospheric slant path delays determined with the technique of ray-tracing through the meteorological data of numerical weather models (NWM), serves as an alternative way of correcting the influences of the troposphere on the VLBI observations within the analysis. In the presented research, the application of ray-traced delays to the VLBI analysis of sessions in a time span of 16.5 years is investigated. Ray-traced delays have been determined with program RADIATE (see Hofmeister in Ph.D. thesis, Department of Geodesy and Geophysics, Faculty of Mathematics and Geoinformation, Technische Universitat Wien. http://resolver.obvsg.at/urn:nbn:at:at-ubtuw:1-3444 , 2016) utilizing meteorological data provided by NWM of the European Centre for Medium-Range Weather Forecasts (ECMWF). In comparison with a standard VLBI analysis, which includes the tropospheric gradient estimation, the application of the ray-traced delays to an analysis, which uses the same parameterization except for the a priori slant path delay handling and the used wet mapping factors for the zenith wet delay (ZWD) estimation, improves the baseline length repeatability (BLR) at 55.9% of the baselines at sub-mm level. If no tropospheric gradients are estimated within the compared analyses, 90.6% of all baselines benefit from the application of the ray-traced delays, which leads to an average improvement of the BLR of 1 mm. The effects of the ray-traced delays on the terrestrial reference frame are also investigated. A separate assessment of the RADIATE ray-traced delays is carried out by comparison to the ray-traced delays from the National Aeronautics and Space Administration Goddard Space Flight Center (NASA GSFC) (Eriksson and MacMillan in http://lacerta.gsfc.nasa.gov/tropodelays , 2016) with respect to the analysis performances in terms of BLR results. If tropospheric gradient estimation is included in the analysis, 51.3% of the baselines benefit from the RADIATE ray-traced delays at sub-mm difference level. If no tropospheric gradients are estimated within the analysis, the RADIATE ray-traced delays deliver a better BLR at 63% of the baselines compared to the NASA GSFC ray-traced delays.

Estimation and analysis of Galileo differential code biases

Abstract: When sensing the Earth’s ionosphere using dual-frequency pseudorange observations of global navigation satellite systems (GNSS), the satellite and receiver differential code biases (DCBs) account for one of the main sources of error. For the Galileo system, limited knowledge is available about the determination and characteristic analysis of the satellite and receiver DCBs. To better understand the characteristics of satellite and receiver DCBs of Galileo, the IGGDCB (IGG, Institute of Geodesy and Geophysics, Wuhan, China) method is extended to estimate the satellite and receiver DCBs of Galileo, with the combined use of GPS and Galileo observations. The experimental data were collected from the Multi-GNSS Experiment network, covering the period of 2013–2015. The stability of both Galileo satellite and receiver DCBs over a time period of 36 months was thereby analyzed for the current state of the Galileo system. Good agreement of Galileo satellite DCBs is found between the IGGDCB-based DCB estimates and those from the German Aerospace Center (DLR), at the level of 0.22 ns. Moreover, high-level stability of the Galileo satellite DCB estimates is obtained over the selected time span (less than 0.25 ns in terms of standard deviation) by both IGGDCB and DLR algorithms. The Galileo receiver DCB estimates are also relatively stable for the case in which the receiver hardware device stays unchanged. It can also be concluded that the receiver DCB estimates are rather sensitive to the change of the firmware version and that the receiver antenna type has no great impact on receiver DCBs.

Differences between mean tide level and mean sea level

Abstract: This paper discusses the differences between mean tide level (MTL) and mean sea level (MSL) as demonstrated using information from a global tide gauge data set. The roles of the two main contributors to differences between MTL and MSL (the M4 harmonic of the M2 semidiurnal tide, and the combination of the diurnal tides K1 and O1) are described, with a particular focus on the spatial scales of variation in MTL–MSL due to each contributor. Findings from the tide gauge data set are contrasted with those from a state-of-the-art global tide model. The study is of interest within tidal science, but also has practical importance regarding the type of mean level used to define land survey datums. In addition, an appreciation of MTL–MSL difference is important in the use of the historical sea level data used in climate change research, with implications for some of the data stored in international databanks. Particular studies are made of how MTL and MSL might differ through the year, and if MTL is measured in daylight hours only, as has been the practice of some national geodetic agencies on occasions in the past.

Tropospheric refractivity and zenith path delays from least-squares collocation of meteorological and GNSS data

Abstract: Precise positioning requires an accurate a priori troposphere model to enhance the solution quality. Several empirical models are available, but they may not properly characterize the state of troposphere, especially in severe weather conditions. Another possible solution is to use regional troposphere models based on real-time or near-real time measurements. In this study, we present the total refractivity and zenith total delay (ZTD) models based on a numerical weather prediction (NWP) model, Global Navigation Satellite System (GNSS) data and ground-based meteorological observations. We reconstruct the total refractivity profiles over the western part of Switzerland and the total refractivity profiles as well as ZTDs over Poland using the least-squares collocation software COMEDIE (Collocation of Meteorological Data for Interpretation and Estimation of Tropospheric Pathdelays) developed at ETH Zurich. In these two case studies, profiles of the total refractivity and ZTDs are calculated from different data sets. For Switzerland, the data set with the best agreement with the reference radiosonde (RS) measurements is the combination of ground-based meteorological observations and GNSS ZTDs. Introducing the horizontal gradients does not improve the vertical interpolation, and results in slightly larger biases and standard deviations. For Poland, the data set based on meteorological parameters from the NWP Weather Research and Forecasting (WRF) model and from a combination of the NWP model and GNSS ZTDs shows the best agreement with the reference RS data. In terms of ZTD, the combined NWP-GNSS observations and GNSS-only data set exhibit the best accuracy with an average bias (from all stations) of 3.7 mm and average standard deviations of 17.0 mm w.r.t. the reference GNSS stations.

A first modeling of dynamic and static crustal strain field from near-field dilatation measurements: example of the 2013 M_w 6.2 Ruisui earthquake, Taiwan

Abstract: We analyze the high-resolution dilatation data for the October 2013 $$M_w$$ 6.2 Ruisui, Taiwan, earthquake, which occurred at a distance of 15–20 km away from a Sacks–Evertson dilatometer network. Based on well-constrained source parameters ( $$\hbox {strike}=217^\circ $$ , $$\hbox {dip}=48^\circ $$ , $$\hbox {rake}=49^\circ $$ ), we propose a simple rupture model that explains the permanent static deformation and the dynamic vibrations at short period ( $$\sim $$ 3.5–4.5 s) for most of the four sites with less than 20 % of discrepancies. This study represents a first attempt of modeling simultaneously the dynamic and static crustal strain using dilatation data. The results illustrate the potential for strain recordings of high-frequency seismic waves in the near-field of an earthquake to add constraints on the properties of seismic sources.

Quantifying deformation in North Borneo with GPS

Abstract: The existence of intra-plate deformation of the Sundaland platelet along its eastern edge in North Borneo, South-East Asia, makes it an interesting area that still is relatively understudied. In addition, the motion of the coastal area of North-West Borneo is directed toward a frontal fold-and-thrust belt and has been fueling a long debate on the possible geophysical sources behind it. At present this fold-and-thrust belt is not generating significant seismic activity and may also not be entirely active due to a decreasing shelfal extension from south to north. Two sets of Global Positioning System (GPS) data have been used in this study; the first covering a time period from 1999 until 2004 (ending just before the Giant Sumatra–Andaman earthquake) to determine the continuous Sundaland tectonic plate motion, and the second from 2009 until 2011 to investigate the current deformations of North Borneo. Both absolute and relative positioning methods were carried out to investigate horizontal and vertical displacements. Analysis of the GPS results indicates a clear trend of extension along coastal regions of Sarawak and Brunei in North Borneo. On the contrary strain rate tensors in Sabah reveal that only insignificant and inconsistent extension and compression occurs throughout North-West Borneo. Moreover, station velocities and rotation rate tensors on the northern part of North Borneo suggest a clockwise (micro-block) rotation. The first analysis of vertical displacements recorded by GPS in North-West Borneo points to low subsidence rates along the western coastal regions of Sabah and inconsistent trends between the Crocker and Trusmadi mountain ranges. These results have not been able to either confirm or reject the hypothesis that gravity sliding is the main driving force behind the local motions in North Borneo. The ongoing Sundaland–Philippine Sea plate convergence may also still play an active role in the present-day deformation (crustal shortening) in North Borneo and the possible clockwise rotation of the northern part of North Borneo as a micro-block. However, more observations need to be collected to determine if the northern part of North Borneo indeed is (slowly) moving independently.

A clear link connecting the troposphere and ionosphere: ionospheric reponses to the 2015 Typhoon Dujuan

Abstract: The global navigation satellite system (GNSS) total electron content (TEC) sequences were used to capture the arrival time and location of the ionosphere disturbances in response to the 2015 Typhoon Dujuan. After removing the de-trended TEC variation, the clear ionosphere disturbances on the typhoon landing day could be distinguished, and these disturbances disappeared from the TEC sequences before and after the typhoon landing day. The foF2 data observed by Xiamen ionosonde station also show ionosphere disturbances. Based on the advantages of GNSS multi-point observations, the disturbances horizontal velocity in the ionosphere were estimated according to the linear theory for a dispersion relation of acoustic gravity waves (AGWs) in an isothermal atmosphere. The average horizontal velocity ( $$\sim $$ 240 m/s) and the radial velocity ( $$\sim $$ 287 m/s) were used in the two-dimensional grid search for the origin point on the Earth’s surface. The origin area was determined to be on the eastern side of Taiwan. Lastly, a possible physical mechanism is discussed in this study. When typhoons land on Taiwan, the severe convective storms and the drag effect from the Central Mountains create an ideal location for development of AGWs. Topographic conditions, like the high lapse rate, contribute to the formation of AGWs, which then propagates into the ionosphere altitude.