Retrieval of the change of precipitable water vapor with zenith tropospheric delay in the Chinese mainland

As a preliminary step for assessing the impact of global positioning system (GPS) refractive delay data in numerical weather prediction (NWP) models, the GPS zenith tropospheric delays (ZTD) are analyzed from 28 permanent GPS sites in the Chinese mainland. The objectives are to estimate the GPS ZTD and their variability in this area. The differences between radiosonde precipitable water vapor (PWV) and GPS PWV have a standard deviation of 4 mm in delay, a bias of 0.24 mm in delay, and a correlation coefficient of 0.94. The correlation between GPS ZTD and radiosonde PWV amounts to 0.89, indicating that the variety of tropospheric zenith delay can reflect the change of precipitable water vapor. The good agreement also guarantees that the information provided by GPS will benefit the NWP models. The time series of GPS ZTD, which were derived continuously from 2002 to 2004, are used to analyze the change of precipitable water vapor in Chinese mainland. It shows that the general trend of GPS ZTD is diminishing from the south-east coastland to the north-west inland, which is in accordance with the distribution of Chinese annual amount of rainfall. The temporal distribution of GPS ZTD in the Chinese mainland is that the GPS ZTD reaches maximum in summer, and it reaches minimum in winter. The long term differences between the observational data sources require further study before GPS derived data become useful for climate studies.     

Real-time zenith tropospheric delays in support of numerical weather prediction applications

The Geodetic Observatory Pecný (GOP) routinely estimates near real-time zenith total delays (ZTD) from GPS permanent stations for assimilation in numerical weather prediction (NWP) models more than 12 years. Besides European regional, global and GPS and GLONASS solutions, we have recently developed real-time estimates aimed at supporting NWP nowcasting or severe weather event monitoring. While all previous solutions are based on data batch processing in a network mode, the real-time solution exploits real-time global orbits and clocks from the International GNSS Service (IGS) and Precise Point Positioning (PPP) processing strategy. New application G-Nut/Tefnut has been developed and real-time ZTDs have been continuously processed in the nine-month demonstration campaign (February–October, 2013) for selected 36 European and global stations. Resulting ZTDs can be characterized by mean standard deviations of 6–10 mm, but still remaining large biases up to 20 mm due to missing precise models in the software. These results fulfilled threshold requirements for the operational NWP nowcasting (i.e. 30 mm in ZTD). Since remaining ZTD biases can be effectively eliminated using the bias-reduction procedure prior to the assimilation, results are approaching the target requirements in terms of relative accuracy (i.e. 6 mm in ZTD). Real-time strategy and software are under the development and we foresee further improvements in reducing biases and in optimizing the accuracy within required timeliness. The real-time products from the International GNSS Service were found accurate and stable for supporting PPP-based tropospheric estimates for the NWP nowcasting.     

An inter-comparison of zenith tropospheric delays derived from DORIS and GPS data

Doppler Orbitography Radiopositioning Integrated by Satellite (DORIS) and Global Positioning System (GPS) techniques are similarly affected by propagation delays in the neutral atmosphere (troposphere) and hence make use of similar data processing strategies for reducing this effect. We compare Zenith Tropospheric Delays (ZTDs) estimated from 52 DORIS and GPS station pairs co-located at 35 sites over the 2005–2008 period. We find an overall systematic negative mean bias of −4 mm and a median bias of −2 mm, with a large site-to-site scatter and especially stronger biases over South America, potentially linked to remaining problems related to the South Atlantic Anomaly (SAA) in the current DORIS data processing. The standard deviation of ZTD differences is in the range 4–12 mm over the globe (8 mm on average), with larger values located in the southern hemisphere. The spatial variability of differences is consistent with previous work but remains largely unexplained. DORIS is shown to be much less sensitive to instrumental changes than GPS (only the switch from Alcatel to Starec antenna at Toulouse is detected as an offset of −4 mm in the ZTD time series). On the opposite, discontinuities and spurious annual signals are found in the GPS ZTD solutions. A discontinuity of +5 mm is found on 5 November 2006, linked to the switch from relative to absolute GPS antenna models used in the data processing. The use of modified GPS antennas (e.g. at GODE) or improved antenna models is shown to reduce the spurious annual signal (e.g. from 5 mm to 2 mm at METS). Overall, the agreement between both techniques is good, though DORIS shows a significantly larger random scatter. The high stability and good spatial and temporal coverage make DORIS a potential candidate technique for meteorology and climate studies as long as reasonable time averaging can be applied (e.g. differences are reduced from 8.6 to 2.4 mm with 5-day averages) and no real-time application is considered. This technique could be considered as a potential contributor to Global Geodetic Observing System (GGOS) for climatology.     

Improving the estimation of zenith dry tropospheric delays using regional surface meteorological data

Global Navigation Satellite Systems (GNSS) are emerging as possible tools for remote sensing high-resolution atmospheric water vapour that improves weather forecasting through numerical weather prediction models. Nowadays, the GNSS-derived tropospheric zenith total delay (ZTD), comprising zenith dry delay (ZDD) and zenith wet delay (ZWD), is achievable with sub-centimetre accuracy. However, if no representative near-site meteorological information is available, the quality of the ZDD derived from tropospheric models is degraded, leading to inaccurate estimation of the water vapour component ZWD as difference between ZTD and ZDD. On the basis of freely accessible regional surface meteorological data, this paper proposes a height-dependent linear correction model for a priori ZDD. By applying the ordinary least-squares estimation (OLSE), bootstrapping (BOOT), and leave-one-out cross-validation (CROS) methods, the model parameters are estimated and analysed with respect to outlier detection. The model validation is carried out using GNSS stations with near-site meteorological measurements. The results verify the efficiency of the proposed ZDD correction model, showing a significant reduction in the mean bias from several centimetres to about 5 mm. The OLSE method enables a fast computation, while the CROS procedure allows for outlier detection. All the three methods produce consistent results after outlier elimination, which improves the regression quality by about 20% and the model accuracy by up to 30%.     

Influence of different data fusion methods on the accuracy of three-dimensional displacements field

Combining multi-source data can improve the accuracy and the spatial resolution of the three-dimensional (3-D) displacements field. How to effectively integrate multi-source data to obtain high-precision and high spatial resolution 3-D displacements field is worthy of further study. The stochastic model and fusion model of integrating multi-source data affect the accuracy of data fusion. In this paper, based on the least squares method, the effects of different stochastic models and data fusion models on the 3-D displacements field’s accuracy are studied. The optimal method for estimating large-scale 3-D displacements field from integrated InSAR, leveling and GPS measurements is obtained. Then we realize the integrating InSAR, leveling and GPS measurements to obtain the high-precision 3-D displacements velocity field in Tianjin (China) from 2016 to 2018. The results are validated with GPS measurements at 6 independent stations, with the root mean squares (RMS) residuals of the discrepancies being 2.39 mm/yr, 2.54 mm/yr and 2.83 mm/yr in eastern, northern and vertical directions, respectively. By comparing different stochastic models, the 3-D displacements field obtained from multi-source data is optimized by the variance component estimation-least squares method, which is better than weighted least squares (WLS) method. By comparing different data fusion models, the accuracy of the horizontal displacements velocity is better than that of interpolated GPS results. The horizontal displacements component has a great influence on the vertical displacements velocity accuracy in the process of acquiring the 3-D displacements velocity by integrating InSAR, GPS and leveling measurements. This study provides a reference method for integrating multi-source data to obtain 3-D displacements field. This method effectively utilizes the advantages of GPS, InSAR and leveling measurements, and extends the limitations of single technical in describing surface-time scale applications. The 3-D displacements information with a large spatial scale and high spatial resolution provide a reliable data basis for studying the crustal movement and its dynamic mechanism.     

Evaluation of COMPASS ionospheric model in GNSS positioning

As important products of GNSS navigation message, ionospheric delay model parameters are broadcasted for single-frequency users to improve their positioning accuracy. GPS provides daily Klobuchar ionospheric model parameters based on geomagnetic reference frame, while the regional satellite navigation system of China’s COMPASS broadcasts an eight-parameter ionospheric model, COMPASS Ionospheric Model(CIM), which was generated by processing data from continuous monitoring stations, with updating the parameters every 2 h. To evaluate its performance, CIM predictions are compared to ionospheric delay measurements, along with GPS positioning accuracy comparisons. Real observed data analysis indicates that CIM provides higher correction precision in middle-latitude regions, but relatively lower correction precision for low-latitude regions where the ionosphere has much higher variability. CIM errors for some users show a common bias for in-coming COMPASS signals from different satellites, and hence ionospheric model errors are somehow translated into the receivers’ clock error estimation. In addition, the CIM from the China regional monitoring network are further evaluated for global ionospheric corrections. Results show that in the Northern Hemisphere areas including Asia, Europe and North America, the three-dimensional positioning accuracy using the CIM for ionospheric delay corrections is improved by 7.8%–35.3% when compared to GPS single-frequency positioning ionospheric delay corrections using the Klobuchar model. However, the positioning accuracy in the Southern Hemisphere is degraded due apparently to the lack of monitoring stations there.     

Comparative analysis of four different single-frequency PPP models on positioning performance and atmosphere delay retrieval

Single-frequency precise point positioning (SF-PPP) has attracted increasing attention due to its high precision and cost effectiveness. With various strategies to handle the dominant error, i.e., ionosphere delay, the ionosphere-float (IF), ionosphere-free-half (IFH), ionosphere-corrected (IC), and ionosphere-weighted (IW) SF-PPP models are certain to possess different characteristics and performance levels. This study is dedicated to assessing and comparing the four models from model characteristics, positioning performance, and atmosphere delay retrieval. The model comparison shows that IC and IW models are full-rank while IF and IFH models have a rank deficiency of size one that will result in biased estimations, which means the better solvability of IC and IW models. The experiments are carried out based on the 7-day Global Positioning System (GPS) observations collected at 57 global Multi-GNSS Experiment (MGEX) stations and Global Ionosphere Map (GIM) products. The results indicate that the IW model can accelerate SF-PPP convergence and achieve higher positioning accuracy compared to the other three SF-PPP models, especially in kinematic mode. With convergence criteria of 0.25 m in horizontal and 0.5 m in vertical, the east/north/up convergence times of IW model are 0.5/15.0/25.0 min and 0.5/16.0/36.5 min for static and kinematic modes, respectively. The IW model is able to achieve an instantaneous positioning accuracy of 0.28/0.35/0.75 m. In addition, a real kinematic test also demonstrates the best positioning solutions of IW model. Regarding troposphere delay retrieval, the IF, IFH, and IW models obtain a comparable daily accuracy of 3.0 cm on average, while the IC model achieves the worst accuracy of 8.0 cm. For precise ionosphere delay estimation, IW model only needs an average initialization time of 34.3 min, but a longer initialization time of 51.6 min is required for IF model. The daily precision of ionosphere delay estimation for IW model can reach up to 10.8 cm. At the present accuracy of GIM products, it is suggested that the IW model should be adopted for SF-PPP first due to its superior performance in positioning and atmosphere delay retrieval.     

Improved predictions of equatorial TEC for real time applications

It is important to use models developed specifically for the equatorial ionospheric estimation for real-time applications, particularly in Satellite Navigation. This work demonstrates a methodology for improved predictions of VTEC in real time using the model developed for the equatorial ionosphere by the authors. This work has been done using TEC data of the low solar activity period of 2005 obtained using dual frequency GPS receivers installed under the GAGAN project of ISRO. For the purpose, the model is first used in conjunction with Kriging technique. Improvement in accuracy is observed when compared with the estimations from the model alone using the measurements as true reference. Further improvement is obtained by Bayesian combination of these estimates with independent Neural Network based predictions. Statistical performance of improvement is provided. An improvement of ∼1 m in confidence level of estimation of VTEC is obtained.     

DORIS and GPS monitoring of the Gavdos calibration site in Crete

Due to its specific geographical location as well as its geodetic equipment (DORIS, GNSS, microwave transponder and tide gauges), the Gavdos station in Crete, Greece is one of the very few sites around the world used for satellite altimetry calibration. To investigate the quality of the Gavdos geodetic coordinates and velocities, we analyzed and compared here DORIS and GPS-derived results obtained during several years of observations. The DORIS solution is the latest ignwd11 solution at IGN, expressed in ITRF2008, while the GPS solution was obtained using the GAMIT software package. Current results show that 1–2 mm/yr agreement can be obtained for 3-D velocity, showing a good agreement with current geophysical models. In particular, the agreement obtained for the vertical velocity is around 0.3–0.4 mm/yr, depending on the terrestrial reference frame. As a by-product of these geodetic GPS and DORIS results, Zenith Tropospheric Delays (ZTDs) estimations were also compared in 2010 between these two techniques, and compared to ECMWF values, showing a 6.6 mm agreement in dispersion without any significant difference between GPS and DORIS (with a 97.6% correlation), but with a 13–14 mm agreement in dispersion when comparing to ECMWF model (with only about 90% correlation for both techniques). These tropospheric delay estimations could also provide an external calibration of the tropospheric correction used for the geophysical data of satellite altimetry missions.     

Tightly combined GPS/Galileo RTK for short and long baselines: Model and performance analysis

To ensure the compatibility and interoperability with modernized GPS, Galileo satellites are capable of broadcasting navigation signals on carrier phase frequencies that overlap with GPS, i.e., GPS/Galileo L1-E1/L5-E5a. Moreover, the GPS/Galileo L2-E5b signals have different frequencies with wavelength differences smaller than 4.2?mm. Such overlapping and narrowly spaced signals between GPS and Galileo bring the opportunity to use the tightly combined double-differenced (DD) model for precise real-time kinematic (RTK) positioning, resulting in improved performance of ambiguity resolution and positioning with respect to the classical standard or loosely combined DD model. In this paper, we focus on the model and performance assessment of tightly combined GPS/Galileo L1-E1/L2-E5b/L5-E5a RTK for short and long baselines. We first investigate the tightly combined GPS/Galileo DD observational model for both short and long baselines with simultaneously considering the GPS/Galileo overlapping and non-overlapping frequencies. Particularly, we introduce a reparameterization approach to solve the rank deficiency that caused by the correlation between the DISB parameters and the DD ionospheric parameters for both overlapping and non-overlapping frequencies. Then we present performance assessment for the tightly combined GPS/Galileo RTK model with real-time estimation of the differential inter-system bias (DISB) parameters for short and long baselines in terms of ratio value, ambiguity dilution of precision (ADOP), ambiguity conditional number, decorrelation number, search count, empirical success rate, time-to-first-fix (TTFF), and positioning accuracy. Results from both static and kinematic experiments demonstrated that compared to the loosely combined model, the tightly combined model can deliver improved performance of ambiguity resolution and precise positioning with different satellite visibility. For the car-driven short baseline experiment with 10° elevation cut-off angle, the tightly combined model can not only significantly increase the ratio value by approximately 27.5% (from 16.0 to 20.4), but also reduce the ambiguity ADOP, the conditional number, and the search count in LAMBDA by approximately 22.2% (from 0.027 to 0.021 cycles), 14.9% (from 199.2 to 169.6), and 25.4% (from 150.1 to 112.0), respectively. Comparable decorrelation number, empirical success rate, and positioning accuracy are also obtained. For the car-driven long baseline experiment, it is also observed that the ambiguity resolution performance in terms of the ratio value, the decorrelation number, the condition number, and the search count are significantly improved by approximately 18.5% (from 2.7 to 3.2), 22.0% (from 0.186 to 0.227), 55.9% (from 937.6 to 413.7), and 10.3% (from 43.8 to 39.3), respectively. Moreover, comparable ADOP, empirical success rate, and positioning accuracy are obtained as well. Additionally, the TTFF can be reduced (from 54.1 to 51.8 epochs with 10° elevation cut-off angle) as well from the results of static experiments.     

Inter-agency comparison of TanDEM-X baseline solutions

TanDEM-X (TerraSAR-X add-on for Digital Elevation Measurement) is the first Synthetic Aperture Radar (SAR) mission using close formation flying for bistatic SAR interferometry. The primary goal of the mission is to generate a global digital elevation model (DEM) with 2 m height precision and 10 m ground resolution from the configurable SAR interferometer with space baselines of a few hundred meters. As a key mission requirement for the interferometric SAR processing, the relative position, or baseline vector, of the two satellites must be determined with an accuracy of 1 mm (1D RMS) from GPS measurements collected by the onboard receivers. The operational baseline products for the TanDEM-X mission are routinely generated by the German Research Center for Geosciences (GFZ) and the German Space Operations Center (DLR/GSOC) using different software packages (EPOS/BSW, GHOST) and analysis strategies. For a further independent performance assessment, TanDEM-X baseline solutions are generated at the Astronomical Institute of the University of Bern (AIUB) on a best effort basis using the Bernese Software (BSW).     

Enhancing the kinematic precise orbit determination of low earth orbiters using GPS receiver clock modelling

Clock error estimation has been the focus of a great deal of research because of the extensive usage of clocks in GPS positioning applications. The receiver clock error in the spacecraft orbit determination is commonly estimated on an epoch-by-epoch basis, along with the spacecraft’s position. However, due to the high correlation between the spacecraft orbit altitude and the receiver clock parameters, estimates of the radial component are degraded in the kinematic approach. Using clocks with high stability, the predictable behaviour of the receiver oscillator can be exploited to improve the positioning accuracy, especially for the radial component. This paper introduces two GPS receiver clock models to describe the deterministic and stochastic property of the receiver clock, both of which can improve the accuracy of kinematic orbit determination for spacecraft in low earth orbit. In particular, the clock parameters are estimated as time offset and frequency offset in the two-state model. The frequency drift is also estimated as an unknown parameter in the three-state model. Additionally, residual non-deterministic random errors such as frequency white noise, frequency random walk noise and frequency random run noise are modelled. Test results indicate that the positioning accuracy could be improved significantly using one day of GRACE flight data. In particular, the error of the radial component was reduced by over 40.0% in the real-time scenario.     

An Integer Precise Point Positioning technique for sea surface observations using a GPS buoy

GPS data dedicated to sea surface observation are usually processed using differential techniques. Unfortunately, the precision of resulting kinematic positions is baseline-length dependent. So, high precision sea surface observations using differential GPS techniques are limited to coasts, lakes, and rivers. Recent improvements in GPS satellite products (orbits, clocks, and phase biases) make phase ambiguity fixing at the zero difference level achievable and opens up the observation of the sea surface without geographical constraints. This paper recalls the concept of the Integer Precise Point Positioning technique and discusses the precision of GPS buoy positioning. A sequential version of the GINS software has been implemented to achieve single epoch GPS positioning. We used 1 Hz data from a two week GPS campaign conducted in the Kerguelen Islands. A GPS buoy has been moored close to a radar gauge and 90 m away from a permanent GPS station. This infrastructure offers the opportunity to compare both kinematic Integer Precise Point Positioning and classical differential GPS positioning techniques to in situ radar gauge data. We found that Precise Point Positioning results are not significantly biased with respect to radar gauge data and that horizontal time series are consistent with differential processing at the sub-centimetre precision level. Nevertheless, standard deviations of height time series with respect to radar gauge data are typically [4–5] cm. The dominant driver for noise at this level is attributed to errors in tropospheric estimates which propagate into position solutions.     

The impact of microwave absorber and radome geometries on GNSS measurements of station coordinates and atmospheric water vapour

We have used microwave absorbing material in different geometries around ground-based Global Navigation Satellite System (GNSS) antennas in order to mitigate multipath effects on the estimates of station coordinates and atmospheric water vapour. The influence of a hemispheric radome – of the same type as in the Swedish GPS network SWEPOS – was also investigated. Two GNSS stations at the Onsala Space Observatory were used forming a 12 m baseline. GPS data from October 2008 to November 2009 were analyzed by the GIPSY/OASIS II software using the Precise Point Positioning (PPP) processing strategy for five different elevation cutoff angles from 5° to 25°. We found that the use of the absorbing material decreases the offset in the estimated vertical component of the baseline from ∼27 mm to ∼4 mm when the elevation cutoff angle varies from 5° to 20°. The horizontal components are much less affected. The corresponding offset in the estimates of the atmospheric Integrated Water Vapour (IWV) decreases from ∼1.6 kg/m² to ∼0.3 kg/m². Changes less than 5 mm in the offsets in the vertical component of the baseline are seen for all five elevation cutoff angle solutions when the antenna was covered by a hemispheric radome. Using the radome affects the IWV estimates less than 0.4 kg/m² for all different solutions. IWV comparisons between a Water Vapour Radiometer (WVR) and the GPS data give consistent results.     

Accuracy assessment of single and double difference models for the single epoch GPS compass

The single epoch GPS compass is an important field of study, since it is a valuable technique for the orientation estimation of vehicles and it can guarantee a total independence from carrier phase slips in practical applications. To achieve highly accurate angular estimates, the unknown integer ambiguities of the carrier phase observables need to be resolved. Past researches focus on the ambiguity resolution for single epoch; however, accuracy is another significant problem for many challenging applications. In this contribution, the accuracy is evaluated for the non-common clock scheme of the receivers and the common clock scheme of the receivers, respectively. We focus on three scenarios for either scheme: single difference model vs. double difference model, single frequency model vs. multiple frequency model and optimal linear combinations vs. traditional triple-frequency least squares. We deduce the short baseline precision for a number of different available models and analyze the difference in accuracy for those models. Compared with the single or double difference model of the non-common clock scheme, the single difference model of the common clock scheme can greatly reduce the vertical component error of baseline vector, which results in higher elevation accuracy. The least squares estimator can also reduce the error of fixed baseline vector with the aid of the multi-frequency observation, thereby improving the attitude accuracy. In essence, the “accuracy improvement” is attributed to the difference in accuracy for different models, not a real improvement for any specific model. If all noise levels of GPS triple frequency carrier phase are assumed the same in unit of cycles, it can be proved that the optimal linear combination approach is equivalent to the traditional triple-frequency least squares, no matter which scheme is utilized. Both simulations and actual experiments have been performed to verify the correctness of theoretical analysis.     

Preliminary analysis of the quality and positioning performance of BDS-3 global interoperable signal B1C&B2a

BeiDou-3 Navigation Satellite System (BDS-3) satellites are equipped with the new generation GNSS signals B1C and B2a, which support the interoperability with GPS and Galileo systems. In this study, the pseudo-range multipath error and carrier phase observation noise of the BDS-3 B1C and B2a signals were evaluated based on zero baseline measurements from the day of year (DOY) 113 to 116, 2020. Further, the precision and performance of the single point positioning (SPP) and precise point positioning (PPP) are assessed at 9 stations. This assessment manifests that the standard deviations (STDs) of the pseudo-range multipath error are about 0.09 ~ 0.22 m, while STDs of the carrier phase observation noise are about 0.075 mm. For the single-frequency SPP, its positioning precision is about 2.03 ~ 4.85 m and 3.29 ~ 10.73 m at the 99.99% confidence level in horizontal and vertical directions, respectively, while the dual-frequency SPP precision is about 1.92 ~ 8.02 m and 4.81 ~ 12.77 m in horizontal and vertical directions, respectively. For the daily static PPP, the convergence time is about 20 ~ 30 min, while the daily positioning precision can reach 1.38 ~ 4.42 cm and -1.31 ~ 4.34 cm in horizontal and vertical directions, respectively. In general, the quality and the SPP and PPP performance of the BDS-3 B1C&B2a signals are comparable to the GPS and Galileo.     

观测资料和卫星钟差对PPP参数收敛影响分析

在GPS 单点定位中, 参数解算的收敛时间和收敛稳定性是重要的研究内容之一, 影响收敛时间和收敛稳定性的因素很多, 本文主要就观测资料的不同采样间隔、卫星钟差资料的不同采样间隔、不同的定位精度要求对精密单点定位中参数收敛时间的影响进行了深入的分析探讨, 以中国上海GPS综合应用网中的12个测站资料为例, 分析了采样间隔、定位精度要求与收敛时间的关系, 并对不同采样间隔的收敛时间进行了统计分析, 得出一些初步结论.      

Contribution analysis of QZSS to single-frequency PPP of GPS/BDS/GLONASS/Galileo

The Quasi-Zenith Satellite System (QZSS) established by the Japan Aerospace Exploration Agency mainly serves the Asia-Pacific region and its surrounding areas. Currently, four in-orbit satellites provide services. Most users of GNSS in the mass market use single-frequency (SF) receivers owing to the low cost. Therefore, it is meaningful to analyze and evaluate the contribution of the QZSS to SF precise point positioning (PPP) of GPS/BDS/GLONASS/Galileo systems with the emergence of GNSS and QZSS. This study compares the performances of three SF PPP models, namely the GRoup and PHase Ionospheric Correction (GRAPHIC) model, GRAPHIC with code observation model, and an ionosphere-constrained model, and evaluated the contribution of the QZSS to the SF PPP of GPS/BDS/GLONASS/Galileo systems. Moreover, the influence of code bias on the SF PPP of the BDS system is also analyzed. A two-week dataset (DOY 013–026, 2019) from 10 stations of the MGEX network is selected for validation, and the results show that: (1) For cut-off elevation angles of 15, 20, and 25°, the convergence times for the static SF PPP of GLONASS + QZSS are reduced by 4.3, 30.8, and 12.7%, respectively, and the positioning accuracy is similar compared with that of the GLONASS system. Compared with the BDS single system, the convergence times for the static SF PPP of BDS + QZSS under 15 and 25° are reduced by 37.6 and 39.2%, the horizontal positioning accuracies are improved by 18.6 and 14.1%, and the vertical components are improved by 13.9 and 21.4%, respectively. At cut-off elevation angles of 15, 20, and 25°, the positioning accuracy and precision of GPS/BDS/GLONASS/Galileo + QZSS is similar to that of GPS/BDS/GLONASS/Galileo. And the convergence times are reduced by 7.4 and 4.3% at cut-off elevation angles of 20 and 25°, respectively. In imitating dynamic PPP, the QZSS significantly improves the positioning accuracy of BDS and GLONASS. However, QZSS has little effect on the GPS-only, Galileo-only and GPS/BDS/GLONASS/Galileo. (2) The code bias of BDS IGSO and MEO cannot be ignored in SF PPP. In static SF PPP, taking the frequency band of B1I whose multipath combination is the largest among the frequency bands as an example, the vertical component has a systematic bias of approximately 0.4–1.0 m. After correcting the code bias, the positioning error in the vertical component is lower than 0.2 m, and the positioning accuracy in the horizontal component are improved accordingly. (3) The SF PPP model with ionosphere constraints has a better convergence speed, while the positioning accuracy of the three models is nearly equal. Therefore the GRAPHIC model can be used to get good positioning accuracy in the absence of external ionosphere products, but its convergence speed is slower.     

Coastal sea level changes in Europe from GPS,tide gauge,satellite altimetry and GRACE, 1993–2011

Sea level changes are threatening the human living environments, particularly along the European Coasts with highly dense population. In this paper, coastal sea level changes in western and southern Europe are investigated for the period 1993–2011 using Global Positioning System (GPS), Tide Gauge (TG), Satellite Altimetry (SA), Gravity Recovery and Climate Experiment (GRACE) and geophysical models. The mean secular trend is 2.26 ± 0.52 mm/y from satellite altimetry, 2.43 ± 0.61 mm/y from TG+GPS and 1.99 ± 0.67 mm/y from GRACE mass plus steric components, which have a remarkably good agreement. For the seasonal variations, annual amplitudes of satellite altimetry and TG+GPS results are almost similar, while GRACE Mass+Steric results are a little smaller. The annual phases agree remarkably well for three independent techniques. The annual cycle is mainly driven by the steric contributions, while the annual phases of non-steric (mass component) sea level changes are almost a half year later than the steric sea level changes.