The Implementation of Precise Point Positioning (PPP): A Comprehensive Review

High-precision positioning from Global Navigation Satellite Systems (GNSS) has garnered increased interest due to growing demand in various applications, like autonomous car navigation and precision agriculture. Precise Point Positioning (PPP) offers a distinct advantage over differential techniques by enabling precise position determination of a GNSS rover receiver through the use of external corrections sourced from either the Internet or dedicated correction satellites. However, PPP's implementation has been challenging due to the need to mitigate numerous GNSS error sources, many of which are eliminated in differential techniques such as Real-Time Kinematics (RTK) or overlooked in Standard Point Positioning (SPP). This paper extensively reviews PPP's error sources, such as ionospheric delays, tropospheric delays, satellite orbit and clock errors, phase and code biases, and site displacement effects. Additionally, this article examines various PPP models and correction sources that can be employed to address these errors. A detailed discussion is provided on implementing the standard dual-frequency (DF)-PPP to achieve centimeter- or millimeter-level positioning accuracy. This paper includes experimental examples of PPP implementation results using static data from the International GNSS Service (IGS) station network and a kinematic road test based on the actual trajectory to showcase DF-PPP development for practical applications. By providing a fusion of theoretical insights with practical demonstrations, this comprehensive review offers readers a pragmatic perspective on the evolving field of Precise Point Positioning.

Sensitivity of Shipborne GNSS Estimates to Processing Modeling Based on Simulated Dataset

The atmospheric water vapor is commonly monitored from ground Global Navigation Satellite System (GNSS) measurements, by retrieving the tropospheric delay under the Zenith Wet Delay (ZWD) component, linked to the water vapor content in the atmosphere. In recent years, the GNSS ZWD retrieval has been performed on shipborne antennas to gather more atmospheric data above the oceans for climatology and meteorology study purposes. However, when analyzing GNSS data acquired by a moving antenna, it is more complex to decorrelate the height of the antenna and the ZWD during the Precise Point Positioning (PPP) processing. Therefore, the observation modeling and processing parametrization must be tuned. This study addresses the impact of modeling on the estimation of height and ZWD from the simulation of shipborne GNSS measurements. The GNSS simulation is based on an authors-designed simulator presented in this article. We tested different processing models (elevation cut-off angle, elevation weighting function, and random walk of ZWD) and simulation configurations (the constellations used, the sampling of measurements, the location of the antenna, etc.). According to our results, we recommend processing shipborne GNSS measurements with 3° of cut-off angle, elevation weighting function square root of sine, and an average of 5 mm·h-1/2 of random walk on ZWD, the latter being specifically adapted to mid-latitudes but which could be extended to other areas. This processing modeling will be applied in further studies to monitor the distribution of water vapor above the oceans from systematic analysis of shipborne GNSS measurements.

Modified Two-Point Correction Method for Wide-Spectrum LWIR Detection System

Non-uniformity commonly exists in the infrared focal plane, which behaves as the fixed-pattern noise (FPN) and seriously affects the image quality of long-wave infrared (LWIR) detection systems. The two-point correction (TPC) method is commonly used to reduce image FPN in engineering. However, when a wide-spectrum LWIR detection system calibrated with a black body is used to detect weak and small targets in the sky, FPN still appears in the image, affecting its uniformity. The effects of atmospheric transmittance characteristics of long-range paths on the non-uniformity of wide-spectrum long-wave infrared systems have not been studied. This paper proposes a modified TPC model based on spectral subdivision that introduces atmospheric transmittance. Additionally, the effects of atmospheric transmittance characteristics on the long-wave infrared non-uniform correction coefficient are analyzed. The experimental results for a black body scene and sky scene using a weak and small target detection system with a long-wave Sofradir FPA demonstrate that the wide-spectrum LWIR detection system fully considers atmospheric transmittance when performing calibration based on the TPC method, which can reduce the non-uniformity of the image.

Multi-GNSS-Weighted Interpolated Tropospheric Delay to Improve Long-Baseline RTK Positioning

Until now, RTK (real-time kinematic) and NRTK (Network-based RTK) have been the most popular cm-level accurate positioning approaches based on Global Navigation Satellite System (GNSS) signals in real-time. The tropospheric delay is a major source of RTK errors, especially for medium and long baselines. This source of error is difficult to quantify due to its reliance on highly variable atmospheric humidity. In this paper, we use the NRTK approach to estimate double-differenced zenith tropospheric delays alongside ambiguities and positions based on a complete set of multi-GNSS data in a sample 6-station network in Europe. The ZTD files published by IGS were used to validate the estimated ZTDs. The results confirmed a good agreement, with an average Root Mean Squares Error (RMSE) of about 12 mm. Although multiplying the unknowns makes the mathematical model less reliable in correctly fixing integer ambiguities, adding a priori interpolated ZTD as quasi-observations can improve positioning accuracy and Integer Ambiguity Resolution (IAR) performance. In this work, weighted least-squares (WLS) were performed using the interpolation of ZTD values of near reference stations of the IGS network. When using a well-known Kriging interpolation, the weights depend on the semivariogram, and a higher network density is required to obtain the correct covariance function. Hence, we used a simple interpolation strategy, which minimized the impact of altitude variability within the network. Compared to standard RTK where ZTD is assumed to be unknown, this technique improves the positioning accuracy by about 50%. It also increased the success rate for IAR by nearly 1.

Validating Precise Orbit Determination from Satellite-Borne GPS Data of Haiyang-2D

Haiyang-2D (HY-2D) is the fourth satellite in the marine dynamic satellite series established by China. It was successfully launched on 19 May 2021, marking the era of the 3-satellite network in the marine dynamic environment satellite series of China. The satellite’s precision orbit determination (POD) and validations are of great significance for ocean warning and marine altimetry missions. HY-2D is equipped with a laser reflector array (LRA), a satellite-borne Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS) receiver, and a satellite-borne dual-frequency GPS receiver named HY2 that was independently developed in China. In this paper, the quality of GPS data collected by the HY2 is analyzed based on indicators such as the multipath effect, cycle slips, and data completeness. The results suggest that the receiver can be used in POD missions involving low-Earth-orbit (LEO) satellites. The precise orbits of HY-2D are determined by the reduced-dynamics (RD) method. Apart from POD, validation of orbit accuracy is another important task for LEO POD. Therefore, two external validation methods are proposed, including carrier differential validation using one GPS satellite and inter-satellite differential validation using two GPS satellites. These are based on space-borne carrier-phase data, and the GPS satellites used for POD validation do not participate in orbit determination. The results of SLR range validation cannot illustrate the orbit accuracy in x, y, and z directions particularly, so to make validation results more intuitive, the SLR three-dimensional (3D) validation is proposed based on SLR range validation, and the RMSs in x, y, and z directions are 2.66, 3.32, and 2.69 cm, respectively. The results of SLR 3D validation are the same as those of SLR range validation, which proves that the new external validation method provided by SLR 3D is reliable. The RMSs of carrier differential validation and inter-satellite differential validation are 0.68 and 1.06 cm, respectively. The proposed validation methods are proved to be reliable.

Optimizing the Sampling Area across an Old-Growth Forest via UAV-Borne Laser Scanning, GNSS, and Radial Surveying

Aboveground biomass, volume, and basal area are among the most important structural attributes in forestry. Direct measurements are cost-intensive and time-consuming, especially for old-growth forests exhibiting a complex structure over a rugged topography. We defined a methodology to optimize the plot size and the (total) sampling area, allowing for structural attributes with a tolerable error to be estimated. The plot size was assessed by analyzing the semivariogram of a CHM model derived via UAV laser scanning, while the sampling area was based on the calculation of the absolute relative error as a function of allometric relationships. The allometric relationships allowed the structural attributes from trees’ height to be derived. The validation was based on the positioning of a number of trees via total station and GNSS surveys. Since high trees occlude the GNSS signal transmission, a strategy to facilitate the positioning was to fix the solution using the GLONASS constellation alone (showing the highest visibility during the survey), and then using the GPS constellation to increase the position accuracy (up to PDOP~5−10). The tree heights estimated via UAV laser scanning were strongly correlated (r2 = 0.98, RMSE = 2.80 m) with those measured in situ. Assuming a maximum absolute relative error in the estimation of the structural attribute (20% within this work), the proposed methodology allowed the portion of the forest surface (≤60%) to be sampled to be quantified to obtain a low average error in the calculation of the above mentioned structural attributes (≤13%).

Understanding the Present-Day Spatiotemporal Variability of Precipitable Water Vapor over Ethiopia: A Comparative Study between ERA5 and GPS

Atmospheric water vapor plays a crucial role in atmospheric, climate change, meteorological, and hydrological processes. In a country like Ethiopia, with its complex topography and synoptic-scale spatiotemporal circulation patterns, the analysis of the spatiotemporal variability of precipitable water vapor (PWV) is very challenging, and is hampered by the lack of long observational datasets. In this study, we process the PWV over eight Ethiopian global positioning system (GPS) sites and one close to the Ethiopian eastern border, for the available common period 2013–2020, and compare with the PWV retrieved from the state-of-the-art ERA5 reanalysis. Both PWV datasets agree very well at our sample, with correlation coefficients between 0.96 and 0.99, GPS-PWV show a moderate wet bias compared to ERA5-PWV for the majority of the sites, and an overall root mean square error of 3.4 mm. Seasonal and diurnal cycles are also well captured by these datasets. The seasonal variations of PWV and precipitation at the sites agree very well. Maximum diurnal PWV amplitudes are observed for stations near water bodies or dense vegetation, such as Arbaminch (ARMI) and Bahir Dar (BDMT). At those stations, the PWV behavior at heavy rainfall events has been investigated and an average 25% increase (resp. decrease) from 12 h before (resp. 12 h after) the start of the rainfall event, when the PWV peaks, has been observed.

Evaluation of the Integrity Risk for Precise Point Positioning

Global Navigation Satellite System (GNSS) Precise Point Positioning (PPP) is an attractive positioning technology due to its high precision and flexibility. However, the vulnerability of PPP brings a safety risk to its application in the field of life safety, which must be evaluated quantitatively to provide integrity for PPP users. Generally, PPP solutions are processed recursively based on the extended Kalman filter (EKF) estimator, utilizing both the previous and current measurements. Therefore, the integrity risk should be qualified considering the effects of all the potential observation faults in history. However, this will cause the calculation load to explode over time, which is impractical for long-time missions. This study used the innovations in a time window to detect the faults in the measurements, quantifying the integrity risk by traversing the fault modes in the window to maintain a stable computation cost. A non-zero bias was conservatively introduced to encapsulate the effect of the faults before the window. Coping with the multiple simultaneous faults, the worst-case integrity risk was calculated to overbound the real risk in the multiple fault modes. In order to verify the proposed method, simulation and experimental tests were carried out in this study. The results showed that the fixed and hold mode adopted for ambiguity resolution is critical to an integrity risk evaluation, which can improve the observation redundancy and remove the influence of the biased predicted ambiguities on the integrity risk. Increasing the length of the window can weaken the impact of the conservative assumption on the integrity risk due to the smoothing effect of the EKF estimator. In addition, improving the accuracy of observations can also reduce the integrity risk, which indicates that establishing a refined PPP random model can improve the integrity performance.

Tropospheric Refractivity Profile Estimation by GNSS Measurement at China Big-Triangle Points

Atmospheric radio refractivity has an obvious influence on the signal transmission path and communication group delay effect. The uncertainty of water vapor distribution is the main reason for the large error of tropospheric refractive index modeling. According to the distribution and characteristics of water vapor pressure, temperature, and pressure, which are the basic components of the refractive index, a method for retrieving atmospheric refractivity profile based on GNSS (Global Navigation Satellite System) and meteorological sensor measurement is introduced and investigated in this study. The variation of the correlation between zenith wet delay and water vapor pressure is investigated and analyzed in detail. The partial pressure profiles of water vapor are retrieved with relevance vector machine method based on tropospheric zenith wet delay calculated by single ground-based GPS (Global Positioning System) receiver. The atmospheric temperature and pressure is calculated with the least square method, which is used to fit the coefficients of the polynomial model based on a large number of historical meteorological radiosonde data of local stations. By combining the water vapor pressure profile retrieving from single ground-based GPS and temperature and pressure profile from reference model, the refractivity profile can be obtained, which is compared to radiosonde measurements. The comparison results show that results of the proposed method are consistent with the results of radiosonde. By using over ten years’ (through 2008 to 2017) historical radiosonde meteorological data of different months at China Big-Triangle Points, i.e., Qingdao, Sanya, Kashi, and Jiamusi radiosonde stations, tropospheric radio refractivity profiles are retrieved and modeled. The comparison results present that the accuracies of refractivity profile of the proposed method at Qingdao, Sanya, Kashi, and Jiamusi are about 5.48, 5.63, 3.58, and 3.78 N-unit, respectively, and the annual average relative RMSE of refractivity at these stations are about 1.66, 1.53, 1.49, and 1.23%, respectively.

On Satellite-Borne GPS Data Quality and Reduced-Dynamic Precise Orbit Determination of HY-2C: A Case of Orbit Validation with Onboard DORIS Data

Haiyang-2C (HY-2C) is a dynamic, marine-monitoring satellite that was launched by China and is equipped with an onboard dual-frequency GPS receiver named HY2_Receiver, which was independently developed in China. HY-2C was successfully launched on 21 September 2020. Its precise orbit is an important factor for scientific research applications, especially for marine altimetry missions. The performance of the HY2_Receiver is assessed based on indicators such as the multipath effect, ionospheric delay, cycle slip and data utilization, and assessments have suggested that the receiver can be used in precise orbit determination (POD) missions involving low-Earth-orbit (LEO) satellites. In this study, satellite-borne GPS data are used for POD with a reduced-dynamic (RD) method. Phase centre offset (PCO) and phase centre variation (PCV) models of the GPS antenna are established during POD, and their influence on the accuracy of orbit determination is analysed. After using the PCO and PCV models in POD, the root mean square (RMS) of the carrier-phase residuals is around 0.008 m and the orbit overlap validation accuracy in each direction reaches approximately 0.01 m. Compared with the precise science orbit (PSO) provided by the Centre National d’Etudes Spatiales (CNES), the RD orbit accuracy of HY-2C in the radial (R) direction reaches 0.01 m. The accuracy of satellite laser ranging (SLR) range validation is better than 0.03 m. Additionally, a new method is proposed to verify the accuracy of the RD orbit of HY-2C by using space-borne Doppler orbitography and radiopositioning integrated by satellite (DORIS) data directly. DORIS data are directly compared to the result calculated using the accurate coordinates of beacons and the RD orbit, and the results indicate that the external validation of HY-2C RD orbit has a range rate accuracy of within 0.0063 m/s.

Analysis of the Precipitable Water Vapor Observation in Yunnan–Guizhou Plateau during the Convective Weather System in Summer

The ERA5 reanalysis dataset of the European Center for Medium-Range Weather Forecasts (ECMWF) in the summers from 2015 to 2020 was used to compare and analyze the features of the precipitable water vapor (PWV) observed by six ground-based Global Navigation Satellite System (GNSS) meteorology (GNSS/MET) stations in the Yunnan–Guizhou Plateau. The correlation coefficients of the two datasets ranged between 0.804 and 0.878, the standard deviations ranged between 4.686 and 7.338 mm, and the monthly average deviations ranged between −4.153 and 9.459 mm, which increased with the altitude of the station. Matching the quality-controlled ground precipitation data with the PWV in time and space revealed that most precipitation occurred when the PWV was between 30 and 65 mm and roughly met the normal distribution. We used the vertical integral of divergence of moisture flux (∇p) and S-band Doppler radar networking products combined with the PWV to study the convergence and divergence process and the water vapor delivery conditions during the deep convective weather process from August 24 to 26, 2020, which can be used to analyze the real-time observation capability and continuity of PWV in small-scale and mesoscale weather processes. Furthermore, the 1 h precipitation and the cloud top temperature (ctt) data at the same site were used to demonstrate the effect of PWV on the transit of convective weather systems from different time–space scales.

Modified Interpolation Method of Multi-Reference Station Tropospheric Delay Considering the Influence of Height Difference

In network real-time kinematic (NRTK) positioning, atmospheric delay information is critical for generating virtual observations at a virtual reference station (VRS). The traditional linear interpolation method (LIM) is widely used to obtain the atmospheric delay correction. However, even though the conventional LIM is robust in the horizontal direction of the atmospheric error, it ignores the influence of the vertical direction, especially for the tropospheric error. If the height difference between the reference stations and the rover is large and, subsequently, tropospheric error and height are strongly correlated, the performance of the traditional method is degraded for tropospheric delay interpolation at the VRS. Therefore, considering the height difference between the reference stations and the rover, a modified linear interpolation method (MLIM) is proposed to be applied to a conventional single Delaunay triangulated network (DTN). The systematic error of the double-differenced (DD) tropospheric delay in the vertical direction is corrected first. The LIM method is then applied to interpolate the DD tropospheric delay at the VRS. In order to verify the performance of the proposed method, we used two datasets from the American NOAA continuously operating reference stations (CORS) network with significant height differences for experiments and analysis. Results show that the DD tropospheric delay interpolation accuracy obtained by the modified method is improved by 84.1% and 69.6% on average in the two experiments compared to the conventional method. This improvement is significant, especially for low elevation satellites. In rover positioning analysis, the traditional LIM has a noticeable systematic deviation in the up component. Compared to the conventional method, the positioning accuracy of the MLIM method is improved in the horizontal and vertical directions, especially in the up component. The accuracy of the up component is reduced from tens of centimeters to a few centimeters and demonstrates better positioning stability.

Lithosphere atmosphere ionosphere coupling associated with the 2019 Mw 7.1 California earthquake using GNSS and multiple satellites

Global Navigation Satellite System (GNSS)-based Earthquake (EQ) anomalies in the ionosphere and troposphere provide explicit evidences to study the coupling between seismic events, atmosphere, and ionosphere in epicentral breeding regions consequent to the EQ day in the preparation period. EQs are still not predicted, but the space-based EQ anomalies aid in the development of monitoring pre- and post-seismic precursors around the seismogenic zone and associated fault lineament regions. In this paper, tropospheric and ionospheric anomalies are investigated for the July 06, 2019, M_w 7.1 California EQ from GNSS tropospheric delays and Total Electron Content (TEC), respectively. We noticed that atmospheric and ionospheric anomalies from GNSS stations within 5-10 days before the main shock and storm-induced ionospheric variations occur beyond the 5th day after the EQ. Similarly, synchronized and collocated lower atmospheric anomalies are also recorded in the long-term temporal values of SO₂ and SO₄ within 1-month before and after July 2019, which validates the existence of Lithosphere-Atmosphere-Ionosphere Coupling (LAIC) over the EQ epicenter. On the other hand, EQ anomalies occur during quiet geomagnetic storm activity (Kp < 3; Dst < - 20 nT) and geomagnetic storm triggered high-intensity ionospheric variations during Kp > 3. All these atmospheric and ionospheric perturbations support the development in EQ precursors with satellite measurements, which are indispensable towards the forecasting of future EQ.

The Ground Deformation History of the Neapolitan Volcanic Area (Campi Flegrei Caldera, Somma–Vesuvius Volcano, and Ischia Island) from 20 Years of Continuous GPS Observations (2000–2019)

The Neapolitan volcanic area includes three active and high-risk volcanoes: Campi Flegrei caldera, Somma–Vesuvius, and Ischia island. The Campi Flegrei volcanic area is a typical example of a resurgent caldera, characterized by intense uplift periods followed by subsidence phases (bradyseism). After about 21 years of subsidence following the 1982–1984 unrest, a new inflation period started in 2005 and, with increasing rates over time, is ongoing. The overall uplift from 2005 to December 2019 is about 65 cm. This paper provides the history of the recent Campi Flegrei caldera unrest and an overview of the ground deformation patterns of the Somma–Vesuvius and Ischia volcanoes from continuous GPS observations. In the 2000–2019 time span, the GPS time series allowed the continuous and accurate tracking of ground and seafloor deformation of the whole volcanic area. With the aim of improving the research on volcano dynamics and hazard assessment, the full dataset of the GPS time series from the Neapolitan volcanic area from January 2000 to December 2019 is presented and made available to the scientific community.

A Method to Accelerate the Convergence of Satellite Clock Offset Estimation Considering the Time-Varying Code Biases

Continuous and stable precision satellite clock offsets are an important guarantee for real-time precise point positioning (PPP). However, in real-time PPP, the estimation of a satellite clock is often interrupted for various reasons such as network fluctuations, which leads to a long time for clocks to converge again. Typically, code biases are assumed to stay constant over time in clock estimation according to the current literature. In this contribution, it is shown that this assumption reduces the convergence speed of estimation, and the satellite clocks are still unstable for several hours after convergence. For this reason, we study the influence of different code bias extraction schemes, that is, taking code biases as constants, extracting satellite code biases (SCBs), extracting receiver code biases (RCBs) and simultaneously extracting SCBs and RCBs, on satellite clock estimation. Results show that, the time-varying SCBs are the main factors leading to the instability of satellite clocks, and considering SCBs in the estimation can significantly accelerate the filter convergence and improve the stability of clocks. Then, the products generated by introducing SCBs in the clock estimation based on undifferenced observations are applied to PPP experiments. Compared with the original undifferenced model, clocks estimated using the new method can significantly accelerate the convergence speed of PPP and improve the positioning accuracy, which illustrates that our estimated clocks are effective and superior.

A Regional Model for Predicting Tropospheric Delay and Weighted Mean Temperature in China Based on GRAPES_MESO Forecasting Products

Accurate tropospheric delay (TD) and weighted mean temperature (Tm) are important for Global Navigation Satellite System (GNSS) positioning and GNSS meteorology. For this purpose, plenty of empirical models have been built to provide estimates of TD and Tm. However, these models cannot resolve TD and Tm variations at synoptic timescales since they only model the average annual, semi-annual, and/or daily variations. As a result, the existed empirical models cannot perform well under extreme weather conditions. To address this limitation, we propose to estimate Zenith Hydrostatic Delay (ZHD), Zenith Wet Delay (ZWD), and Tm directly from the stratified numerical weather forecasting products of the mesoscale version of the Global/Regional Assimilation and PrEdiction System (GRAPES_MESO) of China. The GRAPES_MESO forecasting data has a temporal resolution of 3 h, which provides the opportunity to resolve the synoptic variation. However, it is found that the estimated ZWD and Tm exhibit apparent systematic deviation from in situ observation-based estimates, which is due to the inherent biases in the GRAPES_MESO data. To solve this problem, we propose to correct these biases using a linear model and a spherical cap harmonic model. The estimates after correction are termed as the “CTropGrid” products. When validated by the radiosonde data, the CTropGrid product has biases of 1.5 mm, −0.7 mm, and −0.1 K, and Root Mean Square (RMS) error of 8.9 mm, 20.2 mm, and 1.5 K for ZHD, ZWD, and Tm. Compared to the widely used GPT2w model, the CTropGrid products have improved the accuracies of ZHD, ZWD, and Tm by 11.9%, 55.6%, and 60.5% in terms of RMS. When validating the Zenith Tropospheric Delay (ZTD) products (the sum of ZHD and ZWD) using the IGS ZTD data, the CTropGrid ZTD has a bias of −0.7 mm and an RMS of 35.8 mm, which is 22.7% better than the GPT2w model in terms of RMS. Besides the accuracy improvements, the CTropGrid products well model the synoptic-scale variations of ZHD, ZWD, and Tm. Compared to the existing empirical models that only capture the tidal (seasonal and/or diurnal) variations, the CTropGrid products capture well the non-tidal variations of ZHD, ZWD, and Tm, which enhances the tropospheric delay corrections and GNSS water vapor monitoring at synoptic timescales. Therefore, the CTropGrid product is an important progress in GNSS positioning and GNSS meteorology.

Multiscale Post-Seismic Deformation Based on cGNSS Time Series Following the 2015 Lefkas (W. Greece) Mw6.5 Earthquake

In the present work, a multiscale post-seismic relaxation mechanism, based on the existence of a distribution in relaxation time, is presented. Assuming an Arrhenius dependence of the relaxation time with uniform distributed activation energy in a mesoscopic scale, a generic logarithmic-type relaxation in a macroscopic scale results. The model was applied in the case of the strong 2015 Lefkas Mw6.5 (W. Greece) earthquake, where continuous GNSS (cGNSS) time series were recorded in a station located in the near vicinity of the epicentral area. The application of the present approach to the Lefkas event fits the observed displacements implied by a distribution of relaxation times in the range τmin ≈ 3.5 days to τmax ≈ 350 days.

The Impact of Different Ocean Tide Loading Models on GNSS Estimated Zenith Tropospheric Delay Using Precise Point Positioning Technique

Global navigation satellite systems (GNSSs) have become an important tool to derive atmospheric products, such as the total zenith tropospheric delay (ZTD) and precipitable water vapor (PWV) for weather and climate studies. The ocean tide loading (OTL) effect is one of the primary errors that affects the accuracy of GNSS-derived ZTD/PWV, which means the study and choice of the OTL model is an important issue for high-accuracy ZTD estimation. In this study, GNSS data from 1 January 2019 to 31 January 2019 are processed using precise point positioning (PPP) at globally distributed stations. The performance of seven widely used global OTL models is assessed and their impact on the GNSS-derived ZTD is investigated by comparing them against the ZTD calculated from co-located radiosonde observations. The results indicate that the inclusion or exclusion of the OTL effect will lead to a difference in ZTD of up to 3–15 mm for island stations, and up to 1–2 mm for inland stations. The difference of the ZTD determined with different OTL models is quite small, with a root-mean-square (RMS) value below 1.5 mm at most stations. The comparison between the GNSS-derived ZTD and the radiosonde-derived ZTD indicates that the adoption of OTL models can improve the accuracy of GNSS-derived ZTD. The results also indicate that the adoption of a smaller cutoff elevation, e.g., 3° or 7°, can significantly reduce the difference between the ZTDs determined by GNSS and radiosonde, when compared against a 15° cutoff elevation. Compared to the radiosonde-derived ZTD, the RMS error of GNSS-derived ZTD is approximately 25–35 mm at a cutoff elevation of 15°, and 15–25 mm when the cutoff elevation is set to 3°.

Performance Assessment of PPP Surveys with Open Source Software Using the GNSS GPS–GLONASS–Galileo Constellations

In this work, the performance of the multi-GNSS (Global Navigation Satellite System) Precise Point Positioning (PPP) technique, in static mode, is analyzed. Specifically, GPS (Global Positioning System), GLONASS, and Galileo systems are considered, and quantifying the Galileo contribution is one of the main objectives. The open source software RTKLib is adopted to process the data, with precise satellite orbits and clocks from CNES (Centre National d’Etudes Spatiales) and CLS (Collecte Localisation Satellites) analysis centers for International GNSS Service (IGS). The Iono-free model is used to correct ionospheric errors, the GOT-4.7 model is used to correct tidal effects, and Differential Code Biases (DCB) are taken from the Deutsche Forschungsanstalt für Luftund Raumfahrt (DLR) center. Two different tropospheric models are tested: Saastamoinen and Estimate ZTD (Zenith Troposhperic Delay). For the proposed study, a dataset of 31 days from a permanent GNSS station, placed in Palermo (Italy), and a dataset of 10 days from a static geodetic receiver, placed nearby the station, have been collected and processed by the most used open source software in the geomatic community. The considered GNSS configurations are seven: GPS only, GLONASS only, Galileo only, GPS+GLONASS, GPS+Galileo, GLONASS+Galileo, and GPS+GLONASS+Galileo. The results show significant performance improvement of the GNSS combinations with respect to single GNSS cases.

Automatic Calibration of Process Noise Matrix and Measurement Noise Covariance for Multi-GNSS Precise Point Positioning

The Expectation-Maximization algorithm is adapted to the extended Kalman filter to multiple GNSS Precise Point Positioning (PPP), named EM-PPP. EM-PPP considers better the compatibility of multiple GNSS data processing and characteristics of receiver motion, targeting to calibrate the process noise matrix Qt and observation matrix Rt, having influence on PPP convergence time and precision, with other parameters. It is possibly a feasible way to estimate a large number of parameters to a certain extent for its simplicity and easy implementation. We also compare EM-algorithm with other methods like least-squares (co)variance component estimation (LS-VCE), maximum likelihood estimation (MLE), showing that EM-algorithm from restricted maximum likelihood (REML) will be identical to LS-VCE if certain weight matrix is chosen for LS-VCE. To assess the performance of the approach, daily observations from a network of 14 globally distributed International GNSS Service (IGS) multi-GNSS stations were processed using ionosphere-free combinations. The stations were assumed to be in kinematic motion with initial random walk noise of 1 mm every 30 s. The initial standard deviations for ionosphere-free code and carrier phase measurements are set to 3 m and 0.03 m, respectively, independent of the satellite elevation angle. It is shown that the calibrated Rt agrees well with observation residuals, reflecting effects of the accuracy of different satellite precise product and receiver-satellite geometry variations, and effectively resisting outliers. The calibrated Qt converges to its true value after about 50 iterations in our case. A kinematic test was also performed to derive 1 Hz GPS displacements, showing the RMSs and STDs w.r.t. real-time kinematic (RTK) are improved and the proper Qt is found out at the same time. According to our analysis despite the criticism that EM-PPP is very time-consuming because a large number of parameters are calculated and the first-order convergence of EM-algorithm, it is a numerically stable and simple approach to consider the temporal nature of state-space model of PPP, in particular when Qt and Rt are not known well, its performance without fixing ambiguities can even parallel to traditional PPP-RTK.

Precise Point Positioning on the Reliable Detection of Tropospheric Model Errors

Precise point positioning (PPP) is one of the well-known applications of Global Navigation Satellite System (GNSS) and provides precise positioning solutions using accurate satellite orbit and clock products. The tropospheric delay due to the neutral atmosphere for microwave signals is one of the main sources of measurement error in PPP. As one component of this delay, the hydrostatic delay is usually compensated by using an empirical correction model. However, how to eliminate the effects of the wet delay during a weather event is a challenge because current troposphere models are not capable of considering the complex atmosphere around the receiver during situations such as typhoons, storms, heavy rainfall, et cetera. Thus, how positioning results can be improved if the residual wet delays are taken into account needs to be investigated . In this contribution, a real-time procedure of recursive detection, identification and adaptation (DIA) is applied to detect the model errors which have the same effects on both phase and code observables; e.g., the model error caused by the tropospheric delay. Once the model errors are identified, additional parameters are added to the functional model to account for the measurement residuals. This approach is evaluated with Global Positioning System (GPS) data during two rainfall events in Darwin, Australia, proving the usefulness of compensated residual slant wet delay for positioning results. Comparisons with the standard approach show that the precision of the up component is improved significantly during the periods of the weather events; for the two case studies, 72.46% and 64.41% improvements of root mean squared error (RMS) resulted, and the precision of the horizontal component obtained by the proposed approach is also improved more than 30% compared to the standard approach. The results also show that the identified model errors are concentrated at the beginning of both heavy rainfall processes when the front causes significant spatial and temporal gradients of the integrated water vapor above the receiver.

Improving the geometry of Kaguya extended mission data through refined orbit determination using laser altimetry

The Japan Aerospace Exploration Agency's (JAXA) Kaguya spacecraft carried a suite of instruments to map the Moon and its environment globally. During its extended mission, the average altitude was 50 km or lower, and Kaguya science products using these data hence have an increased spatial resolution. However, the geodetic position quality of these products is much worse than that of those acquired during the primary mission (at an altitude of 100 km) because of reduced radiometric tracking and frequent thrusting to maintain spacecraft attitude after the loss of momentum wheels. We have analyzed the Kaguya tracking data using gravity models based on the Gravity Recovery and Interior Laboratory (GRAIL) mission, and by making use of a new data type based on laser altimeter data collected by Kaguya: we adjust the spacecraft orbit such that the altimetry tracks fit a precise topographic basemap based on the Lunar Reconnaissance Orbiter's (LRO) Lunar Orbiter Laser Altimeter (LOLA) data. This results in geodetically accurate orbits tied to the precise LOLA/LRO frame. Whereas previously archived orbits show errors at the level of several a level of several tens of meters. When altimetry data are not available, the combination of GRAIL gravity and radio tracking results in an orbit precision of around several hundreds of meters for the low-altitude phase of the extended mission. Our greatly improved orbits result in better geolocation of the Kaguya extended mission data set.

The Performance of Different Mapping Functions and Gradient Models in the Determination of Slant Tropospheric Delay

Global navigation satellite systems (GNSSs) have become an important tool for remotely sensing water vapor in the atmosphere. In GNSS data processing, mapping functions and gradient models are needed to map the zenith tropospheric delay (ZTD) to the slant total tropospheric delay (STD) along a signal path. Therefore, it is essential to investigate the spatial–temporal performance of various mapping functions and gradient models in the determination of STD. In this study, the STDs at nine elevations were first calculated by applying the ray-tracing method to the atmospheric European Reanalysis-Interim (ERA—Interim) dataset. These STDs were then used as the reference to study the accuracy of the STDs that determined the ZTD together with mapping functions and gradient models. The performance of three mapping functions (i.e., Niell mapping function (NMF), global mapping function (GMF), and Vienna mapping function (VMF1)) and three gradient models (i.e., Chen, MacMillan, and Meindl) in six regions (the temperate zone, Qinghai–Tibet Plateau, Equator, Sahara Desert, Amazon Rainforest, and North Pole) in determining slant tropospheric delay was investigated in this study. The results indicate that the three mapping functions have relatively similar performance above a 15° elevation, but below a 15° elevation, VMF1 clearly performed better than the GMF and NMF. The results also show that, if no gradient model is included, the root-mean-square (RMS) of the STD is smaller than 2 mm above the 30° elevation and smaller than 9 mm above the 15° elevation but shows a significant increase below the 15° elevation. For example, in the temperate zone, the RMS increases from approximately 35 mm at the 10° elevation to approximately 160 mm at the 3° elevation. The inclusion of gradient models can significantly improve the accuracy of STDs by 50%. All three gradient models performed similarly at all elevations and in all regions. The bending effect was also investigated, and the results indicate that the tropospheric delay caused by the bending effect is normally below 13 mm above a 15° elevation, but this delay increases dramatically from approximately 40 mm at a 10° elevation to approximately 200 mm at a 5° elevation, and even reaches 500–700 mm at a 3° elevation in most studied regions.

Cross-Comparison and Methodological Improvement in GPS Tomography

GPS tomography has been investigated since 2000 as an attractive tool for retrieving the 3D field of water vapour and wet refractivity. However, this observational technique still remains a challenging task that requires improvement of its methodology. This was the purpose of this study, and for this, GPS data from the Australian Continuously Operating Research Station (CORS) network during a severe weather event were used. Sensitivity tests and statistical cross-comparisons of tomography retrievals with independent observations from radiosonde and radio-occultation profiles showed improved results using the presented methodology. The initial conditions, which were associated with different time-convergence of tomography inversion, play a critical role in GPS tomography. The best strategy can reduce the normalised root mean square (RMS) of the tomography solution by more than 3 with respect to radiosonde estimates. Data stacking and pseudo-slant observations can also significantly improve tomography retrievals with respect to non-stacked solutions. A normalised RMS improvement up to 17% in the 0–8 km layer was found by using 30 min data stacking, and RMS values were divided by 5 for all the layers by using pseudo-observations. This result was due to a better geometrical distribution of mid- and low-tropospheric parts (a 30% coverage improvement). Our study of the impact of the uncertainty of GPS observations shows that there is an interest in evaluating tomography retrievals in comparison to independent external measurements and in estimating simultaneously the quality of weather forecasts. Finally, a comparison of multi-model tomography with numerical weather prediction shows the relevant use of tomography retrievals to improving the understanding of such severe weather conditions.

Spatial Interpolation of GNSS Troposphere Wet Delay by a Newly Designed Artificial Neural Network Model

Global Navigation Satellite System (GNSS) signals arrive at the Earth in a nonlinear and slightly curved way due to the refraction effect caused by the troposphere. The troposphere delay of the GNSS signal consists of hydrostatic and wet parts. In particular, tropospheric wet delay prediction and interpolation are more difficult than those of the dry component due to the rapid temporal and spatial variation of the water vapor content. Wet delay estimation and interpolation with a sufficient accuracy is an important issue for all parameters obtained by GNSS positioning techniques. In particular, in real-time positioning applications, errors caused by interpolation of the wet troposphere delay are reflected in the height component of about 1 to 2 cm. Furthermore, the amount of water vapor in the troposphere is very important information in weather forecast applications obtained as a function of wet delay. Therefore, real-time monitoring of the troposphere can be achieved with a higher resolution and accuracy by utilizing neural network models for interpolation of the wet tropospheric delay. In addition, in the absence of the GNSS station, wet delays can be interpolated by means of the surrounding stations to the desired location. In this study, a back propagation artificial neural network (BPNN) model based on meteorological parameters obtained from The New Austrian Meteorological Measuring Network (TAWES) was used to interpolate wet troposphere delay. Analysis was carried out at 40 reference stations of the Echtzeit Positionierung Austria (EPOSA) GNSS Network covering the whole of Austria. The interpolation of zenith wet delays based on the artificial neural network was performed by using latitude, longitude, altitude and meteorological parameters (temperature, pressure, weighted mean temperature, and water vapor pressure). These parameters were then subtracted from the artificial neural network model one by one and six different artificial neural networks were designed. In addition, the linear interpolation method (LIN) and inverse distance weighted interpolation method (IDW) were used as conventional interpolation methods. In order to investigate the effect of the network density on interpolation methods, three networks, including 40, 30, and 20 reference stations, were formed and the increased distance effect on interpolation methods was evaluated. In addition, analyses were conducted in winter, spring, and summer to evaluate the seasonal effects on interpolation methods. According to the statistical analysis, the root mean square error (RMSE) values of the IDW, LIN, and BPNN methods were found to be 12.6, 13.4, and 5.9 mm, respectively.

Covariance Analysis of Real-Time Precise GPS Orbit Estimated from Double-Differenced Carrier Phase Observations

The covariance of real-time global positioning system (GPS) orbits has been drawing attention in various fields such as user integrity, navigation performance improvement, and fault detection. The international global navigation satellite system (GNSS) service (IGS) provides real-time orbit standard deviations without correlations between the axes. However, without correlation information, the provided covariance cannot assure the performance of the orbit product, which would, in turn, causes significant problems in fault detection and user integrity. Therefore, we studied real-time GPS orbit covariance characteristics along various coordinates to effectively provide conservative covariance. To this end, the covariance and precise orbits are estimated by means of an extended Kalman filter using double-differenced carrier phase observations of 61 IGS reference stations. Furthermore, we propose a new method for providing covariance to minimize loss of correlation. The method adopted by the IGS, which neglects correlation, requires 4.5 times the size of the covariance to bind orbit errors. By comparison, our proposed method reduces this size from 4.5 to 1.3 using only one additional parameter. In conclusion, the proposed method effectively provides covariance to users.

Real-time Precise Point Positioning with a Xiaomi MI 8 Android Smartphone

The Global Navigation Satellite System (GNSS) positioning technology using smartphones can be applied to many aspects of mass life, and the world’s first dual-frequency GNSS smartphone Xiaomi MI 8 represents a new trend in the development of GNSS positioning technology with mobile phones. The main purpose of this work is to explore the best real-time positioning performance that can be achieved on a smartphone without reference stations. By analyzing the GNSS raw measurements, it is found that all the three mobile phones tested have the phenomenon that the differences between pseudorange observations and carrier phase observations are not fixed, thus a PPP (precise point positioning) method is modified accordingly. Using a Xiaomi MI 8 smartphone, the modified real-time PPP positioning strategy which estimates two clock biases of smartphone was applied. The results show that using multi-GNSS systems data can effectively improve positioning performance; the average horizontal and vertical RMS positioning error are 0.81 and 1.65 m respectively (using GPS, BDS, and Galileo data); and the time required for each time period positioning errors in N and E directions to be under 1 m is less than 30s.

A New Weighting Approach with Application to Ionospheric Delay Constraint for GPS/GALILEO Real-Time Precise Point Positioning

The real-time precise point positioning (RT PPP) technique has attracted increasing attention due to its high-accuracy and real-time performance. However, a considerable initialization time, normally a few hours, is required in order to achieve the proper convergence of the real-valued ambiguities and other estimate parameters. The RT PPP convergence time may be reduced by combining quad-constellation global navigation satellite system (GNSS), or by using RT ionospheric products to constrain the ionosphere delay. But to improve the performance of convergence and achieve the best positioning solutions in the whole data processing, proper and precise variances of the observations and ionospheric constraints are important, since they involve the processing of measurements of different types and with different accuracy. To address this issue, a weighting approach is proposed by a combination of the weight factors searching algorithm and a moving-window average filter. In this approach, the variances of ionospheric constraints are adjusted dynamically according to the principle that the sum of the quadratic forms of weighted residuals is the minimum, and the filter is applied to combine all epoch-by-epoch weight factors within a time window. To evaluate the proposed approach, datasets from 31 Multi-GNSS Experiment (MGEX) stations during the period of DOY (day of year) 023-054 in 2018 are analyzed with different positioning modes and different data processing methods. Experimental results show that the new weighting approach can significantly improve the convergence performance, and that the maximum improvement rate reaches 35.9% in comparison to the traditional method of priori variance in the static dual-frequency positioning mode. In terms of the RMS (Root Mean Square) statistics of positioning errors calculated by the new method after filter convergence, the same accuracy level as that of RT PPP without constraints can be achieved.

Precipitable Water Vapour Retrieval from GPS Precise Point Positioning and NCEP CFSv2 Dataset during Typhoon Events

Radiosonde is extensively used for understanding meteorological parameters in the vertical direction. Four typhoon events, including three landfalls (MERANTI, NEPARTAK, and MEGI) and one non-landfall (MALAKAS), were chosen in analysing the precipitable water vapour (PWV) characteristics in this study. The spatial distribution of the three radiosonde stations in Zhejiang province does not meet the requirement in analysing changes in PWV during typhoon event. Global position system (GPS) observations are an alternative method for deriving the PWV. This enables improvements in the temporal–spatial resolution of PWV computed by the radiosonde measurements. The National Centers for Environmental Prediction (NCEP) re-analysed data were employed for interpolating temperature and atmosphere pressure at the GPS antennas height. The PWV computed from GPS observations and NCEP re-analysed data were then compared with the true PWV. The maximum difference of radiosonde and GPS PWV was not more than 30 mm at Taiz station. The Root-Mean-Square (RMS) of PWV differences between radiosonde and GPS was not more than 5 mm in January, February, March, November, and December. It was slightly greater than 5 mm in April. High RMS in May, June, July, August, September, and October implies that differences in GPS and radiosonde PWVs are evident in these months. Correlation coefficients of GPS and radiosonde PWVs were more than 0.9, indicating that the changes in GPS and radiosonde PWVs are similar. Radiosonde calculated PWVs were used for GPS PWV calibration for understanding the PWV changes during the period of a typhoon event. The results from three landfall typhoons show that the average PWV over Zhejiang province is increasing and approaching China mainland. In contrast, MALAKAS did not make landfall and shows a decreasing PWV trend, although it was heading to China mainland. Generally, the PWV change can be used to predict whether the typhoon will make landfall in these cases. PWV spatial distribution of MERANTI shows that PWV peaks change along the typhoon epicenter over Zhejiang province.

Improving the Performance of Multi-GNSS Time and Frequency Transfer Using Robust Helmert Variance Component Estimation

The combination of multiple Global Navigation Satellite Systems (GNSSs) may improve the performance of time and frequency transfers by increasing the number of available satellites and improving the time dilution of precision. However, the receiver clock estimation is easily affected by the inappropriate weight of multi-GNSSs due to the different characteristics of individual GNSS signals as well as the outliers from observations. Thus, we utilised a robust Helmert variance component estimation (RVCE) approach to determine the appropriate weights of different GNSS observations, and to control for the influence of outliers in these observation in multi-GNSS time and frequency transfer. In order to validate the effectiveness of this approach, four time links were employed. Compared to traditional solutions, the mean improvement of smoothed residuals is 3.43% using the RVCE approach. With respect to the frequency stability of the time links, the RVCE solution outperforms the traditional solution, particularly in the short-term, and the mean improvement is markedly high at 14.89%.

Monitoring Water Surface and Level of a Reservoir Using Different Remote Sensing Approaches and Comparison with Dam Displacements Evaluated via GNSS

Remote sensing allowed monitoring the reservoir water level by estimating its surface extension. Surface extension has been estimated using different approaches, employing both optical (Landsat 5 TM, Landsat 7 ETM+ SLC-Off, Landsat 8 OLI-TIRS and ASTER images) and Synthetic Aperture Radar (SAR) images (Cosmo SkyMed and TerraSAR-X). Images were characterized by different acquisition modes, geometric and spectral resolutions, allowing the evaluation of alternative and/or complementary techniques. For each kind of image, two techniques have been tested: The first based on an unsupervised classification and suitable to automate the process, the second based on visual matching with contour lines with the aim of fully exploiting the dataset. Their performances were evaluated by comparison with water levels measured in situ (r2 = 0.97 using the unsupervised classification, r2 = 0.95 using visual matching) demonstrating that both techniques are suitable to quantify reservoir surface extension. However ~90% of available images were analyzed using the visual matching method, and just 37 images out of 58 using the other method. The evaluation of the water level from the water surface, using both techniques, could be easily extended to un-gauged reservoirs to manage the variations of the levels during normal operation. In addition, during the period of investigation, the use of Global Navigation Satellite System (GNSS) allowed the estimation of dam displacements. The advantage of using as reference a GNSS permanent station positioned relatively far from the dam, allowed the exclusion of any interaction with the site deformations. By comparing results from both techniques, relationships between the orthogonal displacement component via GNSS, estimated water levels via remote sensing and in situ measurements were investigated. During periods of changing water level (April 2011–September 2011 and October 2011–March 2012), the moving average of displacement time series (middle section on the dam crest) shows a range of variability of ±2 mm. The dam deformation versus reservoir water level behavior differs during the reservoir emptying and filling periods indicating a hysteresis-kind loop.

A New Zenith Tropospheric Delay Grid Product for Real-Time PPP Applications over China

Tropospheric delay is one of the major factors affecting the accuracy of electromagnetic distance measurements. To provide wide-area real-time high precision zenith tropospheric delay (ZTD), the temporal and spatial variations of ZTD with altitude were analyzed on the bases of the latest meteorological reanalysis product (ERA-Interim) provided by the European Center for Medium-Range Weather Forecasts (ECMWF). An inverse scale height model at given locations taking latitude, longitude and day of year as inputs was then developed and used to convert real-time ZTD at GPS stations in Crustal Movement Observation Network of China (CMONOC) from station height to mean sea level (MSL). The real-time ZTD grid product (RtZTD) over China was then generated with a time interval of 5 min. Compared with ZTD estimated in post-processing mode, the bias and error RMS of ZTD at test GPS stations derived from RtZTD are 0.39 and 1.56 cm, which is significantly more accurate than commonly used empirical models. In addition, simulated real-time kinematic Precise Point Positioning (PPP) tests show that using RtZTD could accelerate the BDS-PPP convergence time by up to 32% and 65% in the horizontal and vertical components (set coordinate error thresholds to 0.4 m), respectively. For GPS-PPP, the convergence time using RtZTD can be accelerated by up to 29% in the vertical component (0.2 m).

ZY3-02 Laser Altimeter Footprint Geolocation Prediction

Successfully launched on 30 May 2016, ZY3-02 is the first Chinese surveying and mapping satellite equipped with a lightweight laser altimeter. Calibration is necessary before the laser altimeter becomes operational. Laser footprint location prediction is the first step in calibration that is based on ground infrared detectors, and it is difficult because the sample frequency of the ZY3-02 laser altimeter is 2 Hz, and the distance between two adjacent laser footprints is about 3.5 km. In this paper, we build an on-orbit rigorous geometric prediction model referenced to the rigorous geometric model of optical remote sensing satellites. The model includes three kinds of data that must be predicted: pointing angle, orbit parameters, and attitude angles. The proposed method is verified by a ZY3-02 laser altimeter on-orbit geometric calibration test. Five laser footprint prediction experiments are conducted based on the model, and the laser footprint prediction accuracy is better than 150 m on the ground. The effectiveness and accuracy of the on-orbit rigorous geometric prediction model are confirmed by the test results. The geolocation is predicted precisely by the proposed method, and this will give a reference to the geolocation prediction of future land laser detectors in other laser altimeter calibration test.

VMF3/GPT3: refined discrete and empirical troposphere mapping functions

Incorrect modeling of troposphere delays is one of the major error sources for space geodetic techniques such as Global Navigation Satellite Systems (GNSS) or Very Long Baseline Interferometry (VLBI). Over the years, many approaches have been devised which aim at mapping the delay of radio waves from zenith direction down to the observed elevation angle, so-called mapping functions. This paper contains a new approach intended to refine the currently most important discrete mapping function, the Vienna Mapping Functions 1 (VMF1), which is successively referred to as Vienna Mapping Functions 3 (VMF3). It is designed in such a way as to eliminate shortcomings in the empirical coefficients b and c and in the tuning for the specific elevation angle of 3 ∘ . Ray-traced delays of the ray-tracer RADIATE serve as the basis for the calculation of new mapping function coefficients. Comparisons of modeled slant delays demonstrate the ability of VMF3 to approximate the underlying ray-traced delays more accurately than VMF1 does, in particular at low elevation angles. In other words, when requiring highest precision, VMF3 is to be preferable to VMF1. Aside from revising the discrete form of mapping functions, we also present a new empirical model named Global Pressure and Temperature 3 (GPT3) on a5 ∘ × 5 ∘ as well as a1 ∘ × 1 ∘ global grid, which is generally based on the same data. Its main components are hydrostatic and wet empirical mapping function coefficients derived from special averaging techniques of the respective (discrete) VMF3 data. In addition, GPT3 also contains a set of meteorological quantities which are adopted as they stand from their predecessor, Global Pressure and Temperature 2 wet. Thus, GPT3 represents a very comprehensive troposphere model which can be used for a series of geodetic as well as meteorological and climatological purposes and is fully consistent with VMF3.

Physical applications of GPS geodesy: a review

Geodesy, the oldest science, has become an important discipline in the geosciences, in large part by enhancing Global Positioning System (GPS) capabilities over the last 35 years well beyond the satellite constellation's original design. The ability of GPS geodesy to estimate 3D positions with millimeter-level precision with respect to a global terrestrial reference frame has contributed to significant advances in geophysics, seismology, atmospheric science, hydrology, and natural hazard science. Monitoring the changes in the positions or trajectories of GPS instruments on the Earth's land and water surfaces, in the atmosphere, or in space, is important for both theory and applications, from an improved understanding of tectonic and magmatic processes to developing systems for mitigating the impact of natural hazards on society and the environment. Besides accurate positioning, all disturbances in the propagation of the transmitted GPS radio signals from satellite to receiver are mined for information, from troposphere and ionosphere delays for weather, climate, and natural hazard applications, to disturbances in the signals due to multipath reflections from the solid ground, water, and ice for environmental applications. We review the relevant concepts of geodetic theory, data analysis, and physical modeling for a myriad of processes at multiple spatial and temporal scales, and discuss the extensive global infrastructure that has been built to support GPS geodesy consisting of thousands of continuously operating stations. We also discuss the integration of heterogeneous and complementary data sets from geodesy, seismology, and geology, focusing on crustal deformation applications and early warning systems for natural hazards.

Comprehensive Comparisons of Satellite Data, Signals, and Measurements between the BeiDou Navigation Satellite System and the Global Positioning System

The Chinese BeiDou navigation satellite system (BDS) aims to provide global positioning service by 2020. The combined use of BDS and Global Positioning System (GPS) is proposed to provide navigation service with more stringent requirements. Actual satellite data, signals and measurements were collected for more than one month to analyze the positioning service qualities from both BDS and GPS. In addition to the conversions of coordinate and timing system, five data quality analysis (DQA) methods, three signal quality analysis (SQA) methods, and four measurement quality analysis (MQA) methods are proposed in this paper to improve the integrated positioning performance of BDS and GPS. As shown in the experiment results, issues related to BDS and GPS are resolved by the above proposed quality analysis methods. Thus, the anomalies in satellite data, signals and measurements can be detected by following the suggested resolutions to enhance the positioning performance of the combined use of BDS and GPS in the Asia Pacific region.

Evaluation of Empirical Tropospheric Models Using Satellite-Tracking Tropospheric Wet Delays with Water Vapor Radiometer at Tongji, China

An empirical tropospheric delay model, together with a mapping function, is commonly used to correct the tropospheric errors in global navigation satellite system (GNSS) processing. As is well-known, the accuracy of tropospheric delay models relies mainly on the correction efficiency for tropospheric wet delays. In this paper, we evaluate the accuracy of three tropospheric delay models, together with five mapping functions in wet delays calculation. The evaluations are conducted by comparing their slant wet delays with those measured by water vapor radiometer based on its satellite-tracking function (collected data with large liquid water path is removed). For all 15 combinations of three tropospheric models and five mapping functions, their accuracies as a function of elevation are statistically analyzed by using nine-day data in two scenarios, with and without meteorological data. The results show that (1) no matter with or without meteorological data, there is no practical difference between mapping functions, i.e., Chao, Ifadis, Vienna Mapping Function 1 (VMF1), Niell Mapping Function (NMF), and MTT Mapping Function (MTT); (2) without meteorological data, the UNB3 is much better than Saastamoinen and Hopfield models, while the Saastamoinen model performed slightly better than the Hopfield model; (3) with meteorological data, the accuracies of all three tropospheric delay models are improved to be comparable, especially for lower elevations. In addition, the kinematic precise point positioning where no parameter is set up for tropospheric delay modification is conducted to further evaluate the performance of tropospheric delay models in positioning accuracy. It is shown that the UNB3 model is best and can achieve about 10 cm accuracy for the N and E coordinate component while 20 cm accuracy for the U coordinate component no matter the meteorological data is available or not. This accuracy can be obtained by the Saastamoinen model only when meteorological data is available, and degraded to 46 cm for the U component if the meteorological data is not available.

Assessment of Three Tropospheric Delay Models (IGGtrop, EGNOS and UNB3m) Based on Precise Point Positioning in the Chinese Region

Tropospheric delays are one of the main sources of errors in the Global Navigation Satellite System (GNSS). They are usually corrected by using tropospheric delay models, which makes the accuracy of the models rather critical for accurate positioning. To provide references for suitable models to be chosen for GNSS users in China, we conduct herein a comprehensive study of the performances of the IGGtrop, EGNOS and UNB3m models in China. Firstly, we assess the models using 5 years’ Global Positioning System (GPS) derived Zenith Tropospheric Delay (ZTD) series from 25 stations of the Crustal Movement Observation Network of China (CMONOC). Then we study the effects of the models on satellite positioning by using various Precise Point Positioning (PPP) cases with different tropospheric delay resolutions, the observation data processed in PPP is from 21 base stations of CMONOC for a whole year of 2012. The results show that: (1) the Root Mean Square (RMS) of the IGGtrop model is about 4.4 cm, which improves the accuracy of ZTD estimations by about 24% for EGNOS and 19% for UNB3m; (2) The positioning error in the vertical component of the PPP solution obtained by using the IGGtrop model is about 15.0 cm, which is about 30% and 21% smaller than those of the EGNOS and UNB3m models, respectively. In summary, the IGGtrop model achieves the best performance among the three models in the Chinese region.

ITG: A New Global GNSS Tropospheric Correction Model

Tropospheric correction models are receiving increasing attentions, as they play a crucial role in Global Navigation Satellite System (GNSS). Most commonly used models to date include the GPT2 series and the TropGrid2. In this study, we analyzed the advantages and disadvantages of existing models and developed a new model called the Improved Tropospheric Grid (ITG). ITG considers annual, semi-annual and diurnal variations, and includes multiple tropospheric parameters. The amplitude and initial phase of diurnal variation are estimated as a periodic function. ITG provides temperature, pressure, the weighted mean temperature (Tm) and Zenith Wet Delay (ZWD). We conducted a performance comparison among the proposed ITG model and previous ones, in terms of meteorological measurements from 698 observation stations, Zenith Total Delay (ZTD) products from 280 International GNSS Service (IGS) station and Tm from Global Geodetic Observing System (GGOS) products. Results indicate that ITG offers the best performance on the whole.

High frequency variations of Earth Rotation Parameters from GPS and GLONASS observations

The Earth's rotation undergoes changes with the influence of geophysical factors, such as Earth's surface fluid mass redistribution of the atmosphere, ocean and hydrology. However, variations of Earth Rotation Parameters (ERP) are still not well understood, particularly the short-period variations (e.g., diurnal and semi-diurnal variations) and their causes. In this paper, the hourly time series of Earth Rotation Parameters are estimated using Global Positioning System (GPS), Global Navigation Satellite System (GLONASS), and combining GPS and GLONASS data collected from nearly 80 sites from 1 November 2012 to 10 April 2014. These new observations with combining different satellite systems can help to decorrelate orbit biases and ERP, which improve estimation of ERP. The high frequency variations of ERP are analyzed using a de-trending method. The maximum of total diurnal and semidiurnal variations are within one milli-arcseconds (mas) in Polar Motion (PM) and 0.5 milli-seconds (ms) in UT1-UTC. The semidiurnal and diurnal variations are mainly related to the ocean tides. Furthermore, the impacts of satellite orbit and time interval used to determinate ERP on the amplitudes of tidal terms are analyzed. We obtain some small terms that are not described in the ocean tide model of the IERS Conventions 2010, which may be caused by the strategies and models we used or the signal noises as well as artifacts. In addition, there are also small differences on the amplitudes between our results and IERS convention. This might be a result of other geophysical excitations, such as the high-frequency variations in atmospheric angular momentum (AAM) and hydrological angular momentum (HAM), which needs more detailed analysis with more geophysical data in the future.

Precise point positioning with the BeiDou navigation satellite system

By the end of 2012, China had launched 16 BeiDou-2 navigation satellites that include six GEOs, five IGSOs and five MEOs. This has provided initial navigation and precise pointing services ability in the Asia-Pacific regions. In order to assess the navigation and positioning performance of the BeiDou-2 system, Wuhan University has built up a network of BeiDou Experimental Tracking Stations (BETS) around the World. The Position and Navigation Data Analyst (PANDA) software was modified to determine the orbits of BeiDou satellites and provide precise orbit and satellite clock bias products from the BeiDou satellite system for user applications. This article uses the BeiDou/GPS observations of the BeiDou Experimental Tracking Stations to realize the BeiDou and BeiDou/GPS static and kinematic precise point positioning (PPP). The result indicates that the precision of BeiDou static and kinematic PPP reaches centimeter level. The precision of BeiDou/GPS kinematic PPP solutions is improved significantly compared to that of BeiDou-only or GPS-only kinematic PPP solutions. The PPP convergence time also decreases with the use of combined BeiDou/GPS systems.