GNSS Precise Point Positioning Research Articles

Investigation of the effects of Kahramanmaraş earthquake series on Cyprus Arc, Dead Sea fault, Hatay regions and stations close to two earthquakes epicenters

In various parts of the globe, there have been several earthquakes of a modest size. Monitoring the change of the points over time is a key component of typical techniques for extracting dynamic responses. This technique was unable to completely extract all of the earthquake’s dynamic properties. The GNSS precise point positioning (PPP) may be a useful tool for obtaining values of the point’s displacement that are more exact up to millimeters, which can help to overcome these flaws and evaluate the seismic wave of such earthquakes. Ultimately, PPP is a crucial tool for getting the precise observations. In this study, Canadian Spatial Reference System Precise Point Positioning (CSRS-PPP) approach to analyze the station’s displacement components and the station’s heights in periods from the two Kahramanmaraş earthquakes. The earthquake sequences that occurred in Turkey’s Kahramanmaraş in 2023 is an example of complicated faulting brought on by interactions between three plates close to the Hatay Triple Junction (HTJ). While the relative plate movements in this area are minimal (usually less than 10 mm/year), even sluggish plate motion zones may nevertheless see earthquakes that are quite destructive. Due to the three-plate system’s unusual geometry, a number of large earthquakes with very varied fault orientations were active throughout this series. A 7.8-magnitude earthquake happened on February 6, 2023 in southern Turkey, close to Syria’s northern border. A magnitude 7.5 earthquake, situated about 95 kilometers to the southwest, was occurred nine hours after the first one. The first earthquake was as big as the most powerful one ever recorded there in 1939 and was the most catastrophic to strike earthquake-prone Turkey in more than 20 years. In this study, the effects of two earthquakes in Kahramanmaraş were investigated on the Cyprus Arc, the Dead Sea fault, Hatay and the points close to two earthquakes zone. In the obtained results, it was computed that the greatest horizontal displacement occurred at the HAT2 station with 68.97 cm.

GNSS Real-Time ZTD/PWV Retrieval Based on PPP with Broadcast Ephemerides

GNSS precise point positioning (PPP) plays an important role in retrieving atmospheric water vapor values and performing numerical weather prediction. However, traditional PPP relies on real-time orbits and clocks, which require continuous internet or satellite communication. Improved broadcast ephemerides of GNSSs offer new opportunities for PPP with broadcast ephemerides (BE-PPP) instead of using precise ephemeride products. Therefore, we investigated the feasibility of utilizing BE-PPP for retrieving zenith tropospheric delay (ZTD) and precipitable water vapor (PWV) data. We processed the GPS/Galileo observations from 80 IGS stations during a 30-day experiment to retrieve ZTD values using both real-time PPP (RT-PPP) and BE-PPP solutions. Then, we processed observations from 20 EUREF Permanent GNSS Network (EPN) stations to retrieve PWV data. The IGS final tropospheric products were used to validate the ZTD, and radiosonde (RDS) and ERA5 data were used to validate the PWV. The results show that the real-time ZTD from BE-PPP agrees well with that from RT-PPP: the standard deviation (STD) of the ZTD is 1.07 cm when using BE-PPP and 0.6 cm when using RT-PPP. Furthermore, the STD of the PWV is 1.69 mm when using BE-PPP, and 0.96 mm when using RT-PPP, compared to the ERA5-PWV. Compared to the RDS-PWV, the STD is 3.09 mm when using BE-PPP and 1.39 mm when using RT-PPP. In conclusion, the real-time ZTD/PWV products obtained using the BE-PPP solution are consistent with those of RT-PPP and meet the requirements of NWP, so this method can be used as an effective complement to RT-PPP to expand its application potential.

Tight integration of real-time GNSS PPP and INS: Ionosphere-free combined vs uncombined models

The GNSS Precise Point Positioning (PPP) model is usually established in either an ionospheric-free (IF) combined form or an uncombined (UC) form. These formulations can be equivalent in theory but their applications in practice could still perform differently when integrated with external sensors. In this study, we compared the positioning performance of the two PPP models tightly coupled with the Inertial Navigation System (INS) using a high-grade inertial measurement unit (IMU) in real vehicle navigation tests. The ambiguity resolution (AR) was also exploited in the two PPP models after applying the observable specific biases (OSB) to the GNSS raw code and phase measurements. According to the results, under good satellite observability the UC PPP/INS tightly-coupled integration (TCI) significantly outperforms the IF PPP/INS TCI. The UC TCI model with AR could achieve a positioning accuracy of 4.6 and 3.0 cm in the horizontal and vertical directions, which are improved by 37 % and 63 % respectively relative to the IF TCI model. However, in the case of frequent GNSS signal interruptions or poor satellite observation condition, the IF TCI model shows a superior reliability than the UC TCI. Nevertheless, when the ionospheric parameters are properly constrained in the UC TCI model, substantial improvements in terms of convergence and accuracy are obtained. The UC PPP augmented with external precise ionospheric information would greatly increase the cost, and users may select the appropriate PPP model with INS TCI in real applications in accordance with the demanded accuracy level and measuring conditions.

Improved Multipath Mitigation Using Multiple Trend-Surface Hemispherical Map in GNSS Precise Point Positioning

Improved Multipath Mitigation Using Multiple Trend-Surface Hemispherical Map in GNSS Precise Point Positioning

An Improved Stochastic Model for the Geodetic GNSS Receivers Under Ionospheric Scintillation at Low Latitudes

AbstractThe receiver tracking error stochastic (RTES) model can improve GNSS precise point positioning (PPP) performance under ionospheric scintillation. However, it relies on scintillation products derived from ionospheric scintillation monitoring receivers (ISMRs), which means the RTES model cannot be used for abundant geodetic GNSS receivers. In this study, we propose an improved RTES, referred to as Impr_RTES model, to mitigate scintillation effects on geodetic GNSS receivers at low latitudes, where severe scintillation frequently occurs. In the Impr_RTES model, the tracking error variances at the output of code delay locked loop are calculated by using the index S4c, and these of phase locked loop are modeled by using the rate of total electron content index (ROTI) and S4c. Both S4c and ROTI can be derived from geodetic GNSS receivers. The performance of the Impr_RTES model is validated by using the data sets from ISMR and geodetic receivers, respectively. Using one month of GPS data collected at HNLW station installed with ISMR in Hainan of China from 1 to 28 February in 2023, statistical results indicate that the PPP solution based on Impr_RTES model can improve the positioning accuracy by approximately 22.6%, 23.8%, and 30.2% in the east, north, and up directions, respectively, over the elevation angle stochastic (EAS) model. Meanwhile, the positioning performance of Impr_RTES PPP is comparable to that of RTES PPP. For the GPS data from geodetic receivers, experimental results suggest that compared with EAS, the Impr_RTES model can obviously mitigate scintillation effects on PPP.

Performance analysis of four PPP service software under different intensity geomagnetic storms

Currently, many precise point positioning (PPP) services provide through software or online websites for GNSS positioning studies and applications. Various PPP service software has different positioning performances due to their respective algorithms and versions. In addition, the positioning accuracy and reliability of PPP services lack systematic evaluation, especially in the case of geomagnetic storms. This study presents the PPP performance analysis of the common GNSS PPP software as CSRS-PPP (https://www.geod.nrcan.gc.ca/), APPS (https://apps.gdgps.net/), Net_Diff (http://center.shao.ac.cn/shao_gnss_ac/), and GAMP (https://www.ngs.noaa.gov/gps-toolbox/GAMP) under different geomagnetic storm intensities. The PPP experiments involve data from 916, 885, and 676 GPS stations data on 17 March 2015 (severe), 26 August 2018 (strong), and 15 January 2022 (moderate), respectively. The results showed that the positioning performance of the four PPP software is different in the magnetic storm environment. We found that during geomagnetic storms, the CSRS-PPP software has the highest positioning accuracy and reliability, while the APPS software shows the worst positioning performance. The performance of Net_Diff and GAMP during geomagnetic storms are comparable but are better than that of APPS. Statistical results indicate that the average values of 3D RMS of CSRS-PPP, APPS, Net_Diff, and GAMP under severe storm are 0.14 m, 0.60 m, 0.40 m, and 0.33 m, under strong storm are 0.18 m, 0.65 m, 0.27 m, and 0.33 m, and under moderate storm are 0.25 m, 1.66 m, 0.26 m, and 0.34 m, respectively. The main reason why the CSRS-PPP has the best positioning accuracy under different intensity storms is that it uses the ambiguity-fixed PPP solution, while the other three software use float solution.

GNSS PPP with added QZSS: Positioning and time-frequency transfer

Regional navigation system Quasi-Zenith Satellite System (QZSS) play an important role in positioning, time and frequency transfer for the Asia-Pacific region under high cut-off angle. This paper combines QZSS and the major navigation systems for Precise Point Positioning (PPP) positioning and time–frequency transfer. The time–frequency transfer experimental results show that with the addition of QZSS, the clock difference accuracy and the frequency stability of the corresponding time link are significantly improved for the case of cut-off above 15°. The corresponding range is between 5% and 30% of accuracy, and between 1% and 90% of frequency stability.

An Improved Strategy for Real-Time Troposphere Estimation and Its Application in the Severe Weather Event Monitoring

The water vapor content in the atmosphere is highly correlated with rainfall events, which can be used as a data source for rainfall prediction or drought monitoring. The GNSS PPP (Precise Point Positioning) technique can be used to estimate the troposphere ZWD (Zenith Wet Delay) parameter which can be converted into precipitable water vapor (PWV). In this study, we first investigate the impacts of the weighting strategies, observation noise settings, and gradient estimation on the accuracy of ZWD and positions. A refined strategy is proposed for the troposphere estimation with uncombined raw PPP model, down-weighting of Galileo/GLONASS/BDS code observation by a factor of 3, using a sine2-type elevation-dependent weighting function and estimating the horizontal gradients. Based on the strategy, the correlation of the estimated tropospheric parameters with the rainfall is analyzed based on the data from the “7.20” rainstorm in Henan Province, China. The PWV is first calculated based on the hourly global pressure and temperature (HGPT) model and compared with the results from ERA5 products. Results show their good consistency during the rainfall period or the normal period with a standard deviation of 3 mm. Then, the high correlation between the PWV and the heavy rain rainfall event is validated. Results show that the accumulated PWV maintains a high level before the rainstorm if a sustainable water supply is available, while it decreased rapidly after the rainfall. In comparison, the horizontal gradients and the satellite residuals are less correlated with the water vapor content. However, the gradients can be used to indicate the horizontal asymmetry of the water vapor in the atmosphere.

Performance Evaluation of Near Real-time GNSS PPP Time Transfer with IGS Products

The GNSS time transfer technology is the high precision time transfer method based on the navigation satellite system and has been widely applied in time and frequency. Benefiting from the development of GNSS time transfer technology and the expansion of user needs for real-time time service applications, real-time time transfer technology has become an important research direction. GNSS Precise Point Positioning (PPP) is one of the most commonly used methods of GNSS time transfer technology. With the development of the many facilities, the application of the real-time GNSS PPP has become wider and wider. In this paper, we demonstrate and evaluate the performance of the international GNSS service (IGS) products in the near real-time PPP time transfer technology. A set of the PPP solutions were computed from the observed data from the timekeeping laboratories, and three types of products provided by IGS, including Ultra-Rapid (IGU), Rapid (IGR), and Final (IGS final) orbit and clock offset products. IGS final and IGR products have extremely high accuracy and stability and are used as a reference for the time transfer with IGU product. The near real time clock offset and the comparison link performed with the IGU product can provide a time comparison service with an accuracy of 0. 5ns for near real time applications.

Ionospheric Behavior during the 10 June 2021 Annular Solar Eclipse and Its Impact on GNSS Precise Point Positioning

The main effects of the 10 June 2021 annular solar eclipse on GNSS position estimation accuracy are presented. The analysis is based on TEC measurements made by 2337 GNSS stations around the world. TEC perturbations were obtained by comparing results 2 days prior to and after the day of the event. For the analysis, global TEC maps were created using ordinary Kriging interpolation. From TEC changes, the apparent position variation was obtained using the post-processing kinematic precise point positioning with ambiguity resolution (PPP-AR) mode. We validated the TEC measurements by contrasting them with data from the Swarm-A satellite and four digiosondes in Central/South America. The TEC maps show a noticeable TEC depletion (<−60%) under the moon’s shadow. Important variations of TEC were also observed in both crests of the Equatorial Ionization Anomaly (EIA) region over the Caribbean and South America. The effects on GNSS precision were perceived not only close to the area of the eclipse but also as far as the west coast of South America (Chile) and North America (California). The number of stations with positioning errors of over 10 cm almost doubled during the event in these regions. The effects were sustained longer (∼10 h) than usually assumed.

Validating a New GNSS-Based Sea Level Instrument (CalNaGeo) at Senetosa Cape

The geodetic Corsica site was set up in 1998 in order to perform altimeter calibration of the TOPEX/Poseidon (T/P) mission and subsequently, Jason-1, OSTM/Jason-2, Jason-3 and more recently Sentinel-6 Michael Freilich (launched on November, 21 2020). The aim of the present study held in June 2015 is to validate a recently developed GNSS-based sea level instrument (called CalNaGeo) that is designed with the intention to map Sea Surface Heights (SSH) over large areas. This has been undertaken using the well-defined geodetic infrastructure deployed at Senetosa Cape, and involved the estimation of the stability of the waterline (and thus the instantaneous separation of a GNSS antenna from water level) as a function of the velocity at which the instrument is towed. The results show a largely linear relationship which is approximately 1 mm/(m/s) up to a maximum practical towing speed of ∼10 knots (∼5 m/s). By comparing to the existing “geoid” map, it is also demonstrated that CalNaGeo can measure a sea surface slope with a precision better than 1 mm/km (∼2.5% of the physical slope). Different processing techniques are used and compared including GNSS Precise Point Positioning (PPP, where the goal is to extend SSH mapping far from coastal GNSS reference stations) showing an agreement at the 1-2 cm level.

Impact of Tropospheric Mismodelling in GNSS Precise Point Positioning: A Simulation Study Utilizing Ray-Traced Tropospheric Delays from a High-Resolution NWM

In GNSS analysis, the tropospheric delay is parameterized by applying mapping functions (MFs), zenith delays, and tropospheric gradients. Thereby, the wet and hydrostatic MF are derived under the assumption of a spherically layered atmosphere. The coefficients of the closed-form expression are computed utilizing a climatology or numerical weather model (NWM) data. In this study, we analyze the impact of tropospheric mismodelling on estimated parameters in precise point positioning (PPP). To do so, we mimic PPP in an artificial environment, i.e., we make use of a linearized observation equation, where the observed minus modelled term equals ray-traced tropospheric delays from a high-resolution NWM. The estimated parameters (station coordinates, clocks, zenith delays, and tropospheric gradients) are then compared with the known values. The simulation study utilized a cut-off elevation angle of 3° and the standard downweighting of low elevation angle observations. The results are representative of a station located in central Europe and the warm season. In essence, when climatology is utilized in GNSS analysis, the root mean square error (RMSE) of the estimated zenith delay and station up-component equal about 2.9 mm and 5.7 mm, respectively. The error of the GNSS estimates can be reduced significantly if the correct zenith hydrostatic delay and the correct hydrostatic MF are utilized in the GNSS analysis. In this case, the RMSE of the estimated zenith delay and station up-component is reduced to about 2.0 mm and 2.9 mm, respectively. The simulation study revealed that the choice of wet MF, when calculated under the assumption of a spherically layered troposphere, does not matter too much. In essence, when the ‘correct’ wet MF is utilized in the GNSS analysis, the RMSE of the estimated zenith delay and station up-component remain at about 1.8 mm and 2.4 mm, respectively. Finally, as a by-product of the simulation study, we developed a modified wet MF, which is no longer based on the assumption of a spherically layered atmosphere. We show that with this modified wet MF in the GNSS analysis, the RMSE of the estimated zenith delay and station up-component can be reduced to about 0.5 mm and 1.0 mm, respectively. In practice, its success depends on the ability of current (future) NWM to predict the fourth coefficient of the developed closed-form expression. We provide some evidence that current NWMs are able to do so.

Assessment of the GNSS PPP performance using ultra-rapid and rapid products from different analysis centres

The performance of precise point positioning (PPP) mainly depends on satellite orbit and clock accuracy. Ultra-rapid and rapid orbit/clock products have been creating by analysis centres (ACs) for time-critical applications. In this paper, GPS-, GLONASS-, Galileo-, and BeiDou (BDS-2)-only PPP with ultra-rapid and rapid products from seven ACs (i.e. CODE, ESA, IGS, GFZ, JPL, NRCan, and WUHAN) are investigated for PPP performance. A two-month period in 2020 was chosen for conducting static and kinematic PPP using data from 32 Multi-GNSS Experiment (MGEX) stations. For GPS-only PPP with different ACs, GFZ/NRCan and CODE/NRCan rank first for ultra-rapid and rapid PPP processes, respectively. For GLONASS-only PPP, positioning performances using ultra-rapid products are comparable with each other except for CODE and ESA products. CODE rapid product ranks last for GLONASS-only PPP. For Galileo and BeiDou-only PPP, GFZ AC performs the best for ultra-rapid processes. For Galileo-only PPP using rapid products, CODE ranks first.

Real-time GNSS precise point positioning using improved robust adaptive Kalman filter

Multi-constellation GNSS precise point positioning (PPP) typically uses the extended Kalman filter (EKF) for kinematic applications. Unfortunately, the obtained positioning accuracy in this approach is prone to errors caused by measurement outliers and the system’s dynamic model. An adaptive robust Kalman filter (RKF) was recently developed to mitigate these errors. However, RKF uses empirical values as detection thresholds for the outliers, which requires the measurements to be from the same constellation and of equal precision to obtain an optimal PPP solution. The classification robust adaptive Kalman filter (CAKF) has subsequently been developed to deal with measurements of different precisions, namely pseudorange and carrier-phase measurements. This paper proposes a real-time GPS/Galileo PPP system, which employs a modified version of CAKF called the Improved Robust adaptive Kalman Filter (IRKF). The positioning performance of GPS/Galileo PPP through the IRKF is initially verified in comparison with those obtained through the EKF, RKF, and CAKF using the Centre for Orbit Determination in Europe (CODE) final orbit and clock products in both of static and kinematic modes. The real-time GPS/Galileo PPP solution through the IRKF is then assessed in comparison with its near-real-time counterpart. The results indicate that when the IRKF approach is utilised, the positioning accuracy is significantly improved and the convergence behaviour is enhanced compared with results from EKF, conventional RKF, and CAKF. In the real-time mode, centimeter-level horizontal positioning accuracy is achieved under an open sky environment, while decimeter-level horizontal positioning accuracy is achieved under a challenging environment. On the other hand, decimeter-level accuracy is achieved for the vertical positioning component under all environmental scenarios. Moreover, the positioning accuracy of the real-time solution is comparable to the near-real-time counterpart.

Enabling robust and accurate navigation for UAVs using real-time GNSS precise point positioning and IMU integration

ABSTRACTAccurate navigation is required in many Unmanned Aerial Vehicle (UAV) applications. In recent years, GNSS Precise Point Positioning (PPP) has been recognised as an efficient approach for providing precise positioning services. In contrast to the widely used Real-Time Kinematic (RTK), PPP is independent of reference stations, which greatly broadens its scope of application. However, the accuracy and reliability of PPP can be significantly decreased by poor GNSS satellite geometry and outage. In response, a real-time four-constellation GNSS PPP is applied to improve the geometry in this work, and PPP is tightly coupled with an Inertial Measurement Unit (IMU) to smooth the position and velocity output, thus improving the robustness of the navigation solution. Experimental flight tests are carried out using a UAV in an open-sky area, and GNSS-challenged environments are simulated. The results show that the four-constellation GNSS PPP/IMU integration reduces the Root-Mean-Square (RMS) Three-Dimensional (3D) positioning and velocity error by 76.4% and 67.1%, respectively, in open sky with respect to the one-GNSS PPP. Under scenarios where GNSS measurements are insufficient, the coupled system can still provide continuous solutions. Moreover, the coupled PPP/IMU system can also maintain the convergence of PPP during GNSS-challenged periods and can greatly shorten the re-convergence period of PPP when the UAV returns to the open sky.

GPS\u2009+\u2009Galileo\u2009+\u2009BeiDou precise point positioning with triple-frequency ambiguity resolution

Along with the rapid development of GNSS, not only BeiDou, but also Galileo, and the newly launched GPS satellites can provide signals on three frequencies at present. To fully take advantage of the multi-frequency multi-system GNSS observations on precise point positioning (PPP) technology, this study aims to implement the triple-frequency ambiguity resolution (AR) for GPS, Galileo, and BeiDou-2 combined PPP using the raw observation model. The processing of inter-frequency clock bias (IFCB) estimation and correction in the context of triple-frequency PPP AR has been addressed, with which the triple-frequency uncalibrated phase delay (UPD) estimation is realized for real GPS observations for the first time. In addition, the GPS extra-wide-line UPD quality is significantly improved with the IFCB correction. Because of not being contaminated by the IFCB, the raw UPD estimation method is directly employed for Galileo which currently has 24 satellites in operation. An interesting phenomenon is found that all Galileo satellites except E24 have a zero extra-wide-lane UPD value. With the multi-GNSS observations provided by MGEX covering 15 days, the positioning solutions of GPS + Galileo + BeiDou triple-frequency PPP AR have been conducted and analyzed. The triple-frequency kinematic GNSS PPP AR can achieve an averaged 3D positioning error of 2.2 cm, and an averaged convergence time of 10.8 min. The average convergence time can be reduced by triple-frequency GNSS PPP AR by 15.6% compared with dual-frequency GNSS PPP AR, respectively. However, the additional third frequency has only a marginal contribution to positioning accuracy after convergence.

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.

Beyond three frequencies: an extendable model for single-epoch decimeter-level point positioning by exploiting Galileo and BeiDou-3 signals

GNSS is indispensable to self-driving vehicles by delivering decimeter-level or better absolute positioning solutions. Such a high precision normally requires a convergence time spanning seconds to minutes, which is, however, unrealistic in extremely difficult driving conditions where GNSS signals are obstructed frequently. Such convergences, no matter how short, will greatly risk and discredit autonomous driving in satisfying stringent life safety standards. In this study, we therefore developed an extendable GNSS precise point positioning (PPP) model to exploit the advanced Galileo/BeiDou-3 more-than-three-frequency signals with the goal of achieving instant or single-epoch 10–30 cm positioning accuracy and over 99% availability for the horizontal components over wide areas. In particular, uncombined Galileo/BeiDou-3 signals on all available frequencies were injected simultaneously into PPP to perform single-epoch wide-lane ambiguity resolution (PPP-WAR) after phase bias calibrations on raw observations. Experimenting on the Galileo five-frequency data from 36 stations in Australia, we found that instant PPP-WAR was accomplished at more than 99.5% of all epochs; we achieved an instant positioning accuracy of 0.10 and 0.11 m (1σ) for the east and north components, respectively, using Galileo E1/E5a/E5/E5b/E6 signals from less than 10 satellites, while 0.16 and 0.23 m using BeiDou-3 B1C/B1I/B2a/B2b/B3I signals from only 5–6 satellites per epoch observed by 10 stations within China. Moreover, we carried out vehicle-borne experiments collecting multi-frequency Galileo/BeiDou-3 signals in the case of overpass and tunnel adversities. With 7 Galileo/BeiDou-3 satellites per epoch on average, instant PPP-WAR reached a mean positioning accuracy of 0.23 and 0.24 m for the horizontal components, which can be further improved to 0.14 and 0.12 m when multi-epoch filtering is preferably enabled. More encouragingly, though this positioning accuracy can also be ensured with triple-frequency data, the data redundancy favored by even more frequencies can reduce the high-precision recovery time from up to 4 s to 2 s in the case of total signal blockages. With the rapidly ongoing deployment of Galileo, BeiDou-3 and other GNSS constellations, we can envision an instant global positioning service characterized by around 20 cm horizontal accuracy and over 99% availability for self-driving vehicles.

Geopotential Determination Based on Precise Point Positioning Time Comparison: A Case Study Using Simulated Observation

Based on the general relativity theory, the geopotential difference can be determined by comparing the change in time difference between precise clocks using the precise point positioning (PPP) time transfer technique, referred to as the relativistic PPP time comparison approach. We focused on high-precision time comparison between two high-performance clocks for determining the geopotential difference using this approach, and conducted the simulation experiments to validate this approach. In the experiment, we consider three cases for evaluating the performance of this approach with different types of atomic clocks, namely, the fractional frequency stabilities of the clocks equipped at three selected ground stations (BRUX, OPMT, and PTBB) are $4.0 \times 10^{-13} / \sqrt {\tau }$ (Case 1), $2.3 \times 10^{-14} / \sqrt {\tau }$ (Case 2), and $2.8 \times 10^{-15} / \sqrt {\tau }$ (Case 3) at averaging time ${\tau }$ , respectively, and the accuracy of these clock have been evaluated to be $5.3 \times 10^{-16}$ , $7.8 \times 10^{-17}$ , and $8.6 \times 10^{-18}$ . Two main conclusions can be drawn from the experimental results. First, high-performance clocks can significantly improve the precision for GNSS PPP time transfer. Compared to Case 1, the long-term stabilities of the time link OPMT-BRUX as well as PTBB-BRUX are improved in Cases 2 and 3. Second, the geopotential difference between any two stations can be determined at the decimeter level, and the accuracy of geopotential difference is consistent with the stabilities of the time links in Cases 1-3. In Case 3, the determined geopotential differences between OPMT and BRUX deviate from the EIGEN-6C4 model values by -0.64, m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> / <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> with an uncertainty of 1.11 m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> /s <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , whereas the deviation error between PTBB and BRUX is 0.76 m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> /s <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> with an uncertainty of 1.79 m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> /s <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . The results of this study suggest that a one decimeter-level geopotential difference between two arbitrary stations can be determined based on this approach.

Precise Point Positioning Using World's First Dual-Frequency GPS/GALILEO Smartphone.

The release of the world’s first dual-frequency GPS/Galileo smartphone, Xiaomi mi 8, in 2018 provides an opportunity for high-precision positioning using ultra low-cost sensors. In this research, the GNSS precise point positioning (PPP) accuracy of the Xiaomi mi 8 smartphone is tested in post-processing and real-time modes. Raw dual-frequency observations are collected over two different time windows from both of the Xiaomi mi 8 smartphone and a Trimble R9 geodetic-quality GNSS receiver using a short baseline, due to the lack of a nearby reference station to the observation site. The data sets are first processed in differential modes using Trimble business center (TBC) software in order to provide the reference positioning solution for both of the geodetic receiver and the smartphone. An in-house PPP software is then used to process the collected data in both of post-processing and real-time modes. Precise ephemeris obtained from the multi-GNSS experiment (MGEX) is used for post-processing PPP, while the new NAVCAST real-time GNSS service, Germany, is used for real-time PPP. Additionally, the real-time PPP solution is assessed in both of static and kinematic modes. It is shown that the dual-frequency GNSS smartphone is capable of achieving decimeter-level positioning accuracy, in both of post-processing and real-time PPP modes, respectively. Meter-level positioning accuracy is achieved in the kinematic mode.