Global Positioning System Precise Point Positioning Research Articles

Time Transfer Link fusion algorithm based on wavelet multi-resolution analysis

To raise the precision and stability of time transfer links, a wavelet-based multi-resolution data fusion technique is offered. This approach fixes the “Day-Boundary discontinuities” in global positioning system (GPS) precise point positioning (PPP) link and lessens the diurnal in Two-way satellite time and frequency transfer (TWSTFT) link by integrating the model-based dynamic system analysis method with the statistically based multi-scale signal transformation method. It can also handle data from GPS PPP links and TWSTFT links at different sampling rates. More specifically, after applying wavelet transformation to the raw data and Kalman filtering estimation on various scales, this method uses the Mallat fast reconstruction algorithm of wavelet transform to achieve the fused results. The National Time Service Center (NTSC) and the Physikalisch-Technische Bundesanstalt (PTB) handle time transfer results using this method. Experiments show that this strategy greatly improves the link's short-term stability and can manage atypical interruptions while also boosting the link's robustness and reliability, which has a wide range of possible applications.

Performance of kinematic GPS PPP AR under different ionospheric scintillation conditions

To analyze the performance of Global Positioning System (GPS) Precise Point Positioning (PPP) Ambiguity Resolution (AR) under various ionospheric scintillation environments, we selected GPS data of ionospheric scintillation monitoring receivers (ISMR) and geodetic receivers from high-latitude and low-latitude regions during 2021–2023. We conducted GPS Kinematic PPP using Canadian Spatial Reference System (CSRS) PPP and used the maximum and average values of σφ and S4 as indicators to characterize the intensity of phase scintillation and amplitude scintillation for ISMRs, while the maximum and average values of Rate of Total Electron Content Index (ROTI) to characterize the intensity of ionospheric scintillation for geodetic receivers. We also used ambiguity resolved percentage (ARP) and the 3-Dimensional Root Mean Square (3D RMS) of positioning errors as performance metrics for PPP-AR and PPP. As the maximum and average values of ionospheric scintillation indices increase, the PPP-ARP for high-latitude ISMRs decreases to 90.0 %, and the 3D RMS can reach 0.204 m. During ionospheric quiet conditions, positioning accuracy of GPS PPP can reach the cm-mm level. As the geomagnetic latitude decreases, the scintillation effects on PPP-AR and PPP become more pronounced for high-latitude ISMRs. Compared with high-latitudes, ISMRs located at low-latitudes are more severely affected by scintillation, with PPP-ARP at the station HNLW in China and the station UFBA in Brazil dropping to 80.0 % and 60.0 %, respectively. The 3D RMS can reach 0.288 m and 0.341 m. The results of geodetic receives are consistent with those of ISMRs, with 3D RMS of positioning errors up to 0.240 m and 0.256 m for CYNE and MAL2, respectively, while PPP-ARP drops to 60.4 % and 79.6 %. Additionally, we observed a strong positive correlation between ionospheric scintillation duration and the maximum values of σφ, S4 and ROTI.

Inconsistent pseudorange biases in time links and their effect on BDS and GPS PPP frequency transfer

Precise point positioning (PPP) using the Global Navigation Satellite System (GNSS) phase and code measurements has become the primary technique for time and frequency comparisons. Several scholars have studied multi-GNSS PPP clock comparisons; however, the inconsistent pseudorange bias from receivers with different correlator spaces and front-end designs in pseudorange observations has not been considered. In this study, we analyze the characteristics of the inconsistent biases of the Global Positioning System (GPS) and BeiDou Navigation Satellite System (BDS) and their effects on PPP frequency transfer. The biases are confirmed to exist in receivers from Septentrio, Trimble, Leica and differ by manufacturer. To explicitly investigate the pseudorange bias effects of GPS and BDS on the PPP time and frequency comparisons, nine stations with receivers from three different manufacturers that could track the BDS-2 and BDS-3 signals were selected. Regarding PPP frequency transfer with inhomogeneous receivers, the Modified Allan Deviations (MDEVs) of the GPS and BDS PPP frequency stabilities were significantly optimized after using bias corrections. According to the receiver type classification strategy, the overall improvements in frequency transfer with Trimble-Septentrio and Trimble-Leica can be reached up to 31%, 29%, and 39%, and 38%, 29%, and 31% for GPS, BDS-2, and BDS-3, respectively. Moreover, the convergence time of the clock comparisons was shortened after bias corrections were applied. For GOPE-BRUX and GOPE-MATE links, the corrected cases yielded average clock difference stability improvements of 38%, 35%, and 53% and 35%, 35%, and 23% for GPS, BDS-2, and BDS-3, respectively. The results show that bias corrections are vital and allow for more stable time links for PPP frequency transfer.

A new receiver clock model to enhance BDS-3 real-time PPP time transfer with the PPP-B2b service

A new Precise Point Positioning (PPP) service, called the PPP-B2b service, has been implemented in the BeiDou-3 Navigation Satellite System (BDS-3), which brings new opportunities for time transfer. However, the solution using the traditional PPP method with the PPP-B2b correction still absorbs some unknown errors and needs reconverging when there exist abnormal data. We developed a new receiver clock model to improve PPP time transfer using the PPP-B2b correction. The traditional PPP time transfers using PPP-B2b with BDS-3, Global Positioning System (GPS), and BDS-3/GPS (Scheme1) are compared with the corresponding time transfer with the proposed clock model (Scheme2). The results show that GPS-only PPP is not recommended because of low accuracy of 2 ns. BDS-3 or BDS-3/GPS PPP time transfers in Scheme1 can realize about 0.2 ns accuracy. When the new clock model is applied, the accuracy can be improved by up to 45% and 39.8% for BDS-3 and BDS-3/GPS PPP, respectively. The proposed clock model can significantly improve the short-term frequency stability by 57.4%, but less for the long-term stability.

Assessing the Kinematic GPS Positioning Performance Under the Effect of Strong Ionospheric Disturbance Over China and Adjacent Areas During the Magnetic Storm

AbstractThe geomagnetic storm caused numerous disturbances of the ionosphere, particularly, plasma irregularities, which can affect the accuracy of Global Positioning System (GPS) positioning. This study quantifies the impacts of the ionospheric disturbance on GPS precise point positioning (PPP) solutions during extreme space weather events by taking advantage of 260 GPS stations in China. The results show that the average positioning error in China increased significantly during the ionospheric disturbance on 08 Sep 2017. By comparing the kinematic GPS‐PPP (3‐D) error distribution map and the ROTI index map, it is found that the ionospheric irregularities are one of the main reasons for degrading the GPS positioning accuracy. The statistical analysis results show that when the ionospheric scintillation index S4 is greater than 0.4, the average kinematic GPS‐PPP error calculated by the station is higher than 0.8 m.

Estimation of the ocean tide loading displacements by GPS and GLONASS kinematic Precise Point Positioning

Ocean Tide Loading Displacement (OTLD) parameters, derived by Global Positioning System (GPS) approach, need more time to converge to a stable state and show poor precision of K1 and K2 constituents. Combining multi-system Global Navigation Satellite System (GNSS) data can greatly improve the positioning accuracy and significantly reduce the convergence time compared to single GPS PPP, combined GPS+GLONASS with ambiguity resolved in kinematic Precise Point Positioning (PPP) is improved on the basis of the algorithm of GPS kinematic PPP. We collected eight years of continuous observations of 11 worldwide sites from International GNSS Service to generate three dimensional OTLD parameters of eight constituents using GPS with ambiguity fixed, GLONASS with ambiguity free and combined GPS+GLONASS with ambiguity fixed kinematic PPP approach. The results show the eight constituents derived by GPS_FX and GPS+GLONASS_FX solution need four years and three years to converge to stable values, respectively. GLONASS can significantly improve the convergence rate of K1 and K2 constituents which needs only two years to converge to stable values, and S2 and P1 constituents which need three years to stable values. The results also show the GPS+GLONASS/reference misfits are the smallest for the most constituents in three components (less than 2mm) except for K2 and K1 in vertical and north directions. GLONASS can improve more than 40% in vertical and north components over GPS and GPS+GLONASS for K2 and K1 constituents and show very close agreement with GPS_FX solution in vertical and north component for S2 and P1 constituents. Ambiguity resolved in OTLD estimation can significantly accelerate the convergence and improve the accuracy for eight constituents, especially for combined GPS+GLONASS kinematic PPP mode, but no single constellation mode solution for all eight major constituents exists.

Assessment of GPS/Galileo/BDS Precise Point Positioning with Ambiguity Resolution Using Products from Different Analysis Centers

Suffering from hardware phase biases originating from satellites and the receiver, precise point positioning (PPP) requires a long convergence time to reach centimeter coordinate accuracy, which is a major drawback of this technique and limits its application in time-critical applications. Ambiguity resolution (AR) is the key to a fast convergence time and a high-precision solution for PPP technology and PPP AR products are critical to implement PPP AR. Nowadays, various institutions provide PPP AR products in different forms with different strategies, which allow to enable PPP AR for Global Positioning System (GPS) and Galileo or BeiDou Navigation System (BDS). To give a full evaluation of PPP AR performance with various products, this work comprehensively investigates the positioning performance of GPS-only and multi-GNSS (Global Navigation Satellite System) combination PPP AR with the precise products from CNES, SGG, CODE, and PRIDE Lab using our in-house software. The positioning performance in terms of positioning accuracy, convergence time and fixing rate (FR) as well as time to first fix (TTFF), was assessed by static and kinematic PPP AR models. For GPS-only, combined GPS and Galileo PPP AR with different products, the positioning performances were all comparable with each other. Concretely, the static positioning errors can be reduced by 21.0% (to 0.46 cm), 52.5% (to 0.45 cm), 10.0% (to 1.33 cm) and 21.7% (to 0.33 cm), 47.4% (to 0.34 cm), 9.5% (to 1.16 cm) for GPS-only and GE combination in north, east, up component, respectively, while the reductions are 20.8% (to 1.13 cm), 42.9% (to 1.15 cm), 19.9% (to 3.4 cm) and 20.4% (to 0.72 cm), 44.1% (to 0.66 cm), 10.1% (to 2.44 cm) for kinematic PPP AR. Overall, the positioning performance with CODE products was superior to the others. Furthermore, multi-GNSS observations had significant improvements in PPP performance with float solutions and the TTFF as well as the FR of GPS PPP AR could be improved by adding observations from other GNSS. Additionally, we have released the source code for multi-GNSS PPP AR, anyone can freely access the code and example data from GitHub.

Mitigating high latitude ionospheric scintillation effects on GNSS Precise Point Positioning exploiting 1-s scintillation indices

Ionospheric scintillation refers to rapid and random fluctuations in radio frequency signal intensity and phase, which occurs more frequently and severely at high latitudes under strong solar and geomagnetic activity. As one of the most challenging error sources affecting Global Navigation Satellite System (GNSS), scintillation can significantly degrade the performance of GNSS receivers, thereby leading to increased positioning errors. This study analyzes Global Positioning System (GPS) scintillation data recorded by two ionospheric scintillation monitoring receivers operational, respectively, in the Arctic and northern Canada during a geomagnetic storm in 2019. A novel approach is proposed to calculate 1-s scintillation indices. The 1-s receiver tracking error variances are then estimated, which are further used to mitigate the high latitude scintillation effects on GPS Precise Point Positioning. Results show that the 1-s scintillation indices can describe the signal fluctuations under scintillation more accurately. With the mitigation approach, the 3D positioning error is greatly reduced under scintillation analyzed in this study. Additionally, the 1-s tracking error variance achieves a better performance in scintillation mitigation compared with the previous approach which exploits 1-min tracking error variance estimated by the commonly used 1-min scintillation indices. This work is relevant for a better understanding of the high latitude scintillation effects on GNSS and is also beneficial for developing scintillation mitigation tools for GNSS positioning.

Influence of Precise Products on the Day-Boundary Discontinuities in GNSS Carrier Phase Time Transfer.

Global navigation satellite system (GNSS) precise point positioning (PPP) has been widely used for high-precision time and frequency transfer. However, the day-boundary discontinuities at the boundary epochs of adjacent days or batches are the most significant obstacle preventing PPP from continuous time transfer. The day-boundary discontinuities in station estimates and time comparisons are mainly caused by the code-pseudorange noise during the analysis of observation data in daily batches, where the absolute clock offset is determined by the average code measurements. However, some discontinuities with amplitudes even more than 0.15 ns may still appear in station clock estimates and time comparisons, although several methods had been proposed to remove such discontinuities. The residual small amplitude of the day-boundary discontinuities in some PPP station clock estimates and time comparisons through new GNSSs like Galileo seems larger, especially using precise clock products with large discontinuities. To further understand the origin of the day-boundary discontinuities, the influence of GNSS precise products on the day-boundary discontinuities in PPP station clock estimates and time comparisons is investigated in this paper. Ten whole days of Multi-GNSS Experiment (MGEX) from modified Julian date (MJD) 59028 to 59037 are used as the observation data. For a comparative analysis, the station clock estimates are compared with global positioning system (GPS) and Galileo observations through PPP and network solutions, separately. The experimental results show that the daily discontinuities in current combined GPS final and rapid clock products are less than 0.1 ns, and their influence on the origin of day-boundary discontinuities in PPP station clock estimates and time comparison are statistically negligible. However, the daily discontinuities in individual Analysis Centers (ACs) GPS products are more extensive, and their influence on the origin of the day-boundary discontinuities in GPS PPP station clock estimates cannot be ignored. The day-boundary discontinuities demonstrate random walk noise characteristics and deteriorate the station clocks’ long-term frequency stability, especially at an average time of more than one day. Although Galileo clock daily discontinuities are different from those of GPS, their influence on the day-boundary discontinuities in station clock estimates is nearly similar to the GPS PPP. The influence of daily discontinuities of Galileo clocks on PPP time comparison is similar to GPS and is not particularly critical to time comparison. However, combined and weighted MGEX products should be developed or Galileo IPPP should be used for remote comparison of high-stability clocks.

Characterization of Inter-System Biases in GPS + BDS Precise Point Positioning

With the combination of multi-GNSS data, the precise-point positioning (PPP) technique can improve its accuracy, availability and reliability: Inter-system bias (ISB) is the non-negligible parameter in multi-GNSS PPP. To further enhance the performance of multi-GNSS PPP, it is crucial to analyze the characterization of inter system biases (ISBs) and model them properly. In this contribution, we comprehensively investigate the characterization of ISBs between global positioning system (GPS) and BeiDou navigation satellite system (BDS) in different situations. (1) We estimate ISB by using different precise products from the Center for Orbit Determination (CODE), Deutsches GeoForschungsZentrum (GFZ) and Wuhan University (WHU). The results indicate that the one-day estimates of ISB are stable when using CODE and WHU products, whereas the estimates based on GFZ products vary remarkably. As for the three-day time series of ISB, a sudden jump exists between two adjacent days, which is due to the change of satellite clock datum; (2) We investigate the ISB characterization affected by the ambient environments of the receivers. The result shows that the ISBs estimated from receivers (and antennas) with same type are still inconsistent, which indicates that the ambient environment, probably the temperature, influences the ISB characterization as well, since the receivers are in different areas; (3) We analyze the ISB characterization affected by receiver and antenna type with the same ambient environment. To ensure the same ambient environment, the ultra-short baselines were applied to investigate the ISB characterization affected by the receiver and antenna type. With the insights into ISB characterizations, we carry out combined GPS and BDS PPP with modeling the ISB as time constant, random walk process and white noise. The results suggest that the random walk process outperforms in most cases, since it strengthens the model to some extend and, at the same time, considers the variation of ISBs.

Real-Time Estimation of Low Earth Orbit (LEO) Satellite Clock Based on Ground Tracking Stations

The rapid movement of low Earth orbit (LEO) satellite can improve geometric diversity, which contributes to the rapid convergence of Global Navigation Satellite System (GNSS) precise point positioning (PPP). However, the LEO onboard receiver clock cannot be used directly by PPP users as the LEO satellite clock because the LEO onboard receiver clock and LEO satellite clock absorb different code delays when receiving and transmitting signals. In this study, a real-time estimation approach for the LEO satellite clock based on ground tracking stations was proposed for the first time. The feasibility for the rapid convergence of the LEO satellite clock was analyzed using the satellite time dilution of precision (TDOP) that one satellite is relative to multiple ground tracking stations. The LEO constellation of 168 satellites and observations for 15 ground tracking stations were simulated to verify the proposed method. The experiment results showed that the average convergence time was 31.21 min for the Global Positioning System (GPS) satellite clock, whereas the value for the LEO satellite clock was only 2.86 min. The average root mean square (RMS) and standard deviation (STD) values after convergence were 0.71 and 0.39 ns for the LEO satellite clock, whereas the values were 0.31 and 0.13 ns for the GPS satellite clock. The average weekly satellite TDOP for the LEO satellite was much smaller than that for the GPS satellite. The average satellite TDOPs for all LEO and GPS satellites were 19.13 and 1294.70, respectively. However, the average delta TDOPs caused by satellite motion for all LEO and GPS satellites were both 0.10. Therefore, the rapid convergence of the LEO satellite clock resulted from the better geometric distribution of the LEO satellite relative to ground stations. Despite errors and the convergence time of the LEO satellite clock, the convergence time and positioning accuracy for LEO-augmented GPS and BeiDou Navigation Satellite System (BDS) PPP with the real-time estimated LEO satellite clock can still reach 10.63 min, 1.94 cm, 1.44 cm, and 4.18 cm in the east, north, and up components, respectively. The improvements caused by LEO satellite for GPS/BDS PPP were 59%, 30%, 31%, and 33%, respectively.

Efficiency of Using GNSS-PPP for Digital Elevation Model (DEM) Production

Abstract In the developing countries, cost-effective observation techniques are very important for earthwork estimation, map production, geographic information systems, and hydrographic surveying. One of the most cost-effective techniques is Precise Point Positioning (PPP); it is a Global Navigation Satellite Systems (GNSS) positioning technique to compute precise positions using only a single GNSS receiver. This study aims to evaluate the efficiency of using Global Positioning System (GPS) and GPS/ Globalnaya Navigatsionnaya Sputnikovaya Sistema (GLONASS) post-processed kinematic PPP solution for digital elevation model (DEM) production, which is used in earthwork estimation. For this purpose, a kinematic trajectory has been observed in New Aswan City in an open sky area using dual-frequency GNSS receivers. The results showed that, in case of using GPS/GLONASS PPP solution to estimate volumes, the error in earthwork volume estimation varies between 0.07% and 0.16% according to gridding level. On the other hand, the error in volume estimation from GPS PPP solution varies between 0.40% and 0.99%.

Performance Assessment for Combined GPS and BDS Real-time Precise Point Positioning in the Coastal Region of Bohai Gulf, China

Qu, L.; Huang, H.; Du, M., and Acharya, T.D., 2019. Performance assessment for combined GPS and BDS real-time precise point positioning in the coastal region of Bohai Gulf, China. In: Lee, J.L.; Yoon, J.-S.; Cho, W.C.; Muin, M., and Lee, J. (eds.), The 3rd International Water Safety Symposium. Journal of Coastal Research, Special Issue No. 91, pp. 271-275. Coconut Creek (Florida), ISSN 0749-0208.In this study, we focus on the performance assessment of combined Global Positioning System (GPS) and BeiDou Navigation Satellite System (BDS) real-time Precise Point Positioning (PPP) in the coastal region of Bohai Gulf, China. Firstly, 120 Global Navigation Satellite System (GNSS) stations from Multi-GNSS Experiment (MGEX) network of the International GNSS Service (IGS) were processed to generate ultra-rapid precise orbit of both GPS and BDS satellites, updated with the interval of three hours. Secondly, real-time precise satellite clock errors were estimated to compensate the orbit error with 24 regional stations from Crustal Monitor of Network of China (CMONOC) and MGEX networks. Finally, with those products, the performances of GPS-only, BDS-only and combined GPS and BDS real-time PPP were compared and evaluated. The experimental result illustrated that the ultra-rapid orbit accuracy of BDS-2 satellites was still worse than that of GPS satellites which was sub-decimeter level. Among three types of orbital satellites of BDS-2, the orbital accuracy of medium Earth orbit (MEO) and inclined geosynchronous orbit (IGSO) satellites were at decimeter level while for geostationary Earth orbit (GEO) satellites was at meter-level. The MEO satellites had the best accuracy while the GEO satellites performed the worst. In addition, the 3D accuracy of BDS-only real-time PPP was 10 cm better. Although the accuracy of BDS-2 real-time PPP was still worse than that of GPS and more time was taken for convergence. By adding BDS on top of GPS, the accuracy in the east, north and up components improved 40.0%, 33.3% and 18.5%, respectively, and the convergence time reduced 36.3%, 15.4% and 58.3%, respectively compared to the GPS only.

Robust Kalman Filter Aided GEO/IGSO/GPS Raw-PPP/INS Tight Integration.

Reliable and continuous navigation solutions are essential for high-accuracy location-based services. Currently, the real-time kinematic (RTK) based Global Positioning System (GPS) is widely utilized to satisfy such requirements. However, RTK’s accuracy and continuity are limited by the insufficient number of the visible satellites and the increasing length of base-lines between reference-stations and rovers. Recently, benefiting from the development of precise point positioning (PPP) and BeiDou satellite navigation systems (BDS), the issues existing in GPS RTK can be mitigated by using GPS and BDS together. However, the visible satellite number of GPS + BDS may decrease in dynamic environments. Therefore, the inertial navigation system (INS) is adopted to bridge GPS + BDS PPP solutions during signal outage periods. Meanwhile, because the quality of BDS geosynchronous Earth orbit (GEO) satellites is much lower than that of inclined geo-synchronous orbit (IGSO) satellites, the predicted observation residual based robust extended Kalman filter (R-EKF) is adopted to adjust the weight of GEO and IGSO data. In this paper, the mathematical model of the R-EKF aided GEO/IGSO/GPS PPP/INS tight integration, which uses the raw observations of GPS + BDS, is presented. Then, the influences of GEO, IGSO, INS, and R-EKF on PPP are evaluated by processing land-borne vehicle data. Results indicate that (1) both GEO and IGSO can provide accuracy improvement on GPS PPP; however, the contribution of IGSO is much more visible than that of GEO; (2) PPP’s accuracy and stability can be further improved by using INS; (3) the R-EKF is helpful to adjust the weight of GEO and IGSO in the GEO/IGSO/GPS PPP/INS tight integration and provide significantly higher positioning accuracy.

Evaluation of the GPS Precise Point Positioning technique during the 21 July 2017 Kos-Bodrum (East Aegean Sea) Mw 6.6 earthquake

Precise Point Positioning (PPP) algorithms have been widely used in the Global Positioning System (GPS)-based applications. A PPP technique with a single receiver provides effective solutions where accurate absolute positioning is required. This paper provides the performance assessment of GPS PPP for detecting the displacements caused by an earthquake. For this purpose, the earthquake that occurred on 21 July 2017 at Kos-Bodrum with the impact of Mw 6.6 was investigated by analyzing the data of the permanent GPS stations located around the related region with the PPP technique. The location distances of these GPS stations range from 10 to 89 km to the epicenter of this earthquake. GPS data provided from seven permanent stations from the Continuously Operating Reference Stations-Turkey (CORS-TR) and local Bodrum CORS networks were processed to determine the co-seismic displacements during the earthquake. The data of these stations for days of year (DOYs) 200, 201, 202, and 203 were analyzed with post-process static PPP and kinematic PPP methods. GIPSY-OASIS II v6.4 was used for processing the data and all of the solutions were performed in the ITRF2008 reference frame. Two strategies were followed on the post-process static solutions. In the first strategy, 4-day data with 24-h observations were separately analyzed day by day. In the second strategy, the 24-h data were divided into 3-h duration, which is the minimum duration for optimum PPP solutions, and then the analyses were performed. When the displacements between DOYs 200 and 203 are considered in the 24-h data analysis, significant displacements have been observed through northwest direction in the northern stations whereas MUG1 is excluded. Moreover, there is significant displacement through the southeast direction in the station DATC located in the south of the epicenter. When the 3-h solutions are examined, displacements, especially on n and e directions, are observed starting from the solutions, which include Mw 6.6 earthquake. According to the kinematic PPP solutions, the effects of the Mw 6.6 earthquake can be seen clearly in the stations DATC, ORTA, TRKB, and YALI. Considering all outcomes, the PPP technique with both static and kinematic solutions provides effective results for detecting the displacements during the earthquake.

GPS precise point positioning for UAV photogrammetry

AbstractThe use of Global Positioning System (GPS) precise point positioning (PPP) on a fixed‐wing unmanned aerial vehicle (UAV) is demonstrated for photogrammetric mapping at accuracies of centimetres in planimetry and about a decimetre in height, from flights of 25 to 30 minutes in duration. The GPS PPP estimated camera station positions are used to constrain estimates of image positions in the photogrammetric bundle block adjustment, as with relative GPS positioning. GPS PPP alleviates all spatial operating constraints associated with the installation and the use of ground control points, a local ground GPS reference station or the need to operate within the bounds of a permanent GPS reference station network. This simplifies operational logistics and enables large‐scale photogrammetric mapping from UAVs in even the most remote and challenging geographic locations.

Analysis on the Potential Performance of GPS and Galileo Precise Point Positioning using Simulated Real-Time Products

With the evolving Global Navigation Satellite System (GNSS) landscape, the International GNSS Service (IGS) has started the Multi-GNSS Experiment (MGEX) to produce precise products for new generation systems. Various analysis centres are working on the estimation of precise orbits, clocks and bias for Galileo, Beidou and Quasi-Zenith Satellite System (QZSS) satellites. However, at the moment these products can only be used for post-processing applications. Indeed, the IGS Real-Time service only broadcasts Global Positioning System (GPS) and Globalnaya Navigatsionnaya Sputnikovaya Sistema (GLONASS) corrections. In this research, a simulator of multi-GNSS observations and real-time precise products has been developed to analyse the performance of GPS-only, Galileo-only and GPS plus Galileo Precise Point Positioning (PPP). The error models in the simulated orbits and clocks were based on the difference between the GPS Real-Time and the Final products. Multiple scenarios were analysed, considering different signals combined in the Ionosphere Free linear combination. Results in a simulated open area environment show better performance of the Galileo-only case over the GPS-only case. Indeed, up 33% and 29% of improvement, respectively, in the accuracy level and convergence time can be observed when using the full Galileo constellation compared to GPS. The dual constellation case provides good improvements, in particular in the convergence time (47% faster than GPS). This paper will also consider the impact of different linear combinations of the Galileo signals, and the potential of the E5 Alternative Binary Offset Carrier (AltBOC) signal. Even though it is significantly more precise than E5a, the PPP performance obtained with the Galileo E1-E5a combination is either better or similar to the one with Galileo E1-E5. The reason for this inconsistency was found in the use of the ionosphere free combination with E1. Finally, alternative methods of ionosphere error mitigation are considered in order to ensure the best possible positioning performance from the Galileo E5 signal in multi-frequency PPP.

Augment BeiDou real-time precise point positioning using ECMWF data

The Chinese BeiDou Navigation Satellite System has shown potential for precise positioning with a comparable accuracy to that of the Global Positioning System (GPS) at the centimeter level for the horizontal component and the sub-centimeter level for the vertical component. However, a longer convergence time limits the performance of BeiDou precise point positioning (PPP) compared to the GPS PPP solutions. In this study, we applied the tropospheric delay information, derived from the European Centre of Medium-Range Weather Forecasts (ECMWF) analysis and prediction data, into the simulated real-time BeiDou-only and BeiDou/GPS PPP to augment the solutions. Observations from stations in Southeast Asia, which are capable of tracking the BeiDou constellation from the International GNSS Service (IGS) Multi-GNSS Experiment and Pilot Project (MGEX) network, are processed with different strategies: the standard PPP and the introduced ECMWF-augmented PPP with analysis and prediction data, respectively. The positioning results demonstrate that the ECMWF-augmented BeiDou-only and BeiDou/GPS PPP methods using prediction data perform as well as those using analysis data. In the case of BeiDou-only PPP scenarios, remarkable advancements of 80.6% for the convergence time are achieved by two ECMWF-augmented PPP solutions with respect to the standard PPP method. For the positioning accuracy, the two proposed augmented PPP methods attain 6.6 cm in three-dimensional (3D) accuracy when the standard PPP solution get converged (10 cm), representing a remarkable improvement of 34%. As for the north/east/up component, improvements of 14.7 and 8% for positioning accuracy are obtained for the north and east components, respectively, while a remarkable improvement of 37.3% is achieved for the vertical component. In terms of the BeiDou/GPS PPP solutions, the ECMWF-augmented PPP scenarios attain over 10% improvements in 3D accuracy in all processing session lengths. These improvements totally come from the vertical component, whereas almost no enhancements are obtained in two horizontal components.

Determination of Ocean Tide Loading Displacement by GPS PPP with Priori Information Constraint of NAO99b Global Ocean Tide Model

ABSTRACTThe published global ocean tide models show good agreement in deep oceans and exhibit differences in complex coastal areas, along with subsequent Ocean Tide Loading Displacement (OTLD) modeling differences. Meanwhile, OTLD parameters (amplitudes and phase lags) derived by Global Positioning System (GPS) Precise Point Positioning (PPP) approach need long time to converge to a stable state and show poor precision of S2, K1, and K2 constituents. Based on the fact that no constraint is imposed in the current kinematic solution, a new method is put forward, in which global ocean tide model predictions are taken as the priori information constraints to speed up the convergence rate and improve the accuracy of the GPS-derived OTLD parameters. First, the data of tide gauge from 01 January 2014 to 31 December 2016 are used to generate the harmonic parameters to evaluate the accuracy of six global ocean tide models and a regional ocean tide model (osu.chinesea.2010). Osu.chinesea.2010 model shows good agreement with the tide gauge results, while NAO99b model presents relatively large difference. The predictions from osu.chinesea.2010 and NAO99b model are employed as reference and the prior information, respectively. Second, continuous observations of 12 GPS sites during 2006–2013 in Hong Kong are collected to generate three dimensional OTLD amplitudes and phase lags of eight constituents using PPP with prior information constraints approach and harmonic analysis. Third, comparing the convergence time of eight constituents from PPP without and with priori information constraints approaches, the results show that the new method can significantly improve the convergence rate of OTLD amplitude estimates which obtain a certain level of stability seven years earlier than that derived by the PPP without priori information constraints. Precision of OTLD parameters derived by the new method is about 1 mm. By comparing with the precision of single PPP approach, the accuracy of eight constituents has been improved, especially for S2, K1, and K2 constituents. Finally, through comparing the different correction effects of OTLD estimates on the coordinates and their time series of the ground GPS stations, the results show that OTLD estimates derived by the new approach have similar influence as the osu.chinasea.2010 ocean tide model. The new method provides an effective means to improve the convergence and precision of the GPS-derived OTLD parameters, and achieve a similar correction as the high precision ocean tide model.

Study of the GPS inter-frequency calibration of timing receivers

When calibrating Global Positioning System (GPS) stations dedicated to timing, the hardware delays of P1 and P2, the P(Y)-codes on frequencies L1 and L2, are determined separately. In the international atomic time (TAI) network the GPS stations of the time laboratories are calibrated relatively against reference stations. This paper aims at determining the consistency between the P1 and P2 hardware delays (called dP1 and dP2) of these reference stations, and to look at the stability of the inter-signal hardware delays dP1–dP2 of all the stations in the network. The method consists of determining the dP1–dP2 directly from the GPS pseudorange measurements corrected for the frequency-dependent antenna phase center and the frequency-dependent ionosphere corrections, and then to compare these computed dP1–dP2 to the calibrated values.Our results show that the differences between the computed and calibrated dP1–dP2 are well inside the expected combined uncertainty of the two quantities. Furthermore, the consistency between the calibrated time transfer solution obtained from either single-frequency P1 or dual-frequency P3 for reference laboratories is shown to be about 1.0 ns, well inside the 2.1 ns uB uncertainty of a time transfer link based on GPS P3 or Precise Point Positioning. This demonstrates the good consistency between the P1 and P2 hardware delays of the reference stations used for calibration in the TAI network.The long-term stability of the inter-signal hardware delays is also analysed from the computed dP1–dP2. It is shown that only variations larger than 2 ns can be detected for a particular station, while variations of 200 ps can be detected when differentiating the results between two stations. Finally, we also show that in the differential calibration process as used in the TAI network, using the same antenna phase center or using different positions for L1 and L2 signals gives maximum differences of 200 ps on the hardware delays of the separate codes P1 and P2; however, the final impact on the P3 combination is less than 10 ps.