Real-time Kinematic Precise Point Positioning Research Articles

Assessing seismic displacements and early warning using kinematic PPP with MADOCA real-time products: A case study of 2023 Kahramanmaraş (Türkiye) earthquakes

Early warning and emergency hazard response studies in large earthquakes require rapid and reliable determination of earthquake magnitude. The magnitude of an earthquake can be estimated based on peak ground displacement (PGD) values captured from high-rate GNSS records. In this study, two major earthquakes that hit Kahramanmaraş Province on February 6, 2023, were investigated by using the real-time Global Navigation Satellite System (GNSS) Precise Point Positioning (PPP) technique to confirm the usability of GNSS in early warning. Data from high-rate (1-Hz) GNSS stations were evaluated with the real-time kinematic PPP approach utilizing the multi-GNSS advanced demonstration tool for orbit and clock analysis (MADOCA) products and JPL's GipsyX software. In addition, static PPP was also used to identify the permanent displacements caused by earthquakes. Static PPP results demonstrated that significant displacements were detected at stations close to the epicenters, particularly the 446.86 cm horizontal displacement in the EKZ1 station. Considering the kinematic PPP results revealed that when PGD values calculated from seismic waves, functional model, and updated coefficients were implemented, the moment magnitude of the Pazarcık earthquake was estimated as Mw 7.78, which was reported as Mw 7.8 by USGS and Mw 7.7 by AFAD, whilst the magnitude of the Elbistan earthquake was computed as Mw 7.56, which was reported as Mw 7.5 by USGS and 7.6 by AFAD. Overall, this study validates the effectiveness of the real-time GNSS PPP as an attractive alternative for analyzing coseismic events and supporting early warning.

Performance Assessment of Multi-GNSS Real-Time Products from Various Analysis Centers

The performance of real-time precise point positioning (PPP) relies primarily on the availability and quality of orbit and clock corrections. In this research, we collected data streams from 12 real-time mount points of IGS Real-Time Service (RTS) or analysis centers for a one-month period and conducted a performance assessment, including product latency and data availability, accuracy of orbit, clock and positioning performance. The epoch availability of GPS, GLONASS, Galileo and BDS was more than 98.5%, 95.79%, 94.20% and 85.9%, respectively. In addition, the orbit and clock errors of different real-time corrections was investigated. Then, PPP in static and kinematic for 16 IGS stations was conducted. The results show the real-time PPP for different products has a longer convergence time and a slightly worse accuracy than those of the post-processing PPP. For static PPP over 24 h, the real-time products of WHU had the best performance, with a mean RMSE of 1.0 cm in the horizontal and vertical directions and a median convergence time of 12.0 min. The products of CAS had the faster convergence speed due to the shortest product latency. Regarding real-time kinematic PPP for GPS only in an hourly batch, the real-time products of WHU and ESA performed best with a mean RMSE of 10.8 cm and 9.5 cm in the horizontal and vertical directions, respectively. Additionally, the PPP for different real-time products with the multi-GNSS combination obtained higher accuracy than those with GPS only in post-processing or real-time mode, and the PPP with the GPS/GLONASS/Galileo/BDS combination had the fastest convergence speed and best positioning performance. The hourly based kinematic PPP results of CAS, DLR, GFZ and WHU with the GREC combination had positioning errors smaller than 5.2 cm.

Analysis of BDS-3 Real-Time Satellite Clock Offset Estimated in Global and Asia-Pacific and the Corresponding PPP Performances

The quality of satellite clock offset affects the performances of positioning, navigation and timing services, and thus it is essential to the Global Navigation Satellite System (GNSS). This research focuses on the estimation of BeiDou Navigation Satellite System (BDS) real-time precise satellite clock offset by using GNSS stations located in the Global and Asia-Pacific region based on the mixed-difference model. The precision of the estimated BDS clock corrections is then analyzed with the classification of the orbit types, satellite generations, and atomic clock types. The results show that the precision of the BDS clock offset estimated in the Asia-Pacific for Geosynchronous Earth Orbit (GEO), Inclined Geosynchronous Satellite Orbit (IGSO) and Medium Earth Orbit (MEO) satellites are 0.204 ns, 0.077 ns and 0.085 ns, respectively, as compared to those of clock offsets estimated in globally distributed stations. The average precision of the BDS-3 satellites clock offset estimated in global region is 0.074 ns, which is much better than the 0.130 ns of BDS-2. Furthermore, analyzing the characteristics of the corresponding atomic clocks can explain the performance of the estimated satellite clock offset, and the stability and accuracy of various parameters of the Passive Hydrogen Maser (PHM) atomic clocks are better than those of Rubidium (Rb) atomic clocks. In the positioning domain, the real-time clocks estimated in the global/Asia-Pacific have been applied to BDS kinematic Precise Point Positioning (PPP) in different regions. The Root Mean Square (RMS) of positioning results in global real-time kinematic PPP is within 4 cm in the horizontal direction and about 6 cm in the vertical direction. Hence, the BDS real-time clock offset can supply the centimeter-level positioning demand around the world.

Real-time ocean precise point positioning with BDS-3 service signal PPP-B2b

For ocean high-precision positioning, the Real-Time Kinematic (RTK) technique exists disadvantages since the positioning accuracy will deteriorate with the baseline elongating. The real-time Precise Point Positioning (PPP) based on Real-Time Service (RTS) may be difficult to operate on ocean since the internet-based communication is unavailable. As an alternative, the PPP-B2b service provided by BeiDou Global Navigation Satellite System (BDS-3) is considered free from these limiting requirements, and it can realize real-time PPP for users in China and surrounding areas. This research focuses on a real-time PPP with BDS-3 service signal PPP‑B2b in ocean high-precision positioning application. The real-time satellite orbit and clock are recovered, and the accuracy are evaluated with collected 10-day PPP-B2b messages. The results indicate that the accuracy of PPP-B2b satellite orbit is better than 0.1 m in the radial component and the satellite clock offsets achieve an accuracy of better than 0.2 ns for both BDS-3 and Global Positioning System (GPS). The land simulated real-time kinematic PPP experiment using 7 International GNSS Service (IGS) stations observations yielded the three-dimensional (3D) positioning accuracy of 11.6 cm for BDS-3 only and 8.3 cm for GPS + BDS-3. Finally, an ocean real-time kinematic PPP positioning experiment is carried out and the data quality of ocean observations are analyzed. The ocean real-time PPP with PPP-B2b corrections achieves the 3D Root Mean Square (RMS) of 21.3 cm for BDS-3-only and 18.2 cm for GPS + BDS-3, which indicates that the PPP-B2b service provided by BDS-3 is prospective in location-based ocean application.

Assessment of Real-Time PPP with Trimble RTX correction service for real-time dynamic displacement monitoring based on high-rate GNSS observations

Real-time displacement monitoring of earth crust and engineering structures with the Global Navigation Satellite System (GNSS) is highly important for detecting and preventing the damage and possible loss of life during natural phenomena. Nowadays, the Real-Time Kinematic Precise Point Positioning (RT-PPP) method using a stand-alone GNSS receiver can provide fast and accurate dynamic displacement. Trimble Real-Time Extended (RTX) technology enables real-time precise positioning with cm-level accuracy in a short convergence time. The present study investigates, for the first time, the dynamic displacement detection performance of RT-PPP based on CenterPoint RTX correction service for early warning systems and rapid risk assessment. To evaluate the performance of Trimble RTX technology, a series of shake table experiments were conducted and harmonic oscillations with different frequencies and amplitudes were generated. Trimble RTX solutions were obtained at 20 Hz sampling rate and compared with Linear Variable Differential Transformer (LVDT) data, considered as reference, in both frequency and time domains. Results show that Trimble RTX technology can accurately detect the frequency of harmonic motions, whose amplitudes are slightly different from LVDT values because of GNSS inherent noise. The average of Root Mean Square Error (RMSE) values obtained from the differences between LVDT and filtered RTX-derived time series for all events is 3.6 mm. These results indicated that the CenterPoint RTX technology could be employed for real-time and near-real-time applications to monitor structural and earthquake-induced motions accurately.

The Performance of Three-Frequency GPS PPP-RTK with Partial Ambiguity Resolution

The correct ambiguity resolution of real-time kinematic precise point positioning (PPP-RTK) plays an essential role in achieving fast, reliable, and high-precision positioning. However, the ambiguity of incorrect fixing will cause poor PPP-RTK positioning performance. Hence, it is essential to optimize the selected strategy of the ambiguity subset to obtain a more reliable ambiguity resolution performance for PPP-RTK. For this reason, a partial ambiguity resolution (PAR) method combining quality control and Schmidt orthogonalization (Gram–Schmidt) is proposed in this study. To investigate the performance of global positioning system (GPS) dual- and three-frequency PPP-RTK comprehensively, the PAR method based on the Gram–Schmidt method was analyzed and compared with the highest elevation angle method, which considered the satellite with the highest elevation angle as the reference satellite. The performance of ambiguity fixing, atmospheric corrections, and positioning were evaluated using five stations in Belgium and its surrounding area. The results showed average epoch fixing rates of 81.01%, 95.92%, 82.05%, and 97.93% in the dual-frequency highest elevation angle (F2-MAX), dual-frequency Gram–Schmidt (F2-ALT), three-frequency highest elevation angle (F3-MAX), and three–frequency Gram–Schmidt (F3-ALT), respectively. In terms of the time to first fix (TTFF), 89.02%, 94.25%, 90.24%, and 95.69% of the single-differenced (SD) narrow lane (NL) ambiguity fell within 3 min in F2-MAX, F2-ALT, F3-MAX, and F3-ALT, respectively. As far as the ionospheric corrections are concerned, the proportion of SD ionospheric residuals within ±0.25 total electron content units (TECU) were 95.08%, 95.93%, 95.68%, and 96.98% for the F2-MAX, F2-ALT, F3-MAX, and F3-ALT, respectively. The centimeter-level accuracy of both the horizontal and vertical positioning errors can be achieved almost instantaneously in F3-ALT. This is attributed to the accurate and reliable SD NL ambiguity fixing based on the Gram–Schmidt approach.

Investigating GNSS PPP\u2013RTK with external ionospheric constraints

Real-Time Kinematic Precise Point Positioning (PPP–RTK) is inextricably linked to external ionospheric information. The PPP–RTK performances vary much with the accuracy of ionospheric information, which is derived from different network scales, given different prior variances, and obtained under different disturbed ionospheric conditions. This study investigates the relationships between the PPP–RTK performances, in terms of precision and convergence time, and the accuracy of external ionospheric information. The statistical results show that The Time to First Fix (TTFF) for the PPP–RTK constrained by Global Ionosphere Map (PPP–RTK-GIM) is about 8–10 min, improved by 20%–50% as compared with that for PPP Ambiguity Resolution (PPP-AR) whose TTFF is about 13–16 min. Additionally, the TTFF of PPP–RTK is 4.4 min, 5.2 min, and 6.8 min, respectively, when constrained by the external ionospheric information derived from different network scales, e.g. small-, medium-, and large-scale networks, respectively. To analyze the influences of the optimal prior variances of external ionospheric delay on the PPP–RTK results, the errors of 0.5 Total Electron Content Unit (TECU), 1 TECU, 3 TECU, and 5 TECU are added to the initial ionospheric delays, respectively. The corresponding convergence time of PPP–RTK is less than 1 min, about 3, 5, and 6 min, respectively. After adding the errors, the ionospheric information with a small variance leads to a long convergence time and that with a larger variance leads to the same convergence time as that of PPP-AR. Only when an optimal prior variance is determined for the ionospheric delay in PPP–RTK model, the convergence time for PPP–RTK can be shorten greatly. The impact of Travelling Ionospheric Disturbance (TID) on the PPP–RTK performances is further studied with simulation. It is found that the TIDs increase the errors of ionospheric corrections, thus affecting the convergence time, positioning accuracy, and reliability of PPP–RTK.

Enhanced multipath mitigation method based on multi-resolution CNR model and adaptive statistical test strategy for real-time kinematic PPP

This study proposes an enhanced multipath mitigation method based on multi-resolution carrier-to-noise-ratio (CNR) model and adaptive statistical test strategy for real-time kinematic precise point positioning (PPP) applications. The multi-resolution CNR model is established with GPS observation data collected from DOY 152 to 181 of 2019 by 230 globally distributed IGS stations, which used to analyze the relevant factors affecting CNR. Statistical results indicate that the CNR is not only related to the satellite elevation, but also closely related to the receiver types and specific satellite. The maximum difference between different receivers can reach 20 dB for the same satellite at the same elevation. In addition, the performance of the CNR is also obviously different between each satellite, and the maximum difference between different satellites is about 10 dB for the same receiver at the same elevation. Hence, in terms of the method which is based on CNR information for multipath detection and mitigation, the independence of receiver types, satellite and frequency must be considered. With the above analysis, this study developed a multi-resolution CNR model based on different receiver types, different satellites and different elevation firstly. Then, combined with the adaptive statistical test strategy which is based on the difference of CNR between inter-frequency and the difference of CNR between adjacent epochs, the multipath can be detected effectively. For the epoch which affected by multipath, the down-weighted strategy based on CNR is adopted to mitigate the influence of multipath on positioning. Real-time kinematic PPP data are collected to assess the proposed method, and the results demonstrate that the proposed method can detect the multipath effectively, and the detection rate can reach 90.28%. Moreover, after adopting the mitigation strategy, the RMS bias of the east, north and up components are improved about 19.95%, 17.89% and 23.07% compared to the original results, respectively. It is worth noting that this proposed method is also suitable for other GNSS, such as GLONASS and BDS, but the corresponding CNR model must be established simultaneously.

Performance assessment of real-time multi-GNSS integrated PPP with uncombined and ionospheric-free combined observables

For precise position services, the real-time precise point positioning (PPP) is a promising technology. The real-time PPP performance is expected to be improved by multi-system combination. The performance of real-time multi-system PPP needs to be periodically investigated, with the increasing number of available satellites and the continuously improved quality of real-time precise products of satellite clocks and orbits. In this study, a comprehensive performance assessment is conducted for the four-system integrated real-time PPP (FSIRT-PPP) with GPS, BDS, Galileo and GLONASS in both static and kinematic modes. The datasets from 118 stations spanning approximately a month are used for analysis, and the real-time stream CLK93 is employed. The superior performance of FSIRT-PPP is validated by comparing with the results of GPS/BDS, GPS/Galileo, GPS/GLONASS, GPS-only, BDS-only, Galileo-only and GLONASS-only cases. The FSIRT-PPP using ionospheric-free (IF) combined observables can achieve a convergence time of 10.9, 4.8 and 11.8 min and a positioning accuracy of 0.4, 0.5 and 0.7 cm in the static mode in the east, north and up directions, respectively, while the derived statistic is 15.4, 7.0 and 16.4 min, and 1.6, 1.2 and 3.4 cm in the kinematic mode in the three directions, respectively. Moreover, we also compare the position solutions of real-time PPP adopting IF combined and uncombined (UC) observables, and prove the mathematical equivalence between the two PPP models in the converged stage, provided that there are no external ionospheric corrections or constraints given to the estimated ionospheric delays in the UC model. The difference between the fully converged positioning accuracy of IF-based and UC-based real-time PPP is marginal, but the UC-based real-time PPP has longer convergence time due to the influence of the significant unmodeled time-varying errors in the real-time precise products as well as the different parameterization between them. For completeness, the real-time kinematic PPP results in harsh environments and the post-processed PPP results are also presented.

Analysis of GNSS clock prediction performance with different interrupt intervals and application to real-time kinematic precise point positioning

Continuous and timely real-time satellite orbit and clock products are mandatory for real-time precise point positioning (RT-PPP). Real-time high-precision satellite orbit and clock products should be predicted within a short time in case of communication delay or connection breakdown in practical applications. For prediction, historical data describing the characteristics of the real-time orbit and clock can be used as the basis for performing the prediction. When historical data are scarce, it is difficult for many existing models to perform precise predictions. In this paper, a linear regression model is used to predict clock products. Seven-day GeoForschungsZentrum (GFZ) final clock products sampled at 30 s are used to analyze the characteristics of GNSS clocks. It is shown that the linear regression model can be used as the prediction model for the satellite clock products. In addition, the accuracy of the clock prediction for different satellites are analyzed using historical data with different periods (such as 2 and 10 epochs). Experimental results show that the accuracy of the clock with the linear regression prediction model using historical data with 10 epochs is 1.0 ns within 900 s. This is higher accuracy than that achieved using historical data of 2 epochs. Finally, the performance analysis for real-time kinematic precise point positioning (PPP) is provided using GFZ final clock prediction results and state space representation (SSR) clock prediction results when communication delay or connection breakdown occur. Experimental results show that the positioning accuracy without prediction is better than that with prediction in general, whether using the final clock product or the SSR clock product. For the final clock product, the positioning accuracy in the north (N), east (E), and up (U) directions is better than 10.0 cm with all visible GNSS satellites with prediction. In comparison, the 3D positioning accuracy of N, E, and U directions with visible GNSS satellites whose prediction accuracy is better than 0.1 ns using historical data of 10 epochs is improved from 15.0 cm to 7.0 cm. For the SSR clock product, the positioning accuracy of N, E, and U directions is better than 12.0 cm with visible GNSS satellites with prediction. In comparison, the 3D positioning accuracy of N, E, and U directions with visible GNSS satellites whose prediction accuracy is better than 0.1 ns using historical data of 10 epochs is improved from 12.0 cm to 9.0 cm.

A new datum jump detection and mitigation method of Real-Time Service (RTS) clock products

Real-time orbit and clock products are crucial for real-time precise point positioning (PPP) applications. The International Global Navigation Satellite System (GNSS) Service (IGS) launched the Real-Time Service (RTS) in 2013 to provide real-time satellite orbit and clock products which have since found wide applications. Currently, the IGS RTS provides two different types of satellite orbit and clock products: the products generated from individual Analysis Centers such as CLK01, CLK22 and CLK90 and the combination products such as IGS01 and IGS03. These IGS RTS products are different in terms of precision and reliability. First, we verify that the phenomenon of clock datum jumps is obvious in IGS01, which has not been considered by the GNSS community when applying the IGS01 product to the real-time PPP. Afterward, the causes of the clock datum jump are investigated. The results indicate that a switchover of the reference product or a datum jump in the reference product will cause a clock datum jump. In order to solve the clock datum jumps issue, a new clock datum jump detection and mitigation algorithm is proposed. Real-time kinematic PPP experiments are then carried out to validate the proposed satellite clock detection and mitigation algorithm. The positioning results with 27 globally distributed IGS stations show that the root mean square improvements in the north, east and up components are 61.5%, 36.5% and 55.1% after detecting and mitigating the datum jumps.

Evaluation and analysis of real-time precise orbits and clocks products from different IGS analysis centers

To meet the increasing demands from the real-time Precise Point Positioning (PPP) users, the real-time satellite orbit and clock products are generated by different International GNSS Service (IGS) real-time analysis centers and can be publicly received through the Internet. Based on different data sources and processing strategies, the real-time products from different analysis centers therefore differ in availability and accuracy. The main objective of this paper is to evaluate availability and accuracy of different real-time products and their effects on real-time PPP. A total of nine commonly used Real-Time Service (RTS) products, namely IGS01, IGS03, CLK01, CLK15, CLK22, CLK52, CLK70, CLK81 and CLK90, will be evaluated in this paper. Because not all RTS products support multi-GNSS, only GPS products are analyzed in this paper. Firstly, the availability of all RTS products is analyzed in two levels. The first level is the epoch availability, indicating whether there is outage for that epoch. The second level is the satellite availability, which defines the available satellite number for each epoch. Then the accuracy of different RTS products is investigated on nominal accuracy and the accuracy degradation over time. Results show that Root-Mean-Square Error (RMSE) of satellite orbit ranges from 3.8 cm to 7.5 cm for different RTS products. While the mean Standard Deviations of Errors (STDE) of satellite clocks range from 1.9 cm to 5.6 cm. The modified Signal In Space Range Error (SISRE) for all products are from 1.3 cm to 5.5 cm for different RTS products. The accuracy degradation of the orbit has the linear trend for all RTS products and the satellite clock degradation depends on the satellite clock types. The Rb clocks on board of GPS IIF satellites have the smallest degradation rate of less than 3 cm over 10 min while the Cs clocks on board of GPS IIF have the largest degradation rate of more than 10 cm over 10 min. Finally, the real-time kinematic PPP is carried out to investigate the effects of different real-time products. The CLK90 has the best performance and mean RMSE of 26 globally distributed IGS stations in three components are 3.2 cm, 6.6 cm and 8.5 cm. And the second-best positioning results are using IGS03 products.

Satellite-Clock Modeling in Single-Frequency PPP-RTK Processing

The real-time kinematic precise point positioning (PPP-RTK) technique enables integer ambiguity resolution by providing singlereceiver users with information on the satellite phase biases next to the standard PPP corrections. Using undifferenced and uncombined observations, rank deficiencies existing in the design matrix need to be eliminated to formestimable parameters. In this contribution, the estimability of the parameters was studied in single-frequency ionosphere-weighted scenario, given a dynamic satellite-clock model in the network Kalman filter. In case of latency of the network corrections, the estimable satellite clocks, satellite phase biases, and ionospheric delays need to be predicted over short time spans. With and without satellite-clock models incorporated in the network Kalman filter, different approaches were used to predict the network corrections. This contribution shows how the predicted network corrections responded to the presence and absence of satellite-clock models. These differences in the predicted network corrections were also reflected in the user positioning results. Using three different 1-Hz global positioning system (GPS) single-frequency data sets, two user stations in one small-scale network were used to compute the positioning results, applying predicted network corrections. The latency of the network products ranges from 3 to 10 s. It was observed that applying strong satellite-clock constraints in the network Kalman filter (i.e., with the process noise of 1 or 0.5mm per square root of second) reduced the root-mean squares (RMS) of the user positioning results to centimeters in the horizontal directions and decimeters in the vertical direction for latencies larger than 6 s, compared to the cases without a satellite-clock model.

Assessment of Multiple GNSS Real-Time SSR Products from Different Analysis Centers

The real-time State Space Representation (SSR) product of the GNSS (Global Navigation Satellite System) orbit and clock is one of the most essential corrections for real-time precise point positioning (PPP). In this work, the performance of current SSR products from eight analysis centers were assessed by comparing it with the final product and the accuracy of real-time PPP. Numerical results showed that (1) the accuracies of the GPS SSR product were better than 8 cm for the satellite orbit and 0.3 ns for the satellite clock; (2) the accuracies of the GLONASS (GLObalnaya NAvigatsionnaya Sputnikovaya Sistema) SSR product were better than 10 cm for orbit RMS (Root Mean Square) and 0.6 ns for clock STD (Standard Deviation); and (3) the accuracies of the BDS (BeiDou Navigation Satellite System) and Galileo SSR products from CLK93 were about 14.54 and 4.42 cm for the orbit RMS and 0.32 and 0.18 ns for the clock STD, respectively. The simulated kinematic PPP results obtained using the SSR products from CLK93 and CLK51 performed better than those using other SSR products; and the accuracy of PPP based on all products was better than 6 and 10 cm in the horizontal and vertical directions, respectively. The real-time kinematic PPP experiment carried out in Beijing, Tianjin, and Shijiazhuang, China indicated that the SSR product CLK93 from Centre National d’Etudes Spatiales (CNES) had a better performance than CAS01. Moreover, the PPP with GPS + BDS dual systems had a higher accuracy than those with only a GPS single system.

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).

Using external tropospheric corrections to improve GNSS positioning of hot-air balloon

High accurate global navigation satellite systems (GNSS) require to correct a signal delay caused by the troposphere. The delay can be estimated along with other unknowns or introduced from external models. We assess the impact of the recently developed augmentation tropospheric model on real-time kinematic precise point positioning (PPP). The model is based on numerical weather forecast and thus reflects the actual state of weather conditions. Using the G-Nut/Geb software, we processed GNSS and meteorological data collected during the experiment using a hot-air balloon flying up to an altitude of 2000 m. We studied the impacts of random walk noise setting of zenith total delay (ZTD) on estimated parameters and the mutual correlations, the use of external tropospheric corrections, the use of data from a single or dual GNSS constellation and the use of Kalman filter and backward smoothing processing methods. We observed a significant negative correlation of the estimated rover height and ZTD which depends on constraining ZTD estimates. Such correlation caused a degraded performance of both parameters when estimated simultaneously, in particular for a single GNSS constellation. The impact of ZTD constraining reached up to 50-cm differences in the rover height. Introducing external tropospheric corrections improved the PPP solution regarding: (1) shortened convergence, (2) better overall robustness, particularly, in case of degraded satellite geometry, (3) less adjusted parameters with lower correlations. The numerical weather model-driven PPP resulted in 9–12- and 5–6-cm uncertainties in the rover altitude using the Kalman filter and the backward smoothing, respectively. Compared to standard PPP, it indicates better performance by a factor of 1–2 depending on the availability of GNSS constellations, the troposphere constraining and the processing strategy.

Array-Aided Single-Frequency State-Space RTK with Combined GPS, Galileo, IRNSS, and QZSS L5/E5a Observations

The concept of real-time kinematic precise point positioning (PPP-RTK) is to achieve integer ambiguity resolution (IAR) at a single global navigation satellite system (GNSS) user by providing network-derived satellite phase biases (SPBs) in addition to the standard PPP corrections. The integerness of the user ambiguities gets recovered and resolved, obtaining high-precision position solutions with the aid of the precise carrier-phase observables. Most of current PPP-RTK methods focus on processing dual-frequency or multifrequency GNSS network observations. The new developing Indian regional navigation satellite system (IRNSS), however, provides only a single-frequency signal in L-band, and shares the L5 frequency with the American global positioning system (GPS), the European Galileo, and the Japanese quasi-zenith satellite system (QZSS). This contribution proposes a new array-aided state-space RTK (SS-RTK) method following the concept of PPP-RTK, which is applicable to the single-frequency network data processing. A small array of multi-GNSS stations, separated by a few meters, takes the role of reference station to provide a batch of single-frequency RTK corrections. Similar to PPP-RTK, the single-frequency stand-alone user ambiguities are a double-differenced (DD) form after applying the SS-RTK corrections. Based on the proposed array-aided SS-RTK concept, the authors analyze the capability of the single-receiver positioning with IAR using L5/E5a frequency observations from IRNSS, as well as GPS, Galileo, and QZSS. Results from real-data experiments demonstrate that even though stand-alone RTK using current IRNSS satellites is not yet possible, they effectively contribute to the tightly integrated multisystem RTK. By increasing the number of antennas in the array used for SS-RTK corrections, the user would achieve more precise and reliable positions. After increasing the dimension of the array to four antennas, a 4-10% improvement in the IAR success rate is experienced. Moreover, the convergence time of the float solutions, reaching a subdecimeter precision level, reduces from 30 to 40 min (single-antenna array) to about 20 min (four-antenna array).

Validation of performance of real-time kinematic PPP. A possible tool for deformation monitoring

Structural failures (bridge or building collapses) and geohazards (landslides, ground subsidence or earthquakes) are worldwide problems that often lead to significant economic and loss of life. Monitoring the deformation of both natural phenomena and man-made structures is a major key to assessing structural dynamic responses. Actually, this monitoring process is under real-time demand for developing warning and alert systems.One of the most used techniques for real-time deformation monitoring is the Global Navigation Satellite System (GNSS) real-time procedure, where the relative positioning approach, using a well-known reference station, has been applied.This study was conducted to evaluate the actual quality of the real-time kinematic Precise Point Positioning (PPP) GNSS solution for deformation monitoring, where it can be concluded that a promise tool is under development and should be taken into account on actual and near future real-time deformation monitoring studies and applications.

A cycle slip fixing method with GPS + GLONASS observations in real-time kinematic PPP

A key limitation of precise point positioning (PPP) is the long convergence time, which requires about 30 min under normal conditions. Frequent cycle slips or data gaps in real-time operation force repeated re-convergence. Repairing cycle slips with GPS data alone in severely blocked environments is difficult. Adding GLONASS data can supply redundant observations, but adds the difficulty of having to deal with differing wavelengths. We propose a single-difference between epoch (SDBE) method to integrate GPS and GLONASS for cycle slip fixing. The inter-system bias can be eliminated by SDBE, thus only one receiver clock parameter is needed for both systems. The inter-frequency bias of GLONASS satellites also cancels in the SDBE, so cycle slips are preserved as integers, and the LAMBDA method is adopted to search for cycle slips. Data from 7 days of 20 globally distributed IGS sites were selected to test the proposed cycle slip fixing procedure with artificial blocking of the signal; cycle slips were introduced for all un-blocked satellites at each epoch. For a 30-s sampling interval, the average success rate of fixing can be improved from 73 to 98 % by adding GLONASS. Even for a 180-s sampling interval, GPS + GLONASS can achieve a success rate of 81 %. A real-time kinematic PPP experiment was also performed, and the results show that using GPS + GLONASS can achieve continuous high-accuracy real-time PPP without re-convergence.

Single-Frequency Integer Ambiguity Resolution Enabled GPS Precise Point Positioning

AbstractHigh-precision (centimeter-level) real-time kinematic precise point positioning (PPP-RTK) becomes feasible when using precise corrections, as received from a regional Continuously Operating Reference Station network. These network corrections comprise (biased) satellite clocks, (biased) satellite phase biases, and ionospheric delays, where the latter ones are interpolated to the approximate location of the PPP-RTK receiver. Thus far, very fast PPP-RTK integer ambiguity resolution performance has been reported based on dual-frequency Global Positioning System (GPS) data. The availability of ionospheric corrections enables one to carry out PPP-RTK using a single-frequency receiver. Despite that single-frequency integer ambiguity resolution based on a single epoch of data cannot often be successful, fast integer ambiguity resolution is possible when accumulating a short time span of data, assuming that the ambiguities are time constant. In this paper, results of the performance of single-frequency PP...