Static Precise Point Positioning Research Articles

Assessments of GPS satellite orbiting period effects on diurnal and semi-diurnal luni-solar declinations utilizing Galileo satellites

Global Navigation Satellite Systems (GNSS) can observe a variety of surface deformations on Earth, including periodic oscillations at different frequencies. An example of such phenomena is ocean tide loadings (OTL), which result from the redistribution of water mass. The Global Positioning System (GPS) exhibits orbital geometry that causes its revisit and orbital periods to coincide with the diurnal and semi-diurnal luni-solar declination constituents, known as K1 and K2, respectively. Consequently, the system faces challenges in accurately estimating these periodic oscillations due to its orbital artifacts. This study aims to quantify the extent to which GPS orbital artifacts introduce periodic signals into the K1 and K2 constituents by utilizing the Galileo system and determining the most suitable positioning approach. A dataset from the International GNSS Service (IGS), spanning 40 days in 2024 and covering six stations, was analyzed. Coordinates were estimated using both kinematic positioning every 5 minutes and a 6-hour static precise point positioning (PPP) mode with a 3-hour shift. The power spectra for the east, north, and up components indicated that, on average, the GPS system contributes 52.8% to the K1 constituents and 66.3% to the K2 constituents. Despite expectations that the diurnal K1 and semi-diurnal K2 tidal constituents would be more prominent in the power spectra of the GPS comparing to that of natural signature or of other navigation system (Galileo for this study), the diurnal K1 tidal constituent appeared weak in the kinematic mode power spectra for the GPS system. These findings validate that the overlapped-static PPP mode is a more appropriate approach for estimating these periodic deformations.

PPP based on factor graph optimization

Abstract Kalman or Kalman-related filtering methods are routinely applied in precise point positioning (PPP). However, in robot simultaneous localization and mapping (SLAM) systems, the factor graph optimization (FGO) has proved advantages over filtering methods in recent years, e.g., reducing the linearization errors and support of plug-and-play feature for multiple sensor fusion. Therefore, it would be interesting to apply the FGO to PPP. In addition, it will also facilitate the tight integration of PPP with Visual/LiDAR SLAM. In this work, PPP is solved under the factor graph optimization framework. A factor graph for PPP has been constructed. Results from 268 IGS-MGEX stations show that the factor graph optimization method can achieve a similar performance with that of Kalman filtering. First, the positioning accuracy in the convergence period can be improved for PPP based on factor graph optimization because it optimizes the entire state variables based on all the available observations. For applications that do not require real-time processing, the observation after the current states, e.g., future observations, can also be used to enhance the current state estimation. Second, the accuracy of static PPP is almost the same for the two methods with millimeter-accuracy for horizontal directions and centimeter-accuracy for vertical directions. Third, the kinematic PPP for both methods can achieve centimeter-level accuracy in horizontal directions and decimeter-level accuracy in vertical directions. Although the performance is comparable, it is noted that the computational efficiency of factor graph optimization method is still a problem. For each epoch, the average of elapsed time for Kalman filtering is 132 microseconds, while that of factor graph optimization method is 9664 microseconds. The elapsed time of factor graph optimization method can be further improved if the fix-window optimization technique is applied, which will be investigated in the future.

Low-latitude ionospheric responses and positioning performance of ground GNSS associated with the geomagnetic storm on March 13–14, 2022

Interplanetary coronal mass ejections (ICMEs) and the driven geomagnetic storms have a profound influence on the ionosphere, potentially leading to a degradation in positioning performance. In this study, we made a comprehensive analysis of the entire process of the impact of a typical ICME and its driven geomagnetic storm on the low-latitude ionosphere during March 13–14, 2022 (π-day storm) and the positioning performance of Global Navigation Satellite System (GNSS). During the passage of the ICME event, significant ionospheric scintillation, and TEC (total electron content) disturbances were observed in the low-latitude Hong Kong region. The ICME sheath region intensively compressed the magnetosphere via solar wind dynamic pressure enhancement and subsequently drove the storm main phase. It is found that both the magnetospheric compression that formed the storm initial phase and the storm main phase caused ionospheric scintillation. In comparison, the intensity of the ionospheric scintillation caused by the intense magnetospheric compression just before the storm main phase is even more pronounced. We also analyzed the impact of storms on standard point positioning (SPP), precise point positioning (PPP) and real-time kinematic (RTK) techniques. The positioning accuracies of single-frequency SPP and PPP experienced the most severe decline, and there was a noticeable increase in the initialization time for dual-frequency static PPP and RTK during the event. RTK demonstrated a shorter convergence time and higher accuracy during this event, but it was limited to short-baseline RTK (<30 km).

An effective method for improving GNSS precise point positioning performance at the day boundary

Abstract Aiming to address poor self-consistency of the satellite clock and orbit interpolations at the day boundary, which is caused by the discontinuities of their International GNSS Service (IGS) products for two consecutive days, an effective method is proposed to improve the precise point positioning (PPP) performances at the day boundary. According to different orders of Lagrange interpolator and different IGS Analysis Centers products of Center for Orbit Determination in Europe (CODE), GeoForschungsZentrum (GFZ) and Wuhan University (WUH), biases at the day boundaries are estimated and analyzed using a 4 day (DOY 94-97, 2022) data set of GPS, BDS-3 and Galileo from 123 IGS stations. These estimated biases show the time-varying characteristics. The differences in biases across 9th-11th orders of Lagrange interpolator are minimal, and these variances have a negligible impact on positioning. The results show that this poor self-consistency at the day boundary has an obvious influence on the kinematic PPP positioning, especially there is a centimeter-level variation at time of 24:00:00/00:00:00. This influence on the Up direction of kinematic PPP positioning is more serious than other directions. When the bias is estimated and corrected, the kinematic PPP positioning accuracies at the day boundary have a mean improvement of 0.043, 0.064 and 0.027 m for WUH, GFZ and CODE, respectively. The mean improvements for GPS, BDS-3 and Galileo are 0.021, 0.062 and 0.051 m. Additionally, the static PPP performances at the day boundary show the convergence times are shortened by 3.2, 6.2, and 2.5 min for WUH, GFZ and CODE, respectively, when the poor self-consistency of the satellite clock and orbit interpolations is estimated and corrected. Meanwhile, its 0.5 and 1 h positioning accuracies are improved.

UPDs estimation and ambiguity resolution performance evaluation of LEO navigation system

Low-Earth orbit (LEO) satellites have fast motion and thus provide rapid geometric change relation to the ground stations in a short period of time, which are expected to improve the positioning performance. In this study, a LEO constellation of 160 LEO satellites was simulated and simulated LEO observation data at global, European, and American stations were used to estimate the uncalibrated phase delays (UPDs) and achieve static and kinematic precise point positioning (PPP) ambiguity resolution (AR). The quality of the estimated UPD products were evaluated. More than 89 % and 96 % of the wide- and narrow-lane UPDs had a posteriori residual of less than 0.15 and 0.25 cycles, respectively. In static PPP, all ambiguity fixing rates were larger than 63 %. Compared with float solutions, the average convergence time of the fix solutions at the global, European and American stations was accelerated by 8 %, 6 % and 7 %, respectively; the average root-mean-square errors (RMSEs) in the east, north, and up components at the global, European and American stations were decreased by (22 %, 20 %, 15 %), (36 %, 34 %, 28 %) and (44 %, 31 %, 29 %), respectively. In kinematic PPP, all ambiguity fixing rates were larger than 40 %. Compared with float solutions, the average convergence time of the fix solutions at the global, European and American stations was accelerated by 4 %, 19 % and 14 %, respectively; the average RMSEs in the east, north, and up components at the global, European and American stations were decreased by (10 %, 10 %, 7 %), (27 %, 22 %, 11 %) and (32 %, 20 %, 10 %), respectively. In both static and kinematic PPP, AR accelerated the convergence time and improved the positioning accuracy.

Elevating performance in BDS-3 Precise Point Positioning Ambiguity Resolution through LEO augmented constellations

With the help of constellations combined BDS-3 (BeiDou Navigation Satellite System) and LEO (Low Earth Orbit), we aim to improve the performances of PPP (Precise Point Positioning) and PPP Ambiguity Resolution (PPP-AR). First, LEO constellations with 66, 96, 156, 192, 270, and 288 satellites are designed to establish six LEO augmented constellations. Based on four challenge scenarios, PPP of six LEO augmented constellations are performed. Even in the strip-shaped obstruction area losing more than 60% of observations, the positioning accuracies of static PPP are improved by (1.0%, 5.7%, 0.2%) for BDS+66LEO, and (14.9%, 33.7%, 7.5%) for BDS+288LEO in the east, north, and up components. The positioning accuracy and convergence time improve quickly as the number of LEO satellites increased from 66 to 156, and slowdown from 192 to 288. Two constellations, BDS+156LEO and BDS+192LEO, are considered to strike the balance of acceptable PPP performance and constellation load. Then, the performance of PPP-AR is realized with the estimated UPD (Uncalibrated Phase Delay). The correlations among geodetic parameters and ambiguities deriving from the post-fit variance–covariance matrix are analyzed to illustrate the enhancement of LEO augmented constellations. Under the condition of 20°elevation angle occlusion with azimuth ranging from 0 to 360°, BDS+156LEO can achieve an ambiguity fix rate of up to 98.37% with a faster mean TTFF (Time To First Fix) of 12.76 min, and the positioning accuracies in the east, north, and up components are improved by 28.2%, 21.4%, and 15.1% respectively, compared with BDS-3. BDS+192LEO realized an 98.42% ambiguity fixing rate, and improved BDS-3 by 31.4%, 26.7% and 11.5% with its TTFF been 12.25 min.

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.

BDS-3 six-frequency precise point positioning: effects of receiver-dependent inter-frequency clock bias and multi-frequency contributions

We find that there is time-varying bias at the receiver in BDS-3 multi-frequency phase observations, which will lead to receiver-dependent inter-frequency clock bias (RIFCB) and damage the rigor of BDS-3 multi-frequency precise point positioning (PPP) model. A unified RIFCB correction method compatible with uncombined and ionospheric-free combined PPP models using any BDS-3 frequencies is proposed. The contributions of multi-frequency integration to BDS-3 static and kinematic PPP performance are evaluated. The results indicate that the RIFCB amplitude can reach 1 dm. If the RIFCB correction is ignored, the phase observation residuals present a systematic bias. RIFCB has potential effects on precise time transfer, ionospheric monitoring, and fractional cycle bias estimation. Experimental results show that the long-term frequency stability of time transfer can be improved by correcting RIFCB. The joint use of all BDS-3 six-frequency signals can significantly shorten the convergence time, and the positioning accuracy can also be slightly improved.

A New Method for Deformation Monitoring of Structures by Precise Point Positioning

Although deformations are mostly insignificant, they can be catastrophic when accumulated to certain amounts. Precise point positioning (PPP) can work with one receiver, preventing problems caused by the base station constrain upon employment of current methods such as real-time kinematics (RTK). However, current methods employing PPP focus on high-frequency monitoring such as earthquake or geological calamity monitoring, and these methods are not suitable for structures. Thus, this study proposes a new method for the deformation monitoring of structures via PPP. First, we obtained the coordinate sequence of structures via static PPP when setting the interval. Then, we transformed the coordinates to the same coordinate system with the same basis. Finally, we decomposed the sequences via empirical mode decomposition (EMD) to obtain a low-frequency part, which is the deformation of the target structure. The result of the monitoring experimentation on IGS stations shows that the monitoring index, Sd, of the sequence under different intervals using this method could be 1–2 mm on average in the directions of E, N, and U, which is much better than the original monitoring sequence. Alongside that, it prevented a fall in accuracy when the interval decreased. Therefore, all results proved the feasibility and validity of the method.

USER IMPLEMENTATION AND ASSESSMENT OF BDS-3 PRECISE POINT POSITIONING AUGMENTATION SERVICE WITH NO ECONOMIC COST

Abstract. The satellite-based precise point positioning (PPP) service enables users with high accuracy positions without Internet connections. Currently, two types of satellite-based PPP services are available. One type is commercial service, such as Trimble CenterPoint RTX service. The second type is non-commercial and cost-free service, including the BDS-3 satellite-based PPP service based on PPP-B2b signals. This service is currently open access to all receiver manufacturers. This contribution firstly presents a detailed instruction on how to apply PPP-B2b signals into positioning. Afterwards, the performance of BDS-3 PPP service is validated with both static and kinematic experiments carried out in Wuhan, China, during day of year 168 and 172, 2022. Results indicate that PPP-B2b signals mainly improve BDS-3 clock precision and GPS orbit accuracy. With BDS-3 PPP-B2b augmentation messages, the static satellite-based PPP shows 3.9/6.9/10.3 mm daily solution repeatability in E/N/U directions, respectively. An average of 13.9 min convergence time and 3.42/2.16/6.65 cm E/N/U positioning accuracy are achieved in the simulated kinematic mode. During a 28-min stepper motor driven movement test, 3.48/14.88 cm 2D/3D kinematic positioning accuracy is obtained using the BDS-3 PPP service.

Stochastic modeling of the receiver clock parameter in Galileo-only and multi-GNSS PPP solutions

In Precise Point Positioning (PPP), the receiver clock parameter is typically estimated independently in each observation epoch, which increases the noise of the estimated station coordinates and troposphere parameters due to correlations. Applying stochastic modeling to the receiver clock parameter stabilizes PPP solutions and reduces clock noise for the time transfer. However, the receiver clock modeling is possible only for the GNSS receivers connected to the utmost stable atomic clocks. We propose receiver clock modeling that involves the Markov stochastic process in the form of a random walk. We test different levels of random walk constraints for GNSS stations equipped with different types of clocks for Galileo-only and multi-GNSS solutions in kinematic and static PPP. In multi-GNSS solutions, the common clock parameter is derived with inter-system biases (ISBs). This raises the question of the constraints that should be imposed on the common clock only or also on the ISBs. We found that similar results can be achieved by imposing constraints on the common clock parameter and estimating ISB as a constant parameter and when constraining the common clock parameter and ISBs with a ratio of 1:100. Other ratios of clock-to-ISB constraints, such as 1:1 and 1:10, give inferior results. In the kinematic PPP, stochastic clock modeling has a marginal impact on the North and East coordinate components, whereas the Up component is substantially improved for GNSS receivers equipped with hydrogen masers. In the static PPP, the clock modeling improves the time transfer, due to the reduced noise of the clocks.

Performance evaluation of BDS-3 new B1C/B2a and legacy B1I/B3I signals: Observational quality, POD and PPP

In addition to the BeiDou regional navigation satellite system (BDS-2) backward compatible B1I and B3I signals, the BeiDou global navigation satellite system (BDS-3) also broadcast the B1C and B2a signals for compatibility with other Global Navigation Satellite System (GNSS), and providing satellite-based augmentation service for the International Civil Aviation Organization. Considering that the majority of the existing researches on the BDS-3 precise orbit determination (POD) and precise point positioning (PPP) are based on the B1I/B3I signals, the special attention that systematically comparing the data quality, POD accuracy and PPP performance through B1I/B3I and B1C/B2a signals is aroused in this paper. Signal characteristics of different receivers and antennas for the aforesaid four various signals were analyzed in terms of the carrier-to-noise density ratio (C/N0), pseudorange multipath and observation noise. The B1C signal exhibits the minimum C/N0 values, and the B3I and B2a signals have the smaller pseudorange multipath errors. The smallest pseudorange noise can be observed form the B2a signal, while the root mean squares (RMSs) for carrier phase noise show tiny differences among the four signals. The BDS-3 POD results indicate that the orbit overlapping arc error in three-dimensional (3D) direction is 0.069 and 0.076 m for the B1C/B2a and B1I/B3I, and the standard deviation of the satellite laser ranging validation is 0.041 m for both the two schemes. The clock offset products were evaluated with respect to the precise clock products from Deutsches GeoForschungsZentrum (GFZ), and the standard deviations (STDs) are 0.166 and 0.176 ns for the B1C/B2a and B1I/B3I. Finally, there is no apparent difference in the RMSs for B1C/B2a and B1I/B3I static PPP, while the convergence time that shortened by 31.4 % can be achieved for B1C/B2a. For kinematic PPP, the 3D RMS is 0.043 m and the convergence time is 31.1 min for the B1C/B2a, which is reduced by 14.0 % and 35.2 %, respectively, compared to B1I/B3I.

Tropospheric Delay Parameter Estimation Strategy in BDS Precise Point Positioning

Tropospheric delay (TD) parameter estimation is a critical issue underlying high-precision data processing for global navigation satellite systems (GNSSs). The most widely used TD parameter estimation methods are the random walk (RW) and piece-wise constant (PWC). The RW method can effectively track rapid variations of tropospheric delay, but it may introduce excessive noise. In contrast, the PWC method introduces less noise, but it is less adaptable to cases of large variations of tropospheric delay. To address the problem of how to choose the optimal TD parameter estimation method, this paper investigates the variation patterns of international GNSS service zenith tropospheric delay (IGS ZTD) products and proposes a combined strategy model for TD parameter estimation. Firstly, this paper avoids the day-boundary jumps problem of IGS ZTD products by grouping based on single-day data. Secondly, this paper introduces discrete point areas (DPAs) to measure the magnitude of the ZTD values and uses comprehensive indicators to reflect the variation of ZTD. Next, based on the Köppen-Geiger climate classification, this study selected five different climate classifications with a total of 20 IGS stations as experimental data. The data assessed span from day of year (DOY) 001 to DOY 365 in 2022. This paper then applied 26 different parameter estimation strategies for static precise point positioning (PPP) data processing, and the parameter estimation strategies that were used include the RW and PWC (with the piece-wise constant ranging from twenty minutes to five hundred minutes at twenty-minute intervals). Finally, ZTD and positioning results were obtained using various parameter estimation methods, and a combined strategy model was established. We selected five different climate classifications of IGS stations as validation data and designed three sets of comparative experiments: RW, PWC120, and the combined strategy model, to verify the effectiveness of the combined strategy model. The experimental results revealed that: RW and the combined strategy model have a comparable ZTD accuracy and both are superior to PWC120. The combined strategy model improves the positioning accuracy in the U direction compared to RW and PWC120. In arid (B) and polar (E) regions with a small variation of TD, the PWC120 strategy displayed a better positioning accuracy than the RW strategy; in equatorial (A) and warm-temperate (C) regions, where there are large variations of TD, the RW strategy exhibited a better positioning accuracy than the PWC120 strategy. The combined strategy model can flexibly select the optimal parameter estimation method according to the comprehensive indicator while ensuring ZTD estimation accuracy; it enhances positioning accuracy.

BDS/GPS/Galileo Precise Point Positioning Performance Analysis of Android Smartphones Based on Real-Time Stream Data

Smartphones with the Android operating system can acquire Global Navigation Satellite System (GNSS) raw pseudorange and carrier phase observations, which can provide a new way for the general public to obtain precise position information. However, only postprocessing precise orbit and clock offset products in some older smart devices are applied in current studies. The performances of precise point positioning (PPP) with the smartphone using real-time products and newly smartphones are still unrevealed, which is more valuable for real-time applications. This study investigates the observation data quality and multi-GNSS real-time PPP performance using recent smartphones. Firstly, the observed carrier-to-noise density ratio (C/N0), number of satellites and position dilution of precision (PDOP) of GNSS observations are evaluated. The results demonstrate that the C/N0 received by Huawei Mate40 is better than that of the Huawei P40 for GPS, BDS, QZSS and Galileo systems, while the GLONASS is poorer, and the PDOP of the Huawei P40 is slightly better than that of Mate40. Additionally, a comprehensive analysis of real-time precise orbit and clock offset products performance is conducted. The experiment result expresses that the orbit and clock offset performance of GPS and Galileo is better than that of BDS-3 and GLONASS, and BDS-2 is the worst. Finally, single- and dual-frequency multi-GNSS combined PPP experiments using observations received from smartphones and real-time products are conducted; the results indicate that the real-time static PPP using a smartphone can achieve decimeter-level positioning accuracy, and kinematic PPP can achieve meter-level positioning accuracy after convergence.

Evaluation and Analysis of the Accuracy of Open-Source Software and Online Services for PPP Processing in Static Mode

It has been proven that precise point positioning (PPP) is a well-established technique to obtain high-precision positioning in the order between centimeters and millimeters. In this context, different studies have been carried out to evaluate the performance of PPP in static mode as a possible alternative to the relative method. However, only a few studies have evaluated the performance of a large number of different open-source software programs and have focused extensively on online free PPP services. Therefore, in this paper, a comprehensive comparison of processing in static mode between different open-source software and the online free PPP services is developed. For the evaluation, different GNSS observation files collected at 45 International GNSS Service (IGS) stations distributed worldwide were processed in static PPP mode. Within this frame of reference, ten open-source PPP software and five online free PPP services were studied. The results from the processing strategy demonstrate that it is possible to obtain precision in the order of millimeters with both open-source software and online PPP services. In addition, online PPP services experienced better performance than some other specialized PPP software. In summary, the results show that the daily solutions for the E (East), N (North), and U (Up) components estimated by the ten open-source software and by the five online free PPP services can reach millimeter precision for some stations. Among the open-source software, the PRIDE-PPPAR presented the best performance with a Root Mean Square Error (RMSE) of 5.52, 5.40, and 6.79 mm in the E, N, and U components, respectively. Alternatively, in the case of the online free PPP services, the APPS and CSRS-PPP produced the most accurate results, with RMSE values less than 12 mm for the three components. Finally, the open-source software and online free PPP services experienced similar positioning performance in the horizontal and vertical components, demonstrating that both can be implemented in static mode without compromising the accuracy of the measurement.

Performance investigation of GLONASS in the static PPP technique with independent short measurement times using online processing services

The precise point positioning (PPP) technique, which is still being developed, provides position accuracy at the centimetre (cm) level and is widely employed in scientific research. In the PPP technique, cm-level accuracy can be achieved by evaluating raw data obtained from a single Global Navigation Satellite Systems (GNSS) receiver using precise satellite orbit and clock correction data and other parameters. The majority of studies in the literature are based on 24-hour data obtained from the International GNSS Service (IGS) and similar stations. However, there are fewer articles in which analyzes based on short-term measurements are taken. In this study; the effect of GLONASS on the static PPP technique was investigated with independent short measurement times. For this purpose, measurements were made at 7 different test points on consecutive days using a single GNSS receiver. A 4-hour static measurement was made at each test point. The data obtained were processed in two different scenarios, only GPS and GPS + GLONASS using the Canadian Spatial Reference System – PPP (CSRS-PPP) and Trimble RTX online process software. The processes were completed at 4, 2, 1, and 0.5 h. As a result of the analysis, it has been observed that GLONASS improves the results by 76%, but negatively affects some solutions (24%). It was also observed that GLONASS drastically reduced the outlier values. With this study, it is aimed to show the accuracy that users who make short-term measurements with a single GNSS receiver can be achieved in the static PPP technique by using GPS + GLONASS systems, with repeated measurements.

Multi-Frequency BDS-3 Real-Time Positioning Performance Assessment Using New PPP-B2b Augmentation Service

A new precise point positioning (PPP)-B2b augmentation service broadcast by the BeiDou Navigation Satellite System (BDS-3) geosynchronous Earth orbit (GEO) satellite can provide real-time and high-precision orbit and clock offset corrections for global navigation satellite system (GNSS) users in China and its surrounding areas. It has great significance and research value for real-time and high-precision positioning applications. First, orbit, clock offset, and differential code bias (DCB) of PPP-B2b products are evaluated. Second, the influence of PPP-B2b service on the enhanced positioning of single-frequency (SF), dual-frequency (DF), and Multi-Frequency (MF) real-time PPP using 30 days of BDS-3 observations is verified. The result shows that the standard deviation (STD) of clock offset and the root mean square (rms) of orbit in the 3-D direction for medium Earth orbit (MEO) satellites are 0.118 ns and 0.286 m, respectively, which is 75.9% and 18.3% higher than that of broadcast ephemeris. The statistical results show that the median positioning accuracy of static SF PPP, DF PPP, and MF PPP is better than 0.20/0.09/0.08 m, and the convergence time is better than 51/10/8 min. The median positioning accuracy of kinematic SF PPP, DF PPP, and MF PPP is better than 0.40/0.12/0.12 m, and the convergence time is better than 145/16/12 min. Using the PPP-B2b products, the positioning accuracy of DF PPP and MF PPP is comparable and close to that of DF PPP using the precise products, while the convergence time of MF PPP is improved by 24.8% and 27.7% over DF PPP in static and kinematic solutions, respectively.

MADOCA: Japanese precise orbit and clock determination tool for GNSS

The Japan Aerospace Exploration Agency (JAXA) has developed Multi-GNSS Advanced Demonstration tool for Orbit and Clock Analysis (MADOCA). This tool estimates orbits and clock offsets of multiple GNSS systems (Multi-GNSS), namely GPS, GLONASS, QZSS, Galileo, and BeiDou. The orbit and clock offsets are estimated in both post-processing with iterative weighted least squares and real-time processing with extended Kalman filter (EKF) using observation data collected from the International GNSS Service (IGS) network and our monitoring station network (MGM-net). Since we began the development in 2011, we have improved the MADOCA’s performance by adopting the precise force and measurement models, the original empirical solar radiation pressure (SRP) model, and processing algorithms for stability and reduction of processing time. In the latest annual evaluation of MADOCA products in 2021, the orbit comparison with the IGS final product for the GPS and GLONASS were 2.8 and 8.0 cm (median value of daily 3D-root mean square (RMS)), respectively, and the results of satellite laser ranging (SLR) residual evaluation for the BeiDou and Galileo were 14.6 and 4.9 cm (RMS), respectively, a performance comparable to the products of the IGS Analysis Centers (ACs). QZSS products, in particular, have achieved the world’s highest level of accuracy as 6.4, 10.1, 9.0, and 10.5 cm (RMS) for the QZS-1, -2, -3, and -4 respectively in the SLR residual evaluation. This was achieved by improving and fine-tuning for the original empirical SRP models. Consequently, the position difference in those products’ static precise point positioning (PPP) reached 1.2 cm (3D-RMS). JAXA has made post-processing and real-time MADOCA products publicly available to users and is promoting experiments using MADOCA products in Japan and abroad.

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.

Multipath mitigation for improving GPS narrow-lane uncalibrated phase delay estimation and speeding up PPP ambiguity resolution

Precise point positioning (PPP) has been recognized as a powerful tool for various geophysical applications. However, the long convergence time required to resolve a reliable ambiguity impedes its further application in time-critical scenarios. Although PPP ambiguity resolution (AR) can shorten the convergence time, its performance is subject to the quality of float ambiguity estimates and the uncalibrated phase delay (UPD), which can be contaminated by multipath errors. Furthermore, the observation residuals derived from PPP are very likely to be affected by the common-mode error (CME), thereby deteriorating the multipath modeling accuracy. The principal component analysis (PCA) is employed to mitigate the CME effect, and the multipath is modeled using a multipath hemispherical map (MHM). Consequently, the narrow-lane (NL) UPDs with multipath correction have better temporal stability and residual distributions than those without correction. Compared with sidereal filtering (SF), the MHM0.5 has comparable residual variance reduction percentages, indicating its capability of capturing high-frequency multipath. For static PPP AR, the averaged time to first fix (TTFF) can be reduced by 24.2% to about 26 min and the convergence time can be achieved within 16.2 min after multipath correction. The pseudorange multipath correction significantly contributes to shortening the TTFF and convergence time. Reducing the resolution of MHM increases the risk of extending the TTFF. For kinematic PPP AR with MHM0.5, the convergence time exhibits a remarkable improvement when compared with that of the uncorrected case (21.7 min versus 40.2 min), and 20% of the stations achieve convergence within 10 min. Meanwhile, a few stations only take one minute to achieve convergence. The contribution of the multipath correction to the fixing rate is comparatively small. After applying MHM0.5, the kinematic positioning accuracies are improved by 35.7%, 12.6%, and 24.4% to 1.26, 1.39, and 2.73 cm for the east, north, and up components, respectively.