Improving Short Term Clock Prediction for BDS-2 Real-Time Precise Point Positioning.

The currently available triple-frequency signals give rise to new prospects for precise point positioning (PPP). However, they also bring new bias, such as time-varying parts of the phase bias in the hardware of receivers and satellites due to the fact that dual-frequency precise clock products cannot be directly applied to triple-frequency observation. These parameters generate phase-based inter-frequency clock bias (PIFCB), which impacts the PPP. However, the PIFCBs of satellites are not present in all GNSSs. In this paper, various IF1213 PPP models are constructed for these parts, namely, the triple-frequency PIFCB (TF-C) model with PIFCB estimation, the TF inter-frequency bias (IFB) (TF-F) model ignoring the PIFCB, and the TF-PIFCB-IFB (TF-CF) model with one system PIFCB estimation. Additionally, this study compares these IF1213 PPP models with the dual-frequency ionosphere-free (DF) model. We conducted single system static PPP, dual-system static and kinematic PPP experiments based on BDS/GPS observation data. The GPS static PPP experiment demonstrates the reliability of the TF-C model, as well as the non-negligibility of the GPS PIFCB. The BDS static PPP experiment demonstrates the reliability of the TF-F and TF-CF models, and that the influence of the BDS-2 PIFCB can be neglected in BDS. The BDS/GPS PPP experimental results show that the third frequency does not significantly improve the positioning accuracy but shortens the convergence time. The positioning accuracy of TF-C and TF-CF for static PPP is better than 1.0 cm, while that for kinematic PPP is better than 2.0 cm and 4.0 cm in the horizontal and vertical components, respectively. Compared with the DF model, the convergence time of the TF-C and TF-CF models for static PPP is improved by approximately 23.5%/18.1%, 13.6%/9.7%, and 19.8%/12.1%, while that for kinematic PPP is improved by approximately 46.2%/49.6%, 33.5%/32.4%, and 35.1%/36.1% in the E, N and U directions, respectively. For dual-system PPP based on BDS/GPS observations, the TF-C model is recommended.

BeiDou navigation satellite system(BDS)has opened service in most of the Asia-Pacific region,it offers the possibility to break the technological monopoly of GPS in the field of high-precision applications,so its performance of precise point positioning(PPP)has been a great concern.Firstly,the constellation of BeiDou regional navigation system and BDS/GPS tracking network is introduced.Secondly,the precise ephemeris and clock offset accuracy of BeiDou satellite based on domestic tracking network is analyzed.Finally,the static and kinematic PPP accuracy is studied,and compared with the GPS.The actual measured numerical example shows that the static and kinematic PPP based on BDS can achieve centimeter-level and decimeter-level respectively,reaching the current level of GPS precise point positioning.

The BeiDou Navigation Satellite System (BDS) offers orbit and clock corrections through the B2b signal, enabling Precise Point Positioning (PPP) without relying on ground communication networks. This capability supports applications such as aerial and maritime mapping. However, achieving high precision during the convergence period remains challenging, particularly for missions with short observation durations. To address this, we analyze the performance of PPP over short periods using PPP-B2b products and propose using the backward smoothing method to enhance the accuracy during the convergence period. Evaluation of the accuracy of PPP-B2b products shows that the orbit and clock accuracy of the BDS surpass those of GPS. Specifically, the BDS achieves orbit accuracies of 0.059 m, 0.178 m, and 0.186 m in the radial, along-track, and cross-track components, respectively, with a clock accuracy within 0.13 ns. The hourly static PPP achieves 0.5 m and 0.1 m accuracies with convergence times of 4.5 and 25 min at a 50% proportion, respectively. Nonetheless, 7.07% to 23.79% of sessions fail to converge to 0.1 m due to the limited availability of GPS and BDS corrections at certain stations. Simulated kinematic PPP requires an additional 1–4 min to reach the same accuracy as the static PPP. Using the backward smoothing method significantly enhances accuracy, achieving 0.024 m, 0.046 m, and 0.053 m in the north, east, and up directions, respectively. For vehicle-based positioning, forward PPP can achieve a horizontal accuracy better than 0.5 m within 4 min; however, during the convergence period, positioning errors may exceed 1.5 m and 3.0 m in the east and up direction. By applying the smoothing method, horizontal accuracy can reach better than 0.2 m, while the vertical accuracy can improve to better than 0.3 m.

In addition to GPS and GLONASS constellation, the number of (Global Navigation Satellite System) GNSS satellites are increasing, it is now possible to evaluate and analyze the position accuracy with multi GNSS constellation. In this paper, statistical assessment of static Precise Point Positioning (PPP) using GPS, GLONASS, dual system GPS/GLONASS, three system GPS/GLONASS/Galileo, GPS/GLONASS/BeiDou and multi system GPS/GLONASS/Galileo/BeiDou PPP combinations is evaluated. Observation data of seven whole days from seven IGS multi GNSS experiment (MGEX) stations is used for analysis. Position accuracy and convergence time is analyzed. Results show that the GPS/GLONASS positioning accuracy increases over GPS PPP. Standard deviations (STDs) of position errors for GPS PPP are 4.63, 3.00 and 6.96 cm in east, north and up components while STDs for GPS/GLONASS PPP are 4.10, 3.42 and 6.50 cm respectively. Root mean square for three dimension (RMS3D) for GPS/GLONASS PPP solution is 8.96 cm. With the addition of Galileo and BeiDou to the combined GPS/GLONASS further enhances the positioning accuracy. Root mean square for horizontal component reach to 5.35 cm of GPS/GLONASS/Galileo/BeiDou PPP solutions. Results analysis of GPS/GLONASS/Galileo PPP solutions show an improvement of convergence time by only 3.81% to achieve accuracy level of 3.0 cm over GPS/GLONASS/BeiDou PPP mode. Results also demonstrate that position accuracy improvement after adding BeiDou observations to the GPS/GLONASS PPP mode is not significant.

Evaluation of BDS-2 real-time orbit and clock corrections from four IGS analysis centers

This study examines the performance of dual-frequency static Precise Point Positioning (PPP) as a function of observation time using three of the most used free online services, namely: the Canadian Spatial Reference System Precise Point Positioning (CSRS-PPP), PPP-WIZARD, and the Automatic Precise Positioning Service (APPS). The comparison has been conducted under open-sky desert conditions, where multipath effects are negligible, and under two processing scenarios: GPS-only and GPS+GLONASS in case of CSRS-PPP & PPP-WIZARD, and GPS-alone in case of APPS. Dual-frequency GNSS data has been collected from ten spatially well-distributed stations across Libya, each observed continuously for 24 hours. Static PPP solutions have been generated for fixing intervals beginning at 1 hour and incrementally increasing to 24 hours. The coordinates of these reference points, provided and approved by Libyan Survey Authority, have been used as the reference for evaluating the accuracy and stability of all time-based solutions. In terms of comparing GPS + GLONASS with GPS-alone, the results of PPP-CSRS & PPP-WIZARD services show that even under optimal open-sky conditions, where multipath is virtually absent and the number of satellite is adequate, utilizing GLONASS observations alongside GPS leads to notable improvements in solution reliability, robustness and overall positioning stability throughout the fixing intervals. These benefits are particularly clear during the first several hours, when PPP solutions are most sensitive to satellite geometry and convergence behavior. This can be shown significantly in the first hour, where the absolute errors in Easting (E), Northing (N), Height (H), 2 Dimensions (2D), and 3 Dimensions (3D) are reduced with GPS+GLONASS by (0.2, 2.2, 3, 1.8 and 2.22 cm) & (6, 6.5, 11, 9, and 13 cm) for PPP-CSRS & PPP-WIZARD, respectively. In addition, although the enhancement in mean absolute positional accuracy becomes marginal for longer observation periods, the multi-constellation configuration significantly reduces the occurrence of outliers and decreases the dispersion of coordinate residuals across all components and the 3D quality obtained via one-hour static dual-frequency PPP with GPS+GLONASS can be reached after 3 to 4 hours fixing time using GPS-alone. As for comparing the performance of the three free online services together, CSRS-PPP ranks first and second, as it has provided the most accurate results and the fastest convergency time, with 3D absolute error of nearly 2 cm & 5 cm for GPS+GLONASS and GPS-alone solutions, respectively after only one hour fixing time. The quality of these two solutions increases with time, reaching the level of less than 1 cm after 6 and 10 hours using multi constellations and GPS-alone, respectively. PPP-WIZARD comes third and fourth, with comparable 3D quality of 7 cm for GPS+GLONASS and acceptable 3D quality of 20 cm for GPS-alone after one hour fixing time. The results show that the quality of the two PPP-WIZARD solutions may not be able to reach the level of 1 cm even after 24 hours observation period. The APPS GPS-alone solution comes last in term of the 3D quality of the first fixing hour with accuracy of 45 cm, but the performance improves quickly comparing to PPP-WIZARD GPS-alone solution and almost matches that of PPP-WIZARD GPS+GLONASS for long period before reaching the level of 1 cm after nearly 20 hours of fixing time. Overall, the findings confirm that multi-constellation GNSS integration is a critical factor in enhancing static PPP performance, particularly for applications requiring high accuracy over short observation periods. Among the investigated services, CSRS-PPP is identified as the most reliable and efficient solution, while PPP-WIZARD and APPS remain viable alternatives for longer observation durations.

The BeiDou navigation satellite system (BDS) currently has 41 satellites in orbits and will reach its full constellation following the launch of the last BDS satellite in June 2020 to provide navigation, positioning, and timing (PNT) services for global users. In this contribution, we investigate the characteristics of inter-system bias (ISB) between BDS-2 and BDS-3 and verify whether an additional ISB parameter should be introduced for the BDS-2 and BDS-3 precise point positioning (PPP). The results reveal that because of different clock references applied for BDS-2 and BDS-3 in the International GNSS Service (IGS) precise satellites clock products and the inconsistent code hardware delays of BDS-2 and BDS-3 for some receiver types, an ISB parameter needs to be introduced for BDS-2 and BDS-3 PPP. Further, the results show that the ISB can be regarded as a constant within a day, the value of which is closely related to the receiver type. The ISB values of the stations with the same receiver type are similar to each other, but a great difference may be presented for different receiver types, up to several meters. In addition, the impact of ISB on PPP has also been studied, which demonstrates that the performance of kinematic PPP could be improved when ISB is introduced.

Because of the special design of BeiDou navigation satellite system (BDS) constellation, the effects of ionospheric scintillation on operational BDS generally are more serious than on the global positioning system (GPS). As BDS is currently providing global services, it is increasingly important to seek strategies to mitigate the scintillation effects on BDS navigation and positioning services. In this study, an improved cycle-slip threshold model is proposed to decrease the high false-alarm rate of cycle-slips under scintillation conditions, thus avoiding the frequent unnecessary ambiguity resets in BDS precise point positioning (PPP) solution. We use one-year (from 23 March 2015 to 23 March 2016) BDS dataset from Hong Kong Sha Tin (HKST) station (22.4°N, 114.2°E; geomagnetic latitude: 15.4°N) to model the cycle-slip threshold and try to make it suitable for three types of BDS satellites and multiple scintillation levels. The availability of our mitigation strategy is validated by using three months (from 1 September 2015 to 30 November 2015) BDS dataset collected at 10 global navigation satellite system (GNSS) stations in Hong Kong. Positioning results demonstrate that our mitigated BDS PPP can prevent the sudden fluctuations of positioning errors induced by the ionospheric scintillation. Statistical results of BDS PPP experiments show that the mitigated solution can maintain an accuracy of about 0.08 m and 0.10 m in the horizontal and vertical components, respectively. Compared with standard BDS PPP, the accuracy of mitigated PPP can be improved by approximately 24.1%, 38.2%, and 47.9% in the east, north, and up directions, respectively. Our study demonstrates that considering different scintillation levels to establish appropriate cycle-slip threshold model in PPP processing can efficiently mitigate the ionospheric scintillation effects on BDS PPP.

The contribution of Multi-GNSS Experiment (MGEX) to precise point positioning

In recent years, many national timing laboratories (NMIs) have installed geodetic global positioning system (GPS) receivers together with their traditional GPS/GLONASS Common View (CV) receivers and two way satellite time and frequency transfer (TWSTFT) equipment. Many of these geodetic receivers operate continuously within the international GNSS service (IGS), and their data are regularly processed by IGS Analysis Centers. From its global network of over 350 stations and its Analysis Centers, the IGS generates precise combined GPS precise ephemeredes and station and satellite clock time series referred to the IGS Time Scale. A processing method called precise point positioning (PPP) is in use in the geodetic community allowing precise recovery of GPS antenna position, clock phase and tropospheric delays by taking advantage of the IGS precise products. Natural resources Canada (NRCan) has developed software implementing the PPP methodology. A previous assessment of PPP, as a promising time transfer method, was carried out at INRiM (formerly IEN) in 2003 [7], showing better stability over short/medium term than GPS CV and GPS P3 methods. Further analysis was carried out in 2005 [12] where, running continuously for period of up of two weeks, the NRCan PPP software was able to reduce the day-boundary discontinuities, allowing specific time-limited campaigns (PTFs). This paper reports on follow-on work performed at INRiM and NRCan to further characterize the PPP method for time transfer applications, involving some of the National Metrology Institutes considered in 2005. We take advantage of continuous PPP processing to develop a procedure to improve the continuity of solutions and to reduce the solution boundary discontinuities present in the daily PPP results.

In GPS Precise Point Positioning (PPP), besides precise positioning, the convergence time and stability are important items in GPS kinematic PPP. There are many factors which may affect it, such as the quality of GPS observation, sampling intervals, parameters estimation model, satellite geometry distribution and accuracy requirement and so on. The effect of different sampling intervals of observations, Satellites Clock Bias (SCB), and different positioning precision on convergence time of kinematic PPP is discussed deeply in this paper. Taking GPS observations from twelve GPS reference stations in Shanghai GPS network as an example, we analyzed the relationship of sampling intervals, positioning precision and convergence time. The convergence time of different sampling intervals is analyzed statistically. The results of the analysis are given in the conclusions.

In recent decades, Precise Point Positioning (PPP) has become a well-established GNSS positioning method that is used in various applications. PPP is characterized by the use of precise satellite products (satellite orbits, clocks, and biases) combined with the accurate modeling of various error sources and elaborate algorithms. This way, PPP allows us to achieve position accuracies at the centimeter or even millimeter level. Nowadays, several institutions provide high-quality multi-GNSS satellite products through the International GNSS Service (IGS). These modern satellite products enable, for example, integer ambiguity fixing and incorporating observations from multiple GNSS in the PPP solution, typically enhancing the PPP performance.In this contribution, we provide an overview of the currently available multi-GNSS satellite products and discuss their potential benefits of using 2+ frequencies and alternatives to the ionosphere-free linear combination. These methods are considered advantageous for improving PPP performance, particularly regarding convergence time. We present PPP results using GPS, GLONASS, Galileo, and BeiDou observations and satellite products from different institutions, focusing on integer ambiguity resolution (PPP-AR). Additionally, we test the combined multi-GNSS product developed by the GNSS Research Center at Wuhan University as part of the IGS PPP-AR Pilot Project. We evaluate the resulting coordinate accuracy, convergence behavior, and ambiguity fixing rates. The PPP investigations are conducted with the open-source raPPPid, part of the Vienna VLBI and Satellite Software (VieVS PPP). 

With the full operation of the global BeiDou navigation satellite system (BDS-3), positioning performance can be further enhanced by BDS-3 combined with the regional BeiDou navigation satellite system (BDS-2). However, due to satellite signals being out of lock and the limited visibility of satellites, the traditional multi-frequency BDS-2/3 precise point positioning (PPP) model is unable to maintain great positioning performance under urban environmental conditions. In this study, a mixed multi-frequency undifferenced and uncombined (UDUC) BDS-2/3 PPP model is presented to improve the positioning performance under urban environmental conditions by making full use of B1I, B1C, B2I, B2a, and B3I signals from all visible BDS satellites. In this model, BDS satellites with single-, dual-, triple- and quad-frequency observations all can participate in PPP. The static and kinematic experiments were carried out using the mixed multi-frequency UDUC BDS-2/3 PPP model to fully assess the positioning performance under urban environmental conditions with comparisons to the multi-frequency model. The static experiments indicated that the mixed multi-frequency UDUC BDS-2/3 PPP could continuously achieve decimeter-level positioning accuracy at a cut-off elevation angle of 40°, but part of the BDS-3 PPP would lose resolution due to limited visible satellites. Furthermore, the initial kinematic vehicle experiment showed that mixed multi-frequency UDUC BDS-2/3 PPP had better satellite geometry and more observation redundancy than the traditional multi-frequency model. Compared with the traditional multi-frequency BDS-2/3 model, the positioning accuracy of the mixed multi-frequency model was improved by 51.6, 35.5, and 39.1%, respectively, in east, north, and up directions. The convergence time was shortened by 40%.

Precise Point Positioning (PPP) is a popular technology for precise applications based on the Global Navigation Satellite System (GNSS). Multi-GNSS combined PPP has become a hot topic in recent years with the development of multiple GNSSs. Meanwhile, with the operation of the real-time service (RTS) of the International GNSS Service (IGS) agency that provides satellite orbit and clock corrections to broadcast ephemeris, it is possible to obtain the real-time precise products of satellite orbits and clocks and to conduct real-time PPP. In this contribution, the real-time multi-GNSS orbit and clock corrections of the CLK93 product are applied for real-time multi-GNSS PPP processing, and its orbit and clock qualities are investigated, first with a seven-day experiment by comparing them with the final multi-GNSS precise product ‘GBM’ from GFZ. Then, an experiment involving real-time PPP processing for three stations in the Multi-GNSS Experiment (MGEX) network with a testing period of two weeks is conducted in order to evaluate the convergence performance of real-time PPP in a simulated kinematic mode. The experimental result shows that real-time PPP can achieve a convergence performance of less than 15 min for an accuracy level of 20 cm. Finally, the real-time data streams from 12 globally distributed IGS/MGEX stations for one month are used to assess and validate the positioning accuracy of real-time multi-GNSS PPP. The results show that the simulated kinematic positioning accuracy achieved by real-time PPP on different stations is about 3.0 to 4.0 cm for the horizontal direction and 5.0 to 7.0 cm for the three-dimensional (3D) direction.

With the development of precise point positioning (PPP), the School of Geodesy and Geomatics (SGG) at Wuhan University is now routinely producing GPS satellite fractional cycle bias (FCB) products with open access for worldwide PPP users to conduct ambiguity-fixed PPP solution. We provide a brief theoretical background of PPP and present the strategies and models to compute the FCB products. The practical realization of the two-step (wide-lane and narrow-lane) FCB estimation scheme is described in detail. With GPS measurements taken in various situations, i.e., static, dynamic, and on low earth orbit (LEO) satellites, the quality of FCB estimation and the effectiveness of PPP ambiguity resolution (AR) are evaluated. The comparison with CNES FCBs indicated that our FCBs had a good consistency with the CNES ones. For wide-lane FCB, almost all the differences of the two products were within ±0.05 cycles. For narrow-lane FCB, 87.8 % of the differences were located between ±0.05 cycles, and 97.4 % of them were located between ±0.075 cycles. The experimental results showed that, compared with conventional ambiguity-float PPP, the averaged position RMS of static PPP can be improved from (3.6, 1.4, 3.6) to (2.0, 1.0, 2.7) centimeters for ambiguity-fixed PPP. The average accuracy improvement in the east, north, and up components reached 44.4, 28.6, and 25.0 %, respectively. A kinematic, ambiguity-fixed PPP test with observation of 80 min achieved a position accuracy of better than 5 cm at the one-sigma level in all three coordinate components. Compared with the results of ambiguity-float, kinematic PPP, the positioning biases of ambiguity-fixed PPP were improved by about 78.2, 20.8, and 65.1 % in east, north, and up. The RMS of LEO PPP test was improved by about 23.0, 37.0, and 43.0 % for GRACE-A and GRACE-B in radial, tangential, and normal directions when AR was applied to the same data set. These results demonstrated that the SGG FCB products can be produced with high quality for users anywhere around the world to carry out ambiguity-fixed PPP solutions.