PPP Performance with Large TEC Gradient and Mitigation Methods

Real-time capability , positioning accuracy and convergence time ar e the keys to the performance of Precise Point Positioning (PPP). In recent years, the development of IGS Real-Time Services (RTS) has improved the performance of real-time PPP to a large extent. Meanwhile, the PPP ambiguity resolution technique, which significantly improves the positioning accuracy and convergence time, has become mature gradually. If the advantages of both techniques can be combined to realize real-time PPP with ambiguity resolution, the application of PPP would be greatly expanded. In this paper, a real-time satellite-satellite single-difference fractional cycle bias (FCB) estimation method based on RTS products is proposed. To meet the demand of real-time PPP, narrow-lane FCBs are forecasted by short-term linear extrapolation. Taking accuracy levels and data amount into consideration, the forecasting interval for real-time wide-lane and narrow-lane FCBs are determined. Finally, the performance of real-time PPP with ambiguity resolution using real-time FCBs is evaluated in both static and kinematic modes. The results show that wide-lane FCBs to be forecasted daily and narrow-lane FCBs to be forecasted every 5 min can satisfy the need of real-time PPP with ambiguity resolution. In static mode, the average time to first fix (TTFF) is 15.97 min, and the average precision of the north, east and up components for hourly solution are 1.51, 1.64 and 2.18 cm respectively. As for kinematic mode, an average TTFF of 24.36 min is needed, and the 3D position error in fixed solution is decreased by 42.59% compared with float solution.

The impacts of ionospheric irregularities on precise point positioning (PPP) have been commonly noticed in the field of the ionosphere and the precise application of the Global Navigation Satellite System. But few attentions have been paid to how ionospheric irregularities deteriorate the performance of PPP. Aiming at exploring the mechanism of degradation of PPP solutions during the period of ionospheric irregularities, this paper investigates the impacts of ionospheric irregularities on the performance of kinematic PPP. The experiment uses GPS observation data sampled at the 30‐s interval over China on the days of 2014, 2015, and 2017 covering some active space weather, for example, solar and geomagnetic activities. The results show that the ionospheric irregularities caused increased positioning errors (decimeter‐ to meter‐level), enlarged phase residuals (decimeter‐level), and increased the number of detected cycle slips in PPP processing in low latitude regions of China. By proposing a novel strategy that compares the number of detected cycle slips from 30 s‐sampling interval data and 1s‐sampling interval data at the same station in an “aligned” mode, we present direct evidence of the existence of the falsely detected cycle slips in 30 s‐sampling interval data by the traditional cycle‐slip detection threshold in PPP processing. We reveal that the unnecessary and frequent reinitialization of ambiguity induced by the falsely detected cycle slips is dominantly responsible for the degradation of kinematic PPP solutions during the period of ionospheric irregularities. Our findings pointed out the direction for the improvement of kinematic PPP performance in the environment of ionospheric irregularities.

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). 

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.

A new PPP algorithm based on uncombined dual-frequency GPS code and phase observables is presented. The algorithms different from traditional ones in which the ionosphere-free code and phase observables are formed. The Line Of Sight (LOS) ionospheric delays are taken as estimate parameters by introducing the constraints of between-epoch temporal behaviour of ionosphere. This alternative approach has the advantage of avoiding adverse effect of amplified multipath and measurement errors existing in the combined observations. A further study of the performance of the proposed algorithm was conducted by comparing with the traditional ones in different case studies. The results show that kinematic positioning accuracy of several centimetres to decimetres is achieved, with an improvement of 6%-30% compared to traditional PPP algorithms, especially in the upper component; the accuracy of receive clock corrections and ZTDs estimation can be better improved to ∼ 0.1ns and ∼4mm respectively, which demonstrates the feasibility and effectiveness of this new algorithm.

Compared to the traditional ionospheric-free (IF) precise point positioning (PPP) model, the undifferenced and uncombined (UU) PPP has the advantages of lower observation noise and the ability to obtain ionospheric information. Thanks to the IGS (International GNSS Service), real-time service (RTS) can provide RT vertical total electron content (VTEC) products, and an enhanced RT UU-PPP based on the RT-VTEC constraints can be achieved. The global performance of the BeiDou Navigation Satellite System-2 (BDS-2) and BDS-3 joint RT UU-PPP using different RTS products was investigated. There is not much difference in the RTS orbit accuracy of medium earth orbit (MEO) satellites among all analysis centers (ACs), and the optimal orbit accuracy is better than 5, 9, and 7 cm in the radial, along-track, and cross-track directions, respectively. The orbit accuracy of inclined geosynchronous orbit (IGSO) satellites is worse than that of MEO satellites. Except for CAS of 0.46 ns, the RTS clock accuracy of MEO satellites for other ACs achieves 0.2–0.27 ns, and the corresponding accuracy is about 0.4 ns for IGSO satellites. In static positioning, due to the limited accuracy of RT-VTEC, the convergence time of the enhanced RT UU-PPP is longer than that of RT IF-PPP for most ACs and can be better than 25 and 20 min in the horizontal and vertical components, respectively. After convergence, the 3D positioning accuracy of the static RT UU-PPP is improved by no more than 8.7%, and the optimal horizontal and vertical positioning accuracy reaches 3.5 and 7.0 cm, respectively. As for the kinematic mode with poor convergence performance, with the introduction of RT-VTEC constraints, the convergence time of RT UU-PPP can be slightly shorter and reaches about 55 and 60 min in the horizontal and vertical components, respectively. Both the horizontal and vertical positioning accuracies of the kinematic RT UU-PPP can be improved and achieve around 7.5 and 10 cm, respectively.

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

GLONASS-based precise point positioning and performance analysis

Nowadays, both BDS-3 and Galileo can provide global positioning and navigation services. This contribution carried out a comprehensive analysis and validation of positioning performance in terms of positioning accuracy (RMS) and convergence time, which are derived from BDS-3 and Galileo precise point positioning (PPP) solutions at a global scale. Meanwhile, the comparison with GPS was demonstrated. The performance and geographical distribution of RMS and convergence time for each satellite system were analyzed. GPS outperforms the other two systems on a global scale. Galileo and BDS-3, on the other hand, only perform moderately well in certain latitude zones. The combination of dual systems related to each single system is analyzed. For the dual-system combinations, the combination of systems presents a definite advantage over Galileo and BDS-3, and this advantage is more pronounced for the kinematic PPP. For GPS, the combination with Galileo and BDS-3 has little improvement in positioning performance. For the dual-system combination based on Galileo and BDS-3, the RMS and convergence time can be improved by 50% compared with the single system. The influence of single-system kinematic PPP selection for precise products from different MGEX analysis centers on positioning performance was studied. Among the five precise products, grg products have the best positioning performance for GPS, while cod products have the best positioning performance for Galileo and BDS-3. The difference in RMS and convergence time between 2 cm and 15 min can be caused by different precise product selections.

Precise Point Positioning (PPP) has been demonstrated as a simple and effective approach for user positioning. The key issue in PPP is how to shorten convergence time and improve positioning efficiency. Recent researches mainly focus on the ambiguity resolution by correcting residual phase errors at a single station. The success of this approach (referred to hereafter as NORM-PPP) is subject to how rapidly one can fix wide-lane and narrow-lane ambiguities to achieve the first ambiguity-fixed solution. The convergence time of NORM-PPP is receiver type dependent, and normally takes 15–20 min. Different from the general algorithm and theory by which the float ambiguities are estimated and the integer ambiguities are fixed, we concentrate on a differential PPP approach: the satellite- and epoch differenced (SDED) approach. In general, the SDED approach eliminates receiver clocks and ambiguity parameters and thus avoids the complicated residual phase modeling procedure. As a further development of the SDED approach, we use a regional augmentation network to derive tropospheric delay and remaining un-modeled errors at user sites. By adding these corrections and applying the Robust estimation, the weak mathematic properties due to the ED operation is much improved. Implementing this new approach, we need only two epochs of data to achieve PPP positioning converging to centimeter-positioning accuracy. Using seven days of GPS data at six CORS stations in Shanghai, we demonstrate the success rate, defined as the case when three directions converging to desired positioning accuracy of 10 cm, reaches 100% when the interval between the two epochs is longer than 15 min. Comparing the results of 15 min' interval to that of 10 min', it is observed that the position RMS improves from 2.47, 3.95, 5.78 cm to 2.21, 3.93, 4.90 cm in the North, East and Up directions, respectively. Combining the SDED coordinates at the starting point and the ED relative coordinates thereafter, we demonstrate the performance of RTK PPP with standard deviation of 0.80, 1.34, 0.97 cm in the North, East and Up directions.

The fast motion of low earth orbit (LEO) satellite contributes to the geometric diversity, allowing for rapid convergence of precise point positioning (PPP). In this contribution, we investigate the PPP performance of the LEO constellation-augmented full operational capability (FOC) multi-GNSS. We design six LEO constellations with different satellite numbers, orbit altitudes and orbit types, together with the FOC multi-GNSS constellations, and then simulate both the onboard LEO and ground-based observations. The multi-GNSS POD result shows much better orbit accuracy of 3.3, 2.7 and 2.6 cm in radial, along-track and cross-track components, respectively, compared with that of 10.3, 9.2 and 8.9 cm for GPS-only POD. Furthermore, the performance of LEO-augmented multi-GNSS PPP is evaluated. With the augmentation of 60-, 96-, 192- and 288-satellite LEO constellation, the multi-GNSS PPP convergence time can be shortened from 9.6 to 7.0, 3.2, 2.1 and 1.3 min, respectively, in midlatitude region. For LEO-augmented GPS- and BDS-only PPP, the improvement is more significant with the convergence time dramatically shortened by 90% from about 25 to within 3 min with 192- or 288-satellite constellation. The augmentation capability is also found to be associated with station latitude, and the higher latitude, the better performance. To enable about more than 70% significant reduction on convergence time, as well as considering the cost, the 192-satellite LEO constellation scheme is suggested. In terms of orbit altitude, the scheme of 1000 km presents better performance than that of 600 km. As for orbit type, the performances are comparable for polar and sun-synchronous orbits. Additionally, LEO-only PPP can be achieved with the convergence time of about 6.5 min.

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.

In recent years, the development of low-orbit satellite navigation enhancement systems has been rapid. Low-orbit navigation satellites have relatively low orbital altitudes, high signal landing power, and fast speed, which are expected to solve the problem of long convergence time for real-time precise single-point positioning of GNSS. This article evaluates and analyses the enhanced positioning performance of typical low-orbit satellite constellations. The study selected three representative low-orbit satellite constellations, combined with GPS, BDS, and GALILEO global satellite navigation systems. By establishing evaluation models and simulating data, a comprehensive evaluation was conducted on the coverage performance of precise point positioning. The results indicate that low-orbit satellite constellations have significant advantages in navigation enhancement and can effectively shorten the convergence time of GNSS precise point positioning. At the same time, the study also revealed the performance differences between different constellation systems, providing important references for the design and optimization of future low-orbit satellite navigation systems.

This paper investigates the impact of multi-GNSS integration on the convergence performance of Precise Point Positioning (PPP), using observations from GPS, Galileo, and BDS constellations. Dual-frequency data from two IGS stations, BRUX and PTBB, on October 2, 2023, were processed using CNES CLK93 precise orbit and clock products. Two system configurations were evaluated: GPS and GPS+Galileo+BDS. Results show that the inclusion of Galileo and BDS significantly improves satellite geometry and observability, effectively accelerating convergence. Compared to GPS-only, the tripleconstellation configuration reduced convergence epochs in the East and North components by more than 50%, while maintaining similar performance in the Up direction. Additionally, PPPderived clock differences between BRUX and PTBB exhibited faster stabilization and reduced noise under the multi-GNSS solution, confirming its advantage in both positioning and timing applications.

Major geomagnetic storms produce dramatic gradients in the ionosphere's total electron content (TEC) that cause errors in GPS‐dependent navigation systems, such as those used by the U. S. Coast Guard and the Federal Aviation Administration. Here we describe the first use of GPS signals to detect large‐scale gradients in TEC very similar to those found during ionospheric storms but produced instead by the exhaust gases of a large Titan rocket launched from the Kennedy Space Center. The severe ionospheric perturbations of 30 April 2005, observed simultaneously by optical emission from the thermosphere and by GPS diagnostics of the ionosphere, describe a unique type of space weather effect caused by nonnatural sources.