LEO constellation-augmented multi-GNSS for rapid PPP convergence

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 recruitment of the Low Earth Orbit (LEO) constellation is recognized as an effective way to augment Global Navigation Satellite System (GNSS) Precise Point Positioning (PPP) in the near future. Its potential to accelerate PPP convergence has been proved with simulated data. However, the mechanism of how the geometric change of LEO accelerates the convergence of GNSS PPP has not been studied from a theoretical perspective, which hampers the understanding and exploitation of the enhancement of LEO. In this article, the convergence mechanism of LEO enhanced GNSS PPP is investigated in terms of theoretical analysis and simulated verification. To show the characteristics of the ambiguities during convergence, eigenvalue decomposition is used to divide the ambiguities into orthogonal components, named geometric-related component, clock-error-related component, and independent component. The results show that the precision of geometric-related components of ambiguities, which correlates with position parameters, is low at a single epoch, while the precision can be greatly improved with the fast geometric change of LEO. On the other hand, the precision of clock-error-related components of ambiguities, which correlates with clock errors, cannot be improved by fast geometric change of LEO constellation due to its irrelevance to geometry, which causes the precision of each ambiguity to be low. Further investigations show that single-differenced ambiguities could overcome this drawback and are beneficial to ambiguity resolution.

The precise point positioning (PPP) is widely used as a typical representative of GNSS. But the main challenge of dual-frequency PPP is that it requires quite a long time to succeed in the ambiguity-fixed so it takes more than 30 min to obtain centimeter-level accuracy. A combination of GPS and low earth orbit (LEO) satellites can improve the diversity of available satellites' geometric distribution and reduce the correlation of observation data between epochs. Then the accuracy of float solution will be promoted and the ambiguity of GPS will take less time to get fixed. The purpose of this paper is to reduce the convergence time of PPP by the contribution of LEO satellites which have low earth orbit and move speedily. We adopt a free-ionosphere PPP model to combine GPS and LEO satellites. Numerous experimental results show that GPS/LEO PPP requires much less convergence time and gets higher positioning accuracy than that of PPP with GPS alone. In addition, an analysis is also made to compare GPS/LEO PPP and GPS/GLONASS PPP. The results indicate that GPS/LEO PPP also requires much less convergence time and gets higher positioning accuracy than that of GPS/GLONASS PPP when increasing the same number of available satellites. This proved that LEO satellites have more contribution to PPP performance than MEO.

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). 

The precise point positioning (PPP) technique generally takes tens of minutes to converge, severely limiting its use. This longer convergence time is mainly due to the slower variation of satellite geometry in space and the stronger correlation of unknown parameters to be estimated. Fortunately, the lower orbit altitude of Low Earth Orbit (LEO) satellites contributes to the fast variation of the satellites’ spatial geometry. In addition, high-precision atmospheric delay information has become readily available, which can help decrease unknown parameters’ correlation. This study proposes a double-augmentation PPP approach with accelerated convergence by tightly integrating the LEO/atmosphere-augmented information. The GNSS observations in both mid-latitude and low-latitude areas, and simulated LEO observations under a Walker/polar mixed constellation, are used to validate the double-augmentation PPP approach. Test results in both areas indicate that the double-augmentation PPP can converge within 0.8 min, improving the convergence time by over 73%, and over 83% compared to the LEO-only augmented PPP and atmosphere-only augmented PPP.

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.

Single-Frequency Precise Point Positioning Using Multi-Constellation GNSS: GPS, GLONASS, Galileo and BeiDou

The bottleneck of Precise Point Positioning (PPP) is the long convergence time for achieving the centimeter accuracy. Some researchers put forward to improve the diversity of available satellites’ geometric distribution and reduce the correlation of observation data by deploying the Low Earth Orbit (LEO) constellations in addition to the medium and high-orbit satellites. The prerequisite is to get the precise orbit products of all these orbiting satellites. This paper studies the combined precise orbit determination for high-, medium-, and low-orbit navigation satellite systems. In order to investigate the theory and algorithms of the high–medium–low POD and to study the effect of LEO to the POD of high-orbit satellites and the influence of ground data from LEO to its own POD, we simulate all the data, including high orbit to low orbit, medium orbit to low orbit, high orbit to ground stations, medium orbit to ground stations, and low orbit to ground stations. The results show that the combined POD can improve the precision of high-orbit satellites significantly, especially for the along-track component, which can reach to sub-decimeter even centimeter level. Also, the precision of LEO POD can be improved with the data from ground stations.

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.

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

Rapid convergence of precise point positioning (PPP) solutions to cm-level precision is a key factor for many applications. One means of accelerating this convergence is to exploit the benefit of information on the ionosphere. In order to preserve the integer nature of carrier-phase ambiguities in PPP, it is imperative that ionospheric corrections be provided with a set of compatible satellite phase biases. When using the decoupled-clock model, global ionospheric maps (GIMs) currently provided by the International GNSS Service are not directly applicable to PPP with ambiguity resolution. This paper describes a methodology for incorporating external ionospheric corrections into this model. It is shown that the use of both GIMs and ambiguity resolution can potentially reduce the convergence time of PPP to 10-cm horizontal accuracies from 30 to 4.5 minutes (68th percentile), while a regional network with inter-station spacing of 150 km can reach this threshold instantaneously under favorable ionospheric conditions. © 2014 Her Majesty the Queen in Right of Canada. NAVIGATION. © 2014 the Institute of Navigation.

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.

The availability of multiple signals from different Global Navigation Satellite System (GNSS) constellations provides opportunities for improving positioning accuracy and initial convergence time. With dual-frequency observations from the four constellations (GPS, GLONASS, Galileo, and BeiDou), it is possible to investigate combined GNSS precise point positioning (PPP) accuracy and stability. The differences between GNSS systems result in inter-system biases (ISBs). We consider several ISB values such as GPS-GLONASS, GPS-Galileo, and GPS-BeiDou. These biases are compliant with key parameters defined in the multi-GNSS PPP processing. In this study, we present a unified PPP method that sets ISB values as fixed or constant. A comprehensive analysis that includes satellite visibility, position dilution of precision, position accuracy is performed to evaluate a unified PPP method with constrained cut-off elevation angles. Compared to the conventional PPP solutions, our approach shows more stable positioning at a constrained cut-off elevation angle of 50 degrees.

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.

Atmospheric wet delay caused by Precipitable Water Vapor (PWV) significantly impacts the performance of many geodetic surveying systems such as Global Navigation Satellite System (GNSS). In this study, we use wet delay corrections forecast by the Weather Research and Forecasting (WRF) model to enhance GNSS Precise Point Positioning (PPP) during two observation periods with two different weather conditions, that is, period 1: March 01 to 14, 2020 (average PWV: 23.5 kg/m2) and period 2: June 02 to 15, 2020 (flooding weather with average PWV: 55.6 kg/m2), over the South China. PWV data from 277 to 263 GNSS stations are assimilated into WRF model to enhance the WRF water vapor forecasting capability for period 1 and period 2, respectively. Wet delay corrections from two different WRF configurations, that is, WRF no data assimilation and WRF with assimilation of GNSS PWV, are used to augment the PPP. Totally, eight WRF‐enhanced PPP schemes are tested. The results show that WRF‐enhanced PPP schemes generally have a better positioning performance in the up component than traditional PPP. After using WRF wet delay corrections, for static mode, the vertical positioning accuracy is improved by 14.6% and 33.7% for period 1 and period 2, respectively. The corresponding convergence time are reduced by 41.8% and 25.0% for period 1 and period 2, respectively. For kinematic mode, the positioning accuracy improvements in the up component reach 13.8% and 19.0% for period 1 and period 2, respectively. The kinematic PPP convergence time is reduced by up to 8.2% for period 1.