Satellite- and Epoch Differenced Precise Point Positioning Based on a Regional Augmentation Network

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.

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). 

Uncalibrated phase delay estimation and ambiguity resolution for BDS-3 six-frequency uncombined PPP with legacy B1I/B3I and new B1C/B2a/B2b/B2a + b signals

Abstract. PPP-RTK has been widely investigated to take the advantages of both real-time kinematic (RTK) and precise point positioning (PPP) techniques. Prior to PPP-RTK, the conventional RTK based on the use of a single base station, on the one hand, has been extended to work within a regional network of multiple base stations, known as network RTK (NRTK). The RTK and NRTK enable fast ambiguity resolution over a short baseline or a local region. PPP, on the other hand, eliminates the need to establish any local network like NRTK, which is able to work in a single receiver mode but it suffers long convergence time in ambiguity resolution. PPP-RTK therefore can provide fast ambiguity resolution capability like RTK and NRTK. Current PPP-RTK techniques however still face challenges in supporting mass-market applications such as mobile devices and autonomous vehicles. Although PPP-RTK system (a combination of RTK and PPP technologies) can help expand the coverage of RTK and speed up the ambiguity resolution in PPP, the deployment and maintenance of a dense network of permanent base stations and a central data processing infrastructure for generation of SSR corrections increases not only the system cost but also the system complexity. This is particularly an obstacle for mass-market applications. In this paper, a new RTK approach is described. First it is based on a single base station state-space-representation (SSR) correction generation strategy to support fast ambiguity resolved PPP. Further it presents a new peer-to-peer propagation strategy to form a real-time dynamically generated network of base stations to support mass-market application users with unbounded coverage. As a result, the new approach eliminates the need to deploy and maintain a dense network of permanent base stations and central data processing infrastructure as required in a conventional PP-RTK system.

Ambiguity resolution plays an important role in surveying using Precise Point Positioning (PPP) and relative positioning techniques that require high accuracy. In this study, ambiguity resolution performance of PPP and relative positioning under the unobstructed (with 7° cut-off angle) and constrained environment (with 25° cut-off angle, such as nearby buildings and street-canyons) using final/ultra-rapid orbit and clock products are investigated for different observation time. Seventeen globally distributed stations and six baselines of lengths from 270 km to 2100 km are chosen for conducting PPP and relative positioning, respectively. A 31-day period in January 2018 is chosen for processing using 24-, 12-, 6-, 4-, 2- and 1-h observations. The results indicate that sub-mm to cm levels of improvement in horizontal and vertical coordinate components are generally observed with ambiguity resolution for PPP and relative positioning techniques compared to the float counterparts. Moreover, accuracy degradation of ambiguity resolution compared to float solution is observed generally in the vertical component using the 25° elevation cut-off angle for both techniques. As the observation time increases, the accuracy improvements from ambiguity resolution decrease for each technique. In addition, fixing to the wrong integer ambiguities are generally seen with a short observation time and a 25° elevation cut-off angle for both techniques due to the poor satellite geometry. As far as baseline length in relative technique is concerned, the testing results show that there is no direct relation between baseline length and the accuracy improvement from ambiguity resolution compared to the float solution. The results also reveal that the coordinates obtained from ambiguity resolution does not significantly change in the relative technique using final or ultra-rapid orbit/clock products, whereas the changes in PPP are significant for most of the stations.

For time-critical precise applications, one popular technology is the real-time precise point positioning (PPP). In recent years, there has been a rapid development in the BeiDou Navigation Satellite System (BDS), and the constellation of global BDS (BDS-3) has been fully deployed. In addition to the regional BDS (BDS-2) constellation, the real-time stream CLK93 has started to support the BDS-3 constellation, indicating that the real-time PPP processing involving BDS-3 observations is feasible. In this study, the global positioning performance of real-time PPP with BDS-3/BDS-2 observations is initially evaluated using the datasets from 147 stations. In the east, north and upward directions, positioning accuracy of 1.8, 1.2 and 2.5 cm in the static mode, and of 6.7, 5.1 and 10.4 cm in the kinematic mode can be achieved for the BDS-3/BDS-2 real-time PPP, respectively, while the corresponding convergence time with a threshold of 10 cm is 32.9, 23.7 and 32.8 min, and 66.9, 42.9 and 69.1 min in the two modes in the three directions, respectively. To complete this, the availability of BDS-3/BDS-2 constellations, the quality of BDS-3/BDS-2 real-time precise satellite products, and the BDS-3/BDS-2 post-processed PPP solutions are also analyzed. For comparison, the results for the GPS are also presented.

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

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.

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.

Conventional ambiguity resolution (AR) strategy of directly fixing all raw frequency ambiguities for uncombined precise point positioning (PPP) generally requires a long initial time to ensure fixing reliability. The rich signals from multi-frequency GNSS can provide new opportunities for rapid PPP AR. In this paper, based on a unified multi-frequency uncombined PPP model, the raw frequency ambiguities are linearly transformed to the between-satellite-single-differenced extra-wide-lane (EWL), wide-lane (WL), and narrow-lane (NL) ambiguities, and a cascading ambiguity resolution (CAR) method of fixing EWL/WL/NL ambiguities sequentially is proposed. Meanwhile, a partial ambiguity fixing (PAF) strategy with ambiguity subset adaptively selected based on the successively increased elevations is also adopted in each step to improve the fixing rate. Further, experiments with globally distributed stations are carried out to verify the algorithm. With the constraints of EWL/WL AR, the precision of NL ambiguity and its variance-covariance matrix can be effectively optimized, so the time to first fix (TTFF) is significantly shortened, and the ratio value is also improved to varying degrees. As for BDS-only solution, the average TTFF is shortened from 23.7 min to 10.9 min, with an improvement over 50%; for GPS/BDS, GPS/Galileo, and GPS/Galileo/BDS combined solutions, the TTFF is shortened from 14.3 min, 9.4 min, and 6.7 min to 8.1 min, 2.6 min, and 1.8 min, which are, respectively, shortened by 43.4%, 72.3%, and 73.1%. In general, the proposed CAR strategy can shorten the TTFF of multi-GNSS multi-frequency PPP to about 2 min. The performance of EWL/WL/NL ambiguity-fixed solutions is also analyzed. The NL solution is generally at centimeter-level accuracy over the entire period; however, limited by the atmosphere errors during the convergence stage, the EWL/WL solutions can only obtain decimeter-level accuracy, and the difference between them and NL solution gradually decreases with the continuous improvement of atmosphere accuracy.

Precise Point Positioning (PPP) is an increasingly recognized precisely the GPS/GNSS positioning technique. In order to improve the accuracy of PPP, the error sources in PPP measurements should be reduced as much as possible and the ambiguities should be correctly resolved. The correct ambiguity resolution requires a careful control of residual errors that are normally categorized into random and systematic errors. To understand effects from two categorized errors on the PPP ambiguity resolution, those two GPS datasets are simulated by generating in locations in South Korea (denoted as SUWN) and Hong Kong (PolyU). Both simulation cases are studied for each dataset; the first case is that all the satellites are affected by systematic and random errors, and the second case is that only a few satellites are affected. In the first case with random errors only, when the magnitude of random errors is increased, L1 ambiguities have a much higher chance to be incorrectly fixed. However, the size of ambiguity error is not exactly proportional to the magnitude of random error. Satellite geometry has more impacts on the L1 ambiguity resolution than the magnitude of random errors. In the first case when all the satellites have both random and systematic errors, the accuracy of fixed ambiguities is considerably affected by the systematic error. A pseudorange systematic error of 5 cm is the much more detrimental to ambiguity resolutions than carrier phase systematic error of 2 mm. In the 2 nd case when only a portion of satellites have systematic and random errors, the L1 ambiguity resolution in PPP can be still corrected. The number of allowable satellites varies from stations to stations, depending on the geometry of satellites. Through extensive simulation tests under different schemes, this paper sheds light on how the PPP ambiguity resolution (more precisely L1 ambiguity resolution) is affected by the characteristics of the residual errors in PPP observations. The numerical examples recall the PPP data analysts that how accurate the error correction models must achieve in order to get all the ambiguities resolved correctly.

During high-level solar activity time, frequent ionospheric irregularities lead to large total electron content (TEC) gradient. precise point positioning (PPP) performance can be significantly degraded under the unfavorable ionosphere conditions. We analyze the causes and effects of the ionosphere potential impacts on uncombined PPP (UPPP) performance in terms of the ionospheric stochastic model, blunders, and frequent cycle slips. Results show that a large enough stochastic variance is beneficial for better positioning solutions; blunders detection could improve the accuracy; a proper threshold to detect cycle slips could improve the accuracy significantly. Taking these effects into consideration, we can achieve a centimeter accuracy at each direction under the disturbed ionosphere conditions.

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.

For precise positioning in arctic regions with Global Navigation Satellite Systems (GNSS), such as GPS and Glonass, there are a number of issues to be resolved or taken into account. The most important ones are satellite geometry, ionospheric effects and distribution of correction data. Precise Point Positioning (PPP) is currently the standard for precise offshore positioning. PPP requires a sparse global network of GNSS reference stations to estimate precise satellite orbit and clock parameters in real-time. These parameters are transmitted to users, who can compute their position with an accuracy of 0.1 m using code and carrier observations. The main disadvantage of PPP is that in general it takes a long time to converge to this accuracy, about 30–45 minutes. GNSS carrier observations are similar to pseudo ranges, but have an additional bias which needs to be estimated. Under certain conditions, these biases are integer. This property is used in what is generally referred to as Real-Time Kinematic (RTK) positioning, a technique which uses corrections generated at reference stations to make sure these ambiguities are integer. Integer Ambiguity Resolution (IAR) results in RTK accuracies of 0.01–0.03 m or better and short convergence times, ranging from instantaneous to several minutes for long inter-station distances. The disadvantage is the limited area of applicability, because RTK in general does not use precise orbits and clocks. Current research focuses on the combination of PPP and RTK techniques. The main goal is to achieve cm accuracy with a sparse network of reference stations. Another goal is to reduce convergence time. Applications are in the field of precise real-time offshore positioning in general, and subsidence monitoring and tidal estimation in particular. Results will be presented from standard PPP and PPP combined with IAR for arctic regions and from a test bed in the Gulf of Mexico. These results, although preliminary, indicate centimeter level accuracy is indeed possible, also in the arctic. We will also look at further improvements, mainly in convergence time, using all operational satellites and signals from current and future navigation systems.

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.