Ionospheric Effect Mitigation for Real-Time Single-Frequency Precise Point Positioning

Single-frequency (SF) receivers are much cheaper than that of dual-frequency (DF). Even though DF precise point positioning (PPP) is nowadays applied in the time community, the cost of equipment is one of the key considerations for time users. Furthermore, the hardware delay calibration of single-frequency devices is simpler than that of dual-frequency devices. In addition, there is no literature to study real-time SF PPP time transfer. In this contribution, the possibility of time transfer using SF PPP was studied. The Un-combined SF PPP was employed for time transfer with ionospheric-constraint using real-time precise products. In this case, 18 multi-GNSS experiment (MGEX) stations and one time lab station were used to study real-time SF PPP time transfer using GPS, Galileo and BDS-2/3 satellites with 20-day. The results suggested that real-time single-frequency PPP can meet time transfer. the standard deviation (STD) of the clock difference obtained from GPS-only, Galileo-only and BDS-2/3 single-frequency PPP are about (0.51, 0.54, 0.91) ns, respectively. The frequency stability of real-time single-frequency PPP can achieve (1E-12, 1E-13, 1E-13) level at short-term and (1E-13, 1E-13, 1E-14) level at long-term, respectively, for BDS-2/3, Galileo-only and GPS-only based.

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

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.

The performance of real-time single-frequency precise point positioning is demonstrated in terms of position accuracy. This precise point positioning technique relies on predicted satellite orbits, predicted global ionospheric maps, and in particular on real-time satellite clock estimates. Results are presented using solely measurements from a user receiver on the L1-frequency (C1 and L1), for almost 3 months of data. The empirical standard deviations of the position errors in North and East directions are about 0.15 m, and in Up direction about 0.30 m. The 95% errors are about 0.30 m in the horizontal directions, and 0.65 m in the vertical. In addition, single-frequency results of six receivers located around the world are presented. This research reveals the current ultimate real-time single-frequency positioning performance. To put these results into perspective, a case study is performed, using a moderately priced receiver with a simple patch antenna.

One of the challenges in the innovative application of global navigation satellite systems (GNSS) lies in real-time single-frequency precise point positioning (RT-SFPPP). The well-known problems associated with SFPPP are its slow convergence and lower positioning accuracy due to the effects of various errors inherited by the GNSS positioning, including the atmospheric error. In order to mitigate the two above-mentioned problems, several scenarios for the reduction of the atmospheric delays in RT-SFPPP, including the ionospheric constraint and tropospheric constraint, were investigated in this research. The performance of the RT-SFPPP utilizing the above-mentioned methods was evaluated using one-week observations from multi-GNSS experiment stations in a simulated kinematic mode. Results showed that the convergence time of the RT-SFPPP was significantly shortened when the slant ionospheric delays derived from the real-time ionospheric products provided by Centre National d’Études Spatiales were applied as the pseudo-observations. Results also showed that the convergence time of GPS + GLONASS RT-SFPPP can be reduced by modeling the frequency-dependent part of the GLONASS receiver uncalibrated code delay as a quadratic polynomial function of GLONASS frequency number. The a priori zenith wet delays (ZWDs) derived from forecast Vienna Mapping Functions 3 (VMF3_FC) were compared to the reference ZWDs from globally distributed radiosonde stations. The mean root mean square error of the a priori ZWDs resulting from VMF3_FC at 381 radiosonde stations in 2020 was 1.53 cm compared to the radiosonde-based ZWDs. When the ZWDs derived from VMF3_FC were used as pseudo-observations in the position estimation system, the convergence time for the vertical positioning reaching a 0.3 m accuracy was considerably shortened.

Real-time precise point positioning (PPP) has been evolved as a powerful technique to achieve globally homogenous decimeter or even centimeter positioning accuracy, which is widely used for maritime precise positioning applications. Currently, the research of the real-time PPP for maritime applications mainly focuses on GPS and GLONASS. In addition, the real-time PPP for kinematic maritime positioning is at least limited by two issues, (i) The real-time availability of the correction products for satellite orbits and clocks; (ii) The error correction related to the marine environment, especially for the estimation of wet zenith troposphere delay (ZWD) is challenged by complex fluctuations of marine atmospheric weather and the severe multipath caused by the sea clutter reflection. In this contribution, using the State-Space Representation correction products based on Radio Commission for Maritime Services (RTCM-SSR), we develop a GPS/BDS real-time kinematic maritime PPP. On the one hand, a piece-wise method is adopted to estimate the ZWD and the horizontal gradient. On the other hand, a robust sequential least squares (RSLSQ) PPP estimator is adopted based on IGG-III model to restrain the unmolded gross error. Based on the 6 h maritime data, the results show that the up direction accuracy and the convergence time of GPS, BDS and GPS/BDS, respectively, are improved based on 0.5 window length for ZWD estimation and the RSLSQ estimator. In addition, the horizontal accuracy of real-time single BDS and GPS using RTCM-SSR can achieve the accuracy of sub-decimeter level when the positioning error is convergence. Compared with the single constellation, the positioning accuracy and the convergence time of the real-time GPS/BDS using RTCM-SSR improves, respectively, by 10 and 18%, and the kinematic positioning accuracy in horizontal is better than 30 cm.

Real-Time (RT) Precise Point Positioning (PPP) uses precise satellite orbits and clock corrections, and employs a separate receiver for positioning. With the growing demand, RT PPP is becoming an increasingly popular research topic. The ambiguity resolution (AR) can significantly improve the positioning accuracy and convergence time of PPP, so it is essential to study PPPAR in RT mode. In this paper, 37 MGEX stations from around the world are chosen, and the RT orbit, clock, and phase biases products broadcast by the Centre National d’Etudes Spatiales (CNES) are applied to PPPAR. Additionally, the residuals of the RT phase biases products, convergence time, and positioning accuracy are investigated. The results indicate that GPS products have the best quality of AR, with wide-lane (WL) and narrow-lane (NL) residuals of 98.9% and 95.3%, respectively, within ±0.25 cycles. Within ±0.25 cycles, the WL and NL residuals of the Galileo are 98.2% and 94.3%, respectively. Within ±0.25 cycles, the (Beidou Navigation Satellite System) BDS has a poor quality of AR, with WL and NL residuals of 97.3% and 73.1%, respectively. Due to the poor quality of the BDS AR, the convergence time of the BDS is not calculated in this paper. The convergence time of other systems is significantly reduced after AR processing, and the convergence time of the GPS/Galileo combination is the fastest, being 17.14 min in kinematic mode and only 11.85 min in static mode. The positioning accuracy of the GPS, Galileo, GPS/Galileo, and GPS/Galileo/BDS in the E and U directions is significantly improved after PPPAR.

The availability of raw Global Navigation Satellite System (GNSS) measurements from Android smart devices gives new possibilities for precise positioning solutions, e.g., Precise Point Positioning (PPP). However, the accuracy of the PPP with smart devices currently is a few meters due to the poor quality of the raw GNSS measurements in a kinematic scenario and in urban environments, particularly when the smart devices are placed inside vehicles. To promote the application of GNSS PPP for land vehicle navigation with smart devices, this contribution studies the real-time PPP with smartphones. For data quality analysis and positioning performance validation, two vehicle-based kinematic positioning tests were carried out using two Huawei Mate30 smartphones and two Huawei P40 smartphones with different installation modes: the vehicle-roof mode with smartphones mounted on the top roof outside the vehicle, and the dashboard mode with smartphones stabilized on the dashboard inside the vehicle. To realize high accuracy positioning, we proposed a real-time smartphone PPP method with the data processing strategies adapted for smart devices. Positioning results show that the real-time PPP can achieve the horizontal positioning accuracy of about 1–1.5 m in terms of root-mean-square and better than 2.5 m at the 95th percentile for the vehicle-based kinematic positioning with the experimental smartphones mounted on the dashboard inside the vehicle, which is the real scenario in vehicle navigation.

The release of the world’s first dual-frequency GPS/Galileo smartphone, Xiaomi mi 8, in 2018 provides an opportunity for high-precision positioning using ultra low-cost sensors. In this research, the GNSS precise point positioning (PPP) accuracy of the Xiaomi mi 8 smartphone is tested in post-processing and real-time modes. Raw dual-frequency observations are collected over two different time windows from both of the Xiaomi mi 8 smartphone and a Trimble R9 geodetic-quality GNSS receiver using a short baseline, due to the lack of a nearby reference station to the observation site. The data sets are first processed in differential modes using Trimble business center (TBC) software in order to provide the reference positioning solution for both of the geodetic receiver and the smartphone. An in-house PPP software is then used to process the collected data in both of post-processing and real-time modes. Precise ephemeris obtained from the multi-GNSS experiment (MGEX) is used for post-processing PPP, while the new NAVCAST real-time GNSS service, Germany, is used for real-time PPP. Additionally, the real-time PPP solution is assessed in both of static and kinematic modes. It is shown that the dual-frequency GNSS smartphone is capable of achieving decimeter-level positioning accuracy, in both of post-processing and real-time PPP modes, respectively. Meter-level positioning accuracy is achieved in the kinematic mode.

This paper presents an investigation into the performance of real-time Global Navigation Satellite Systems (GNSS) Precise Point Positioning (PPP) in New Zealand. The motivation of the research is to evaluate the feasibility of using PPP technique and a satellite based augmentation system such as the Japanese Quasi-Zenith Satellite System (QZSS) to deliver a real-time precise positioning solution in support of a nation-wide high accuracy GNSS positioning coverage in New Zealand. Two IGS real-time correction streams are evaluated alongside with the PPP correction messages transmitted by the QZSS satellite known as MDC1. MDC1 corrections stream is generated by Japan Aerospace Exploration Agency (JAXA) using the Multi-GNSS Advanced Demonstration tool for Orbit and Clock Analysis (MADOCA) software and are currently transmitted in test mode by the QZSS satellite. The IGS real-time streams are the CLK9B real-time corrections stream generated by the French Centre National D’études Spatiales (CNES) using the PPP-Wizard software, and the CLK81 real-time corrections stream produced by GMV using their MagicGNSS software. GNSS data is collected from six New Zealand CORS stations operated by Land Information New Zealand (LINZ) over a one-week period in 2015. GPS and GLONASS measurements are processed in a real-time PPP mode using the satellite orbit and clock corrections from the real-time streams. The results show that positioning accuracies of 6 cm in horizontal component and 15 cm in vertical component can be achieved in real-time PPP. The real-time GPS+GLONASS PPP solution required 30 minutes to converge to within 10 cm horizontal positioning accuracy.

Satellite orbit error and clock bias are the keys to precise point positioning (PPP). The traditional PPP algorithm requires precise satellite products based on worldwide permanent reference stations. Such an algorithm requires considerable work and hardly achieves real-time performance. However, real-time positioning service will be the dominant mode in the future. IGS is providing such an operational service (RTS) and there are also commercial systems like Trimble RTX in operation. On the basis of the regional Continuous Operational Reference System (CORS), a real-time PPP algorithm is proposed to apply the coupling estimation of clock bias and orbit error. The projection of orbit error onto the satellite-receiver range has the same effects on positioning accuracy with clock bias. Therefore, in satellite clock estimation, part of the orbit error can be absorbed by the clock bias and the effects of residual orbit error on positioning accuracy can be weakened by the evenly distributed satellite geometry. In consideration of the simple structure of pseudorange equations and the high precision of carrier-phase equations, the clock bias estimation method coupled with orbit error is also improved. Rovers obtain PPP results by receiving broadcast ephemeris and real-time satellite clock bias coupled with orbit error. By applying the proposed algorithm, the precise orbit products provided by GNSS analysis centers are rendered no longer necessary. On the basis of previous theoretical analysis, a real-time PPP system was developed. Some experiments were then designed to verify this algorithm. Experimental results show that the newly proposed approach performs better than the traditional PPP based on International GNSS Service (IGS) real-time products. The positioning accuracies of the rovers inside and outside the network are improved by 38.8% and 36.1%, respectively. The PPP convergence speeds are improved by up to 61.4% and 65.9%. The new approach can change the traditional PPP mode because of its advantages of independence, high positioning precision, and real-time performance. It could be an alternative solution for regional positioning service before global PPP service comes into operation.

Real-time precise point positioning (PPP) is possible through the availability of the real-time satellite orbit and clock corrections to broadcast ephemeris, the real-time broadcast corrections (BCs). The real-time BCs are currently available in global as well as in regional reference frames. In this contribution, PPP usage and the performance of these global and regional BCs are analyzed for the North American Datum of 1983 (NAD83). The limitations of the current regional BC approach for NAD83 are identified and the coordinate differences it leads to compared with the traditional global BC approach are shown. Although the biases as a result of the different reference frame usage are shown to be subcentimeter, it is also shown how they can be reduced or eliminated by modifying either the PPP algorithm or the regional BC approach. Analyses were performed for three different PPP variants, a single-frequency ionosphere-free variant, a dual-frequency ionosphere-free variant, and a single-frequency ionosphere-corrected variant.

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.

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.

PPP-based UAV modeling using Galileo HAS orbit/clock products and RTS smoother