Real-time single-frequency precise point positioning using BDS-3 PPP-B2b corrections

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.

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.

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

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 Fractional Cycle Bias (FCB) product is crucial for the Ambiguity Resolution (AR) in Precise Point Positioning (PPP). Different from the traditional method using the ionospheric-free ambiguity which is formed by the Wide Lane (WL) and Narrow Lane (NL) combinations, the uncombined PPP model is flexible and effective to generate the FCB products. This study presents the FCB estimation method based on the multi-Global Navigation Satellite System (GNSS) precise satellite orbit and clock corrections from the international GNSS Monitoring and Assessment System (iGMAS) observations using the uncombined PPP model. The dual-frequency raw ambiguities are combined by the integer coefficients (4,− 3) and (1,− 1) to directly estimate the FCBs. The details of FCB estimation are described with the Global Positioning System (GPS), BeiDou-2 Navigation Satellite System (BDS-2) and Galileo Navigation Satellite System (Galileo). For the estimated FCBs, the Root Mean Squares (RMSs) of the posterior residuals are smaller than 0.1 cycles, which indicates a high consistency for the float ambiguities. The stability of the WL FCBs series is better than 0.02 cycles for the three GNSS systems, while the STandard Deviation (STD) of the NL FCBs for BDS-2 is larger than 0.139 cycles. The combined FCBs have better stability than the raw series. With the multi-GNSS FCB products, the PPP AR for GPS/BDS-2/Galileo is demonstrated using the raw observations. For hourly static positioning results, the performance of the PPP AR with the three-system observations is improved by 42.6%, but only 13.1% for kinematic positioning results. The results indicate that precise and reliable positioning can be achieved with the PPP AR of GPS/BDS-2/Galileo, supported by multi-GNSS satellite orbit, clock, and FCB products based on iGMAS.

BDS (Beidou Navigation Satellite System) integrates the legacy PNT (Positioning, Navigation, Timing) service and the authorized SBAS (Satellite-Based Augmentation Services) service. To support the requirement of decimeter-level positioning, four types of differential corrections are developed in the BDS SBAS, including the State Space Representation (SSR)-based satellite orbit/clock corrections, the Observation Space Representation (OSR)-based ionospheric grid corrections, and the partition comprehensive corrections. In this study, we summarize the features of these differential corrections, including their definition and usages. The function model of precise point positioning (PPP) for dual- and single-frequency users using the four types of BDS SBAS corrections are proposed. Datasets are collected from 34 stations over one month in 2019, and PPP is performed for all the datasets. Results show that the root mean square (RMS) of the positioning errors for static/kinematic dual-frequency (DF) PPP are of 12 cm/16 cm in horizontal and 18 cm/20 cm in vertical component, while for single-frequency (SF) PPP are of 14 cm/32 cm and 22 cm/40 cm, respectively. With regard to the convergence performance, the horizontal and vertical positioning errors of kinematic DF-PPP can converge to 0.5 m in less than 15 min and 20 min, respectively. As for the kinematic SF-PPP, it could converge to 0.8 m in horizontal and 1.0 m in vertical within 30 min, where the ionosphere-constrained PPP performs better than the UofC PPP approach, owing to the contribution of the ionospheric grid corrections.

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

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.

Global Navigation Satellite System (GNSS) based Precise Point Positioning (PPP) has become the de facto standard for precise real-time offshore positioning applications. Current precision is of the order of 3−5 cm horizontally and twice this value for the vertical. However, this may not yet be good enough for tidal applications. In this contribution we will discuss new developments at Fugro, one of the world’s main providers of precise offshore real-time GNSS positioning services, to further improve PPP precision to the 2−3 cm level in the vertical component worldwide. For demanding applications, it is possible to even further improve this precision. These developments are based on merging PPP techniques (use of precise satellite orbits and clocks) with Integer Ambiguity Resolution (IAR), known from GNSS Real-Time Kinematic (RTK) positioning techniques. PPP IAR requires the generation and distribution to mobile users of Uncalibrated Phase Delays (UPDs) a network of reference stations. The network can be as small as one station or cover the entire globe. Once applied to the data of a mobile receiver, the carrier ambiguities should be integer. Fixing of these ambiguities to their proper integer value will result in significantly improved positioning performance. The infrastructure used to generate precise orbits, clocks and UPDs will be discussed. PPP IAR results will be shown from regional and global test beds, based on Fugro’s precise orbits and clocks for all currently available GNSSs. In addition, it will be shown that the introduction of new systems and signals, like triple-frequency GPS, Galileo and BeiDou, will help to significantly reduce the time required for PPP IAR solutions to converge to this centimeter level of accuracy.

This paper introduces the correction method of real-time precise satellite orbit and clock and the positioning principle of ionospheric-free model and uncombined model of precise point positioning. The positioning accuracy and convergence time of the two models in real-time GPS static precise point positioning are compared by using the GPS observation data of Brux station and DLF10 station and the satellite orbit and clock correction information of CNES station. The static positioning results show that compared with the ionospheric-free model, the uncombined model has slight difference in positioning accuracy, and the convergence time of the uncombined model is longer than that of the ionospheric-free model.

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 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%.

To obtain the coordinates by means of precise point positioning (PPP) technique we need to use the undifferenced GPS pseudocode and carrier phase observations but to obtain the “precise” positioning we need precise orbit and clock data too. This products and other information for obtaining the results by using PPP technique on a centimeter level accuracy can be downloaded from different locations, but the most reliable satellite ephemerides and clock correction are available from International GNSS Service (IGS). In the PPP analysis we determined the parameters such as the receiver clock error, ionospheric delays code biases, code multipath and the total neutral atmosphere delay of the observations. For the determination of the permanent station coordinates, using the PPP technique, we used precise orbit and clock solutions to enable absolute positioning of a single receiver. In this article we present the results obtained by using the PPP technique on the permanent station Oradea, from which we can conclude that the PPP technique can be used for different GNSS application.

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.