A mixed multi-frequency precise point positioning strategy based on the combination of BDS-3 and GNSS multi-frequency observations

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

In addition to GPS and GLONASS constellation, the number of (Global Navigation Satellite System) GNSS satellites are increasing, it is now possible to evaluate and analyze the position accuracy with multi GNSS constellation. In this paper, statistical assessment of static Precise Point Positioning (PPP) using GPS, GLONASS, dual system GPS/GLONASS, three system GPS/GLONASS/Galileo, GPS/GLONASS/BeiDou and multi system GPS/GLONASS/Galileo/BeiDou PPP combinations is evaluated. Observation data of seven whole days from seven IGS multi GNSS experiment (MGEX) stations is used for analysis. Position accuracy and convergence time is analyzed. Results show that the GPS/GLONASS positioning accuracy increases over GPS PPP. Standard deviations (STDs) of position errors for GPS PPP are 4.63, 3.00 and 6.96 cm in east, north and up components while STDs for GPS/GLONASS PPP are 4.10, 3.42 and 6.50 cm respectively. Root mean square for three dimension (RMS3D) for GPS/GLONASS PPP solution is 8.96 cm. With the addition of Galileo and BeiDou to the combined GPS/GLONASS further enhances the positioning accuracy. Root mean square for horizontal component reach to 5.35 cm of GPS/GLONASS/Galileo/BeiDou PPP solutions. Results analysis of GPS/GLONASS/Galileo PPP solutions show an improvement of convergence time by only 3.81% to achieve accuracy level of 3.0 cm over GPS/GLONASS/BeiDou PPP mode. Results also demonstrate that position accuracy improvement after adding BeiDou observations to the GPS/GLONASS PPP mode is not significant.

BeiDou global navigation satellite system (BDS-3), a developed GNSS by China, has the ability to support five different signals, including B1I, B3I, B1C, B2a, and B2b. Meanwhile, BDS-3 has officially provided the satellite-based precise point positioning (PPP) service through the B2b signal (PPP-B2b) since 2021. It’s necessary to conduct a comprehensive analysis on multi-frequency PPP with PPP-B2b corrections. In this study, a multi-frequency undifferenced and uncombined PPP model (UDUC) using PPP-B2b corrections was employed to investigate dual-frequency to five-frequency real-time PPP performance. The results show that compared with the conventional dual-frequency solutions, multi-frequency solutions can improve both the convergence performances and positioning accuracy of PPP-B2b service, especially during the convergence stage. The quad-frequency and five-frequency solutions can achieve the best positioning performance. The static solutions of multi-frequency PPP models reach the centimeter-level accuracy after convergence. In kinematic mode, the convergence time of the five-frequency PPP results is reduced by 23.5% compared with the dual-frequency results. The root mean square (RMS) errors of the five-frequency PPP in the E, N, and U components are 7.1 cm, 4.8 cm, and 12.4 cm, which are improved by 6.8%, 11.5%, and 5.5%, respectively.Graphical

Precise point positioning (PPP) allows for centimeter- to decimeter-level positioning accuracy using a single global navigation satellite system (GNSS) receiver. However, the use of PPP is presently limited due to the time required for the solution to converge or re-converge to the expected accuracy, which typically requires about 30 minutes. This relatively long convergence time is essentially caused by the existing un-modeled GNSS residual errors. Additionally, in urban areas, the number of visible satellites is usually limited when a single satellite constellation is used, which in turn slows down the PPP solution convergence. This, however, can be overcome by combining the observations of two constellations, namely the GPS and Galileo systems. Unfortunately, combining the GPS and Galileo constellations, although enhances the satellite geometry, introduces additional biases that must be considered in the observation mathematical models. These include the GPS-to-Galileo time offset, and Galileo satellite and receiver hardware delays. In addition, the stochastic characteristics of the new Galileo E1 and E5a signals must be determined to a high degree of precision. This can be done by analyzing various sets of GPS and Galileo measurements collected at two stations with short separation. Several PPP models are developed in this dissertation, which combine GPS and Galileo observations in the un-differenced and between-satellite single-difference (BSSD) modes. These include the traditional un-differenced model, the decoupled clock model, the semi-decoupled clock model, and the between-satellite single-difference model. It is shown that the traditional un-differenced GPS/Galileo PPP model, the GPS decoupled clock model, and semi-decoupled clock GPS/Galileo PPP model improve the convergence time by about 25% in comparison with the un-differenced GPS-only PPP model. In addition, the semi-decoupled GPS/Galileo PPP model improves the solution precision by about 25% compared to the traditional un-differenced GPS/Galileo PPP model. Moreover, the BSSD GPS/Galileo PPP model improves the solution convergence time by about 50%, in comparison with the un-differenced GPS PPP model, regardless of the type of BSSD combination used. As well, the BSSD model improves the solution precision by about 50% and 25% when the BSSD loose and tight combinations are used, respectively, in comparison with the un-differenced GPS-only model.

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%.

Abstract. This paper introduces a newly developed model for both single and dual-frequency precise point positioning (PPP), which combines GPS and Galileo observables. As is well known, a drawback of a single GNSS system is the availability of sufficient number of visible satellites in urban areas. Combining GPS and Galileo systems offers more visible satellites to users, which is expected to enhance the satellite geometry and the overall positioning solution. However, combining GPS and Galileo observables introduces additional biases which require rigorous modelling, including the GPS to Galileo time offset (GGTO) and the inter-system bias. This research introduces a new ionosphere-free linear combination model for GPS/Galileo PPP, which accounts for the additional errors and biases. An additional unknown is introduced in the least-squares estimation model to account for the additional biases of the GPS/Galileo PPP solution. It is shown that a sub-decimeter level positioning accuracy and 20% reduction in the solution convergence time can be achieved with the newly developed GPS/Galileo PPP model.

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 legacy Global Navigation Satellite System (GNSS) satellite clock offsets obtained by the dual-frequency undifferenced (UD) ionospheric-free (IF) model absorb the code and phase time-variant hardware delays, which leads to the inconsistency of the precise satellite clock estimated by different frequencies. The dissimilarity of the satellite clock offsets generated by different frequencies is called the inter-frequency clock bias (IFCB). Estimates of the IFCB typically employ epoch-differenced (ED) geometry-free ionosphere-free (GFIF) observations from global networks. However, this method has certain theoretical flaws by ignoring the receiver time-variant biases. We proposed a new undifferenced model coupled with satellite clock offsets, and further converted the IFCB into the code and phase time-variant mixed observable-specific signal bias (OSB) to overcome the defects of the traditional model and simplify the bias correction process of multi-frequency precise point positioning (PPP). The new model not only improves the mixed OSB performance, but also avoids the negative impact of the receiver time-variant biases on the satellite mixed OSB estimation. The STD and RMS of the original OSB can be improved by 7.5–60.9% and 9.4–66.1%, and that of ED OSB (it can reflect noise levels) can be improved by 50.0–87.5% and 60.0–88.9%, respectively. Similarly, the corresponding PPP performance for using new mixed OSB is better than that of using the traditional IFCB products. Thus, the proposed pseudorange and phase time-variant mixed OSB concept and the new undifferenced model coupled with satellite clock offsets are reliable, applicable, and effective in multi-frequency PPP.

Monitoring the response of engineering structures, such as tall buildings, tower and large-scale bridges, under severe loading conditions, such as strong earthquake or wind storm, is an important requirement to verify their design and construction and to evaluate structural condition and reliability. In the last two decades, high-rate real-time or post-processed kinematic differential Global Positioning System (DGPS) has been widely used in dynamic displacement measurements of civil engineering structures. In recent years, interest has increased for Precise Point Positioning (PPP) due to its capability to generate positioning solutions as accurate as DGPS. In this study, the potential of post-processed kinematic PPP in terms of monitoring dynamic displacement response of a structure has been explored based on free damped oscillation events obtained from a model structure, which is able to vibrate in the fundamental and higher modes of vibration. A number of experiments have been carried out and five events, each of which is different character, have been selected to compare PPP results with DPGS results in the time and frequency domain. The results clearly demonstrate that the PPP method, like the DGPS method, offers great potential for the measurement of horizontal and vertical dynamic movement of structures. The impact of a short period (one minute) of observation length on the result of the kinematic PPP method was also investigated in terms of sensing the dynamic movement of a structure. Twenty selected one-minute data-sets extracted from a one-hour original data-set were processed by Canadian spatial reference system PPP and each one-minute PPP solution was compared with the corresponding segment obtained from the one-hour PPP solution. The results show that the one-minute PPP solution is able to extract the fundamental natural frequency of the oscillation in the horizontal and vertical component just like the one-hour PPP solution after the offset is removed and the lower frequency trend component is filtered out.

Multi-frequency observations are now available from GNSSs, thereby bringing new opportunities for precise point positioning (PPP). However, they also introduce new challenges, such as inter-frequency clock bias (IFCB) between the new frequencies and the original dual-frequency observations due to triple-frequency observations, which severely impact the PPP. In this paper, we studied the estimation and correction methods of uncombined inter-frequency clock bias of GPS, BDS-3, and Galileo, analyzed the time-varying characteristics and short-term stability of IFCB, and analyzed the influence of IFCB on the positioning of the GPS, BDS-3, and Galileo, based on a triple-frequency un-differential non-combined PPP model. The obtained results show that the amplitude of Block IIF satellites of the GPS can reach up to 10–20 cm, and the IFCB in BDS-3, Galileo, and GPS Block III satellites can be neglected. After correction by IFCB, the 3D positioning accuracy of the GPS triple-frequency PPP was 1.73 cm and 4.75 cm in the static and kinematic modes, respectively, while the convergence time was 21.64 min and 39.61 min. Compared with the triple-frequency GPS PPP without any correction with IFCB, the static and kinematic 3D positioning accuracy in this work was improved by 27.39% and 17.34%, and the corresponding convergence time was improved by 10.55% and 15.22%, respectively. Furthermore, the delayed IFCB was also used for positioning processing, and it was found that a positioning performance comparable to that of the same day can be obtained. The standard deviation of IFCB for a single satellite was found to be no more than 1 cm, when the IFCB value of a neighboring day was subtracted from the IFCB value of same day, which proves the short-term stability of IFCB.

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

In precise point positioning (PPP) solutions, stochastic modeling of the receiver clock parameter affects solution stability, especially the station up component. This study analyzes GPS + Galileo static and kinematic PPP solutions for 14 GNSS stations equipped with ultra-stable hydrogen masers, utilizing real-time orbit and clock products, such as HAS, IGS, and CNES, as well as final products from CODE. The solution with modeling of the receiver clock parameter enhances stability and precision compared to the reference solution, in which the receiver clocks are estimated independently for each epoch. In static PPP solutions, receiver clock modeling reduces spikes in the clock parameter and improves short-term stability. The most notable improvement of the station up component reaches up to 59, 21, 25, and 38% for HAS, IGS, CNES, and CODE, respectively, in terms of the interquartile range (IQR) of the estimated parameter during the first three processing hours. For kinematic PPP solutions, the maximum reduction of the up component standard deviation is 38, 50, 18, and 26% for HAS, IGS, CNES, and CODE, respectively across all analyzed GNSS stations. Additionally, the IQR analysis of epoch-wise differences in the station up component indicates even greater enhancements, with reductions reaching up to 63, 70, 52, and 83% for HAS, IGS, CNES, and CODE, respectively. Epoch-wise differences indicate short-term stability. The proposed clock modeling improves both the common clock parameter and the vertical component, enhancing PPP solution by increasing stability (reduced variability) and precision (reduced dispersion) across real-time and post-processed GNSS products.

Precise point positioning (PPP) is highly dependent on the precise ephemerides and satellite clock products that are used. Different ephemeris and clock products are available from a variety of different organizations. The aim of this paper is to assess the achievable static positioning accuracy and precision when using different precise ephemerides from three analysis centres Natural Resources Canada (EMX), European Space Agency (ESA) and GeoForschungsZentrum (GFZ), using GPS alone, GLONASS alone, and GPS and GLONASS combined. It will be shown in this paper that the precise products are significantly affected by the time-base of the reference stations, and that this is propagated through to all the estimated satellite clocks. In order to overcome the combined biases in the estimated satellite clock, in the PPP processing, these clocks errors need to be handled with an appropriate variation in the estimated receiver clock. It will also be shown that the precise coordinates of the satellites differ between the analysis centres, and this affects the PPP position estimation at the millimetre level. However, all those products will be shown to result in the same level of precision for all coordinate components and are equivalent to the horizontal precision from a Global Double Difference (GDD) solution. For the horizontal coordinate component, the level of agreement between the PPP solutions, and with the GDD solution, is at the millimetre level. There is a notable, but small, bias in the north coordinate components of the PPP solutions, from the corresponding north component of the GDD solutions. It is shown that this difference is due to the different strategy adopted for the GDD and PPP solutions, with PPP being more affected by the changing satellite systems. The precision of the heights of the receiver sites will be shown to be almost the same across all the PPP scenarios, with all three products. Finally, it will be concluded that accuracy of the height component is system dependent and is related to the behaviour of antenna phase centre with the different constellation type.

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.

Smartphones typically compute position using duty-cycled Global Navigation Satellite System (GNSS) L1 code measurements and Single Point Positioning (SPP) processing with the aid of cellular and other measurements. This internal positioning solution has an accuracy of several tens to hundreds of meters in realistic environments (handheld, vehicle dashboard, suburban, urban forested, etc.). With the advent of multi-constellation, dual-frequency GNSS chips in smartphones, along with the ability to extract raw code and carrier-phase measurements, it is possible to use Precise Point Positioning (PPP) to improve positioning without any additional equipment. This research analyses GNSS measurement quality parameters from a Xiaomi MI 8 dual-frequency smartphone in varied, realistic environments. In such environments, the system suffers from frequent phase loss-of-lock leading to data gaps. The smartphone measurements have low and irregular carrier-to-noise (C/N0) density ratio and high multipath, which leads to poor or no positioning solution. These problems are addressed by implementing a prediction technique for data gaps and a C/N0-based stochastic model for assigning realistic a priori weights to the observables in the PPP processing engine. Using these conditioning techniques, there is a 64% decrease in the horizontal positioning Root Mean Square (RMS) error and 100% positioning solution availability in sub-urban environments tested. The horizontal and 3D RMS were 20 cm and 30 cm respectively in a static open-sky environment and the horizontal RMS for the realistic kinematic scenario was 7 m with the phone on the dashboard of the car, using the SwiftNav Piksi Real-Time Kinematic (RTK) solution as reference. The PPP solution, computed using the YorkU PPP engine, also had a 5–10% percentage point more availability than the RTK solution, computed using RTKLIB software, since missing measurements in the logged file cause epoch rejection and a non-continuous solution, a problem which is solved by prediction for the PPP solution. The internal unaided positioning solution of the phone obtained from the logged NMEA (The National Marine Electronics Association) file was computed using point positioning with the aid of measurements from internal sensors. The PPP solution was 80% more accurate than the internal solution which had periodic drifts due to non-continuous computation of solution.