Real-time Precise Point Positioning Solutions Research Articles

Enabling the Galileo high accuracy service with open-source software: integration of HASlib and RTKLIB

The Galileo high accuracy service (HAS) is a free-of-charge service designed to deliver decimeter-level accuracy in real-time precise point positioning (PPP) applications using global navigation satellite systems (GNSS). With the intention of facilitating the use of HAS corrections with open access tools, we present the open-source library named HASlib and its integration with another open-source library named RTKLIB. HASlib decodes the Reed–Solomon encoded Galileo E6 navigation data pages and outputs the corrections in commonly used formats. This enables the utilization of HAS with conventional GNSS receivers and PPP engines that lack native support for HAS formats. For instance, the outputs from HASlib enable the use of HAS corrections in RTKLIB. In order to validate this integration, we demonstrate that HAS can allow decimeter-level accuracy using only free-of-charge services and tools. We have obtained a 3D root mean square error below 20 cm (1 sigma) after a convergence time of 10–90 min in Finland. This accuracy has overcome classical real-time solutions with broadcast and satellite-based augmentation system (SBAS) data by one order of magnitude. Compared to post-processed multi-GNSS PPP, HAS corrections required longer convergence times, given the real-time nature. Furthermore, our assessment revealed that the longer convergence time, compared to prior literature, was attributed to RTKLIB filtering procedure and geometry deficiencies in high latitudes. Nevertheless, once convergence was attained, a sub-decimeter level of accuracy was observed in both horizontal and vertical components. These findings highlight the effectiveness of Galileo HAS, HASlib, and RTKLIB as powerful tools for providing open-access to real-time PPP solutions.

Assessment of Multi-GNSS RT-PPP Services for the Antarctic Region

The international service that ensures access to data and products of global navigation satellite systems (GNSSs), known as the IGS, runs a real-time service (RTS) project to support users who need real-time access to precise products. Thanks to the RTS project, it is now possible to obtain real-time precise point positioning (RT-PPP) solutions. RT-PPP can be used in many real-time positioning applications that require a high level of accuracy, efficiency, and flexibility, including earth sciences, atmosphere sciences, marine sciences, natural hazards, and many more. In this study, we tested the impact of different worldwide RTS products and satellite configurations on the performance of RT-PPP accuracy, as well as convergence time, in the Antarctic’s challenging environment and extreme atmospheric conditions. We applied RT-PPP solutions using real-time precise products (satellite orbit/clock corrections, and biases to conduct the real-time PPP) provided by the IGS and NAVCAST (a real-time PPP positioning service) based on different GNSS constellations: GPS-only, Galileo-only, and a combination of GPS and Galileo. In this way, the performance of two different real-time (RT) services was compared with each other. At the same time, the effectiveness of the Galileo global navigation satellite system for RT-PPP was also tested, and the Galileo system’s contribution to the GPS-only RT-PPP solution was investigated. The PPP-WIZARD software was used to process the corrections and GNSS data from a reference station in the Antarctic region. Although GPS-only, Galileo-only, and multi-GNSS solutions obtained from both RT services were found to have very close accuracy to each other, the combination of the GPS and Galileo systems produced better accuracy than when using the GPS system alone. According to the numerical results of this study, it was concluded that the real-time PPP technique gave promising results in such a challenging environment of the Antarctic region. However, we also observe that the RT-PPP technique requires a stable and robust internet connection, which might limit its usefulness in remote regions. Overall, we found the RT-PPP technique to be a viable alternative to conventional relative GNSS positioning techniques, especially in areas where continuously operating reference networks or similar networks are lacking.

Low-Cost GNSS and Real-Time PPP: Assessing the Precision of the u-blox ZED-F9P for Kinematic Monitoring Applications

With the availability of low-cost, mass-market dual-frequency GNSS (Global Navigation Satellite System) receivers, standalone processing methods such as Precise Point Positioning (PPP) are no longer restricted to geodetic-grade GNSS equipment only. However, with cheaper equipment, data quality is expected to degrade. This same principle also affects low-cost GNSS antennas, which usually suffer from poorer multipath mitigation and higher antenna noise compared to their geodetic-grade counterparts. This work assesses the quality of a particular piece of low-cost GNSS equipment for real-time PPP and high-rate dynamic monitoring applications, such as strong-motion seismology. We assembled the u-blox ZED-F9P chip in a small and light-weight data logger. With observational data from static experiments—which are processed under kinematic conditions—we assess the precision and stability of the displacement estimates. We tested the impact of different multi-band antenna types, including geodetic medium-grade helical-type (JAVAD GrAnt-G3T), as well as a low-cost helical (Ardusimple AS-ANT2B-CAL) and a patch-type (u-blox ANN-MB) antenna. Besides static tests for the assessment of displacement precision, strong-motion dynamic ground movements are simulated with a robot arm. For cross-validation, we collected measurements with a JAVAD SIGMA G3T geodetic-grade receiver. In terms of precision, we cross-compare the results of three different dual-frequency, real-time PPP solutions: (1) an ambiguity-float solution using the Centre National d’Études Spatiales (CNES) open-source software, (2) an ambiguity-float and an AR (ambiguity-resolved) solution using the raPPPid software from TU Vienna, and (3) and a PPP-RTK solution using the u-blox PointPerfect positioning service. We show that, even with low-cost GNSS equipment, it is possible to obtain a precision of one centimeter. We conclude that these devices provide an excellent basis for the densification of existing GNSS monitoring networks, as needed for strong-motion seismology and earthquake-early-warning.

Multi-GNSS products and services at iGMAS Wuhan Innovation Application Center: strategy and evaluation

Over the past years the International Global Navigation Satellite System (GNSS) Monitoring and Assessment System (iGMAS) Wuhan Innovation Application Center (IAC) dedicated to exploring the potential of multi-GNSS signals and providing a set of products and services. This contribution summarizes the strategies, achievements, and innovations of multi-GNSS orbit/clock/bias determination in iGMAS Wuhan IAC. Both the precise products and Real-Time Services (RTS) are evaluated and discussed. The precise orbit and clock products have comparable accuracy with the precise products of the International GNSS Service (IGS) and iGMAS. The multi-frequency code and phase bias products for Global Positioning System (GPS), BeiDou Navigation Satellite System (BDS), Galileo navigation satellite system (Galileo), and GLObal NAvigation Satellite System (GLONASS) are provided to support multi-GNSS and multi-frequency Precise Point Positioning (PPP) Ambiguity Resolution (AR). Compared with dual-frequency PPP AR, the time to first fix of triple-frequency solution is improved by 30%. For RTS, the proposed orbit prediction strategy improves the three dimensional accuracy of predicted orbit by 1 cm. The multi-thread strategy and high-performance matrix library are employed to accelerate the real-time orbit and clock determination. The results with respect to the IGS precise products show the high accuracy of RTS orbits and clocks, 4–9 cm and 0.1–0.2 ns, respectively. Using real-time satellite corrections, real-time PPP solutions achieve satisfactory performance with horizontal and vertical positioning errors within 2 and 4 cm, respectively, and convergence time of 16.97 min.

Farklı troposfer modellerinin gerçek zamanlı çoklu-GNSS PPP performansına etkisi

With the initialization of IGS (International GNSS Service) real-time service products, real-time Precise Point Positioning (PPP) applications have been a popular topic within the GNSS (Global Navigation Satellite Systems) users. The impact of the troposphere on GNSS signals is one of the most crucial error sources regarding the real-time PPP solution. In the PPP technique, the dry component of tropospheric delay is usually corrected by means of empirical models, while its wet component is estimated as an unknown parameter in the adjustment process. Hence, the troposphere model employed in the PPP solution has a considerable impact on the performance of the obtained solution. Therefore, the main objective of this study is to investigate the impact of different troposphere models on the performance of real-time multi-GNSS PPP. As a part of this study, four different troposphere models, where Saastamoinen and Hopfield models that are most frequently used in GNSS solutions are used together with GPT (Global Pressure and Temperature) 2 and 3 models separately, were constituted. In this context, the observation dataset acquired from a total of 16 different IGS stations over a ten-day period of December 19-28, 2021, were processed utilizing four different troposphere models. In addition to the positioning performance, PPP solutions were also analyzed in terms of zenith total delay (ZTD) estimation. The results show that the best positioning performance can be obtained when the Saastamoinen model is used in combination with GPT3. The three-dimensional positioning accuracy acquired from the corresponding solution is 2.72 cm, which is better than the closest solution by a ratio of 9.2%. Besides, in terms of the ZTD estimation, the best performance is achieved again in the case when the Saastamoinen model is used in combination with GPT3. For the related solution, the accuracy of ZTD estimation is calculated as 1.24 cm and this value indicates a better performance by a ratio of 10.2% compared with the closest solution.

Improved Mitigation Method for the Multipath Delays of BDS-3 Code Observations with the Aid of a Sparse Modeling Algorithm

Global navigation satellite systems are essential for positioning, navigation, and timing services. The quality and reliability of satellite observations determine the system performance, especially in the case of the newly launched global BDS-3 service. However, analyses of multipath delays in BDS-3 satellite observations suggest that there are appreciable errors at different frequencies. Improvement of the accuracy and precision of positioning, navigation, and timing services provided by BDS-3 requires the mitigation of multipath delays of the satellite observations. This paper models the multipath delays of BDS-3 observations using a least-squares combined autoregressive method. Furthermore, a sparse modeling algorithm is proposed to obtain a multipath delay series using total variation and elastic net terms for denoising and eliminating the effect of limited original observations. The estimated coefficients of multipath delays are then set as prior information to correct the next-arc code observations, where the square-root information filter is used in the coefficient estimation. Moreover, four groups of experiments are conducted to analyze the results of modeling the BDS-3 multipath delay using the proposed methods, with single-frequency precise point positioning (PPP) and real-time PPP solutions being selected to test the correction of multipath delays in BDS-3 code observations. The residuals of iGMAS and MGEX station coordinates indicate improvements in eastward, northward, and upward directions of at least 4.1%, 9.6%, and 1.2%, respectively, for the frequency B1I; 6.6%, 5.3%, and 0.2%, respectively, for B3I, 12.5%, 14.3%, and 3.8%, respectively, for B1C; and 5.9%, 7.4%, and 18.1%, respectively, for B2a relative to the use of the traditional method in BDS-3 single-frequency PPP. Furthermore, the real-time double-frequency PPP is optimized by at least 10% for B 1 I + B 3 I and B 1 C + B 2 a . An improved result was obtained with the proposed strategy in a standard point positioning experiment. The proposed multipath delay mitigation method is therefore effective in improving BDS-3 satellite code observations.

Retrieving Precipitable Water Vapor from Real-Time Precise Point Positioning Using VMF1/VMF3 Forecasting Products

Real-time precise point positioning (RT-PPP) has become a powerful technique for the determination of the zenith tropospheric delay (ZTD) over a GPS (global positioning system) or GNSS (global navigation satellite systems) station of interest, and the follow-on high-precision retrieval of precipitable water vapor (PWV). The a priori zenith hydrostatic delay (ZHD) and the mapping function used in the PPP approach are the two factors that could affect the accuracy of the PPP-based ZTD significantly. If the in situ atmospheric pressure is available, the Saastamoinen model can be used to determine ZHD values, and the model-predicted ZHD results are of high accuracy. However, not all GPS/GNSS are equipped with an in situ meteorological sensor. In this research, the daily forecasting ZHD and mapping function values from VMF1 forecasting (VMF1_FC) and VMF3 forecasting (VMF3_FC) products were used for the determination of the GPS-derived PWV. The a priori ZHDs derived from VMF1_FC and VMF3_FC were first evaluated by comparing against the reference ZHDs from globally distributed radiosonde stations. GPS observations from 41 IGS stations that have co-located radiosonde stations during the period of the first half of 2020 were used to test the quality of GPS-ZTD and GPS-PWV. Three sets of ZTDs estimated from RT-PPP solutions using the a priori ZHD and mapping function from the following three VMF products were evaluated: (1) VMF1_FC; (2) VMF3_FC (resolution 5° × 5°); (3) VMF3_FC (resolution 1° × 1°). The results showed that, when the ZHDs from 443 globally distributed radiosonde stations from 1 July 2018 to 30 June 2021 were used as the reference, the mean RMSEs of the ZHDs from the three VMF products were 5.9, 5.4, and 4.3 mm, respectively. The ZTDs estimated from RT-PPP at 41 selected IGS stations were compared with those from IGS, and the results showed that the mean RMSEs of the ZTDs of the 41 stations from the three PPP solutions were 8.6, 9.0, and 8.6 mm, respectively, and the mean RMSEs of the PWV converted from their corresponding ZWDs were 1.9, 2.4, and 1.7 mm, respectively, in comparison with the reference PWV from co-located radiosonde stations. The results suggest that the a priori ZHD and mapping function from VMF1_FC and VMF3_FC can be used for the precise determination of real-time GPS/GNSS-PWV in most regions, especially the VMF3_FC (resolution 1° × 1°) product.

An analysis of BDS-3 real-time PPP: Time transfer, positioning, and tropospheric delay retrieval

With the development of China’s BDS-3, more studies focused on its performance in precise point positioning (PPP), mainly in post-processing mode. This study conducts a comprehensive investigation of BDS-3 real-time PPP with Centre National d’Etudes Spatiales (CNES) real-time products (SSRA00CNE0) from the perspective of time transfer, positioning, and tropospheric delay retrieval. First, the availability and accuracy of BDS-3 real-time products were evaluated over 41 days. The product availability was about 80%. The accuracy of BDS-3 satellite orbit were 0.060, 0.115 and 0.065 m in the radial, along-track, and cross-track component. In addition, the standard deviation (STD) of satellite clock difference was 0.455 ns. Afterwards, precise time transfer, positioning, and Zenith troposphere delay (ZTD) estimation derived from BDS-3 real-time PPP were assessed with 7-day processing. The root mean square (RMS) of smoothed residuals is 0.020 ns, while it is 0.001 ns for BDS-3 PPP with WUM final products for time transfer. Furthermore, the RMS values of positioning errors derived from real-time static BDS-3 PPP positioning were 0.021, 0.010, and 0.03 m in the east (E), north (N), and up (U) component, respectively. Moreover, the RMS of ZTD estimation is 9.9 mm, which is comparable to GPS real-time PPP solutions.

One-step correction strategy for BDS-2/BDS-3 satellite observation code bias and multipath delay

Global navigation satellite systems and positioning, navigation, and timing services, such as the newly developed BeiDou satellite system (BDS), require high-accuracy satellite observations. Satellite-induced code bias is present in BDS-2 satellite observations while it is negligibly present in BDS-3 satellite observations. The traditional method of mitigating BDS code bias involves two steps, first addressing multipath delay and then code bias, and does not obtain optimal results. A one-step strategy is therefore proposed to model and eliminate code bias and multipath delay considering BDS-2 and BDS-3 integrated processing. A combined least-square and autoregressive strategy is selected to estimate the model coefficients of code bias and construct the multipath delay with one solution. Moreover, inter-satellite correlations of BDS-2 and BDS-3 are extracted to improve the weight matrix in the estimation of model coefficients. To verify the proposed strategy, experiments are designed for eight schemes to analyze the coefficients and residuals of modelling code bias. Experimental results indicate that a more stable and accurate code bias model is acquired by introducing inter-satellite correlation; with the one-step strategy, the model residuals are reduced and a more optimal code bias model is output. Meanwhile, the single-frequency precise point positioning (PPP) and real-time PPP of BDS-2 and BDS-3 combined estimations are tested for different stations, frequencies, and code bias models. The results of final positions reveal that accuracy in the Up (U) direction is improved compared with that in the East (E) and North (N) directions; improvements are greater for B1I than for B3I. In general, the one-step strategy enhances the precision of single-frequency (B1I/B3I) PPP, especially in the U direction. However, the effects on BDS ultra-rapid orbit determination are negligible. Equally, the double-frequency real-time PPP solution is improved, compared with adopting the traditional method, by 10.6–64.9%, 0.0–59.1%, and 12.6–67.2% for E, N, and U directions, respectively, through BDS-2/BDS-3 integrated processing. The proposed one-step strategy therefore outperforms the two-step strategy in terms of rapidly processing high-precision BDS observations.

Investigation of real-time carrier phase time transfer using current multi-constellations

Real-time precise point positioning (RTPPP) time transfer has grown up to be a research hotspot. With the operation of IGS real-time products, multi-GNSS RTPPP time transfer has become possible. In our work, CLK93 products are applied for RTPPP time transfer, and the availability and accuracy of real-time products is evaluated over a testing period of 31 days. Then, GPS, Galileo, GLONASS and multi-GNSS RTPPP time transfer are studied and analyzed by performing a 31-day processing with 28 time-links. The results show that the availability of GPS, GLONASS and Galileo are approximately 98%, 99% and 99%, respectively. The mean root mean square (RMS) values of Radial (R), Along (A) and Cross (C) direction for GPS, GLONASS and Galileo satellites are (0.025, 0.035, 0.027) m, (0.025, 0.073, 0.048) m and (0.029, 0.040, 0.035) m, respectively. The mean standard deviation (STD) values of GPS, GLONASS and Galileo satellites are (0.12, 0.38, 0.09) ns. Furthermore, Galileo RTPPP time transfer solutions perform better than GLONASS, and GPS RTPPP show performs best performance among the single-GNSS. Multi-GNSS RTPPP outperforms that of single-GNSS. The mean daily STD values of the difference between GPS, Galileo, GLONASS and multi-GNSS RTPPP solutions and IGS final products are (0.093, 0.103, 0.133, 0.083) ns, respectively. 15360 s stability is (3.87E−15, 4.56E−15, 8.61E−15, 3.73E−15) for GPS, Galileo, GLONASS and multi-GNSS RTPPP solutions at PT11-PTBB.

Precise Point Positioning Using World's First Dual-Frequency GPS/GALILEO Smartphone.

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.

Evaluation of the GPS Precise Orbit and Clock Corrections from MADOCA Real-Time Products.

The Japanese Quasi-Zenith Satellite System (QZSS) is a regional navigation satellite system covering the entire Asia-Oceania region. Except for the standard satellite navigation signals, QZSS satellites also broadcast L6E augmentation signals with real time GNSS precise orbit every 30 s and clock messages every 1 s, which is very important and necessary for Real-Time precise point positioning (RTPPP) applications. In this paper, the MADOCA real-time services derived from L6E augmentation signals were evaluated for both accuracy and availability compared with IGS final products. To avoid the datum difference of GPS orbit between MADOCA real-time and IGS final products, the 7-parameters Helmert transformation was firstly used in this paper, and then the orbit was evaluated on radial, along, and cross-track directions. On the clock evaluation, the mean satellites clock errors were taken as reference clock error, and then the standard deviation (STD) was calculated for each satellite. Furthermore, the signal in space range errors (SISRE) were also summarized to evaluate the ranging-measurement accuracy. Seven-day evaluation results show that satellite orbit, clock errors, and the final SISRE errors range as being 1.8–3.9 cm, 0.04–0.15 ns (1.2–4.5 cm), and 5–10 cm, respectively. For the one-year long-term evaluation, daily SISRE errors in 2018 show consistent performance with that of seven days. Furthermore, the open source software RTKLIB was used to evaluate the kinematic PPP performance based on the MADOCA real-time products, and it shows that the daily positioning accuracy of the 20 globally distributed IGS stations can reach 4.9, 4.2, 11.7, and 12.1 cm in the east, north, up, and 3D directions, respectively. Hence, it is concluded that the current MADOCA real-time ephemeris products can provide orbit and clock products with SISRE on centimeters level with high interval, which could meet the demands of the RTPPP solution and serve real-time users who can access the MADOCA real-time products via L6E signal or internet.

Enhancing real-time precise point positioning time and frequency transfer with receiver clock modeling

Thanks to the international GNSS service (IGS), which has provided an open-access real-time service (RTS) since 2013, real-time precise point positioning (RT-PPP) has become a major topic in the time community. Currently, a few scholars have studied RT-PPP time transfer, and the correlation of the receiver clock offsets between adjacent epochs have not been considered. We present a receiver clock offset model that considers the correlation of the receiver clock offsets between adjacent epochs using an a priori value. The clock offset is estimated using a between-epoch constraint model rather than a white noise model. This approach is based on two steps. First, the a priori noise variance is based on the Allan variance of the receiver clock offset derived from GPS PPP solutions with IGS final products. Second, by applying the between-epoch constraint model, the RT-PPP time transfer is achieved. Our numerical analyses clarify how the approach performs for RT-PPP time and frequency transfer. Based on five commonly used RTS products and six IGS stations, two conclusions are obtained straightforwardly. First, all RT-PPP solutions with different real-time products are capable of time transfer. The standard deviation (STD) values of the clock difference between the PPP solutions with respect to the IGS final clock products are less than 0.3 ns. Second, the STD values are reduced significantly by applying our approach. The reduction percent of STD values ranges from 4.0 to 35.5%. Moreover, the largest improvement ratio of frequency stability is 12 as compared to the solution of the white noise model. Note that the receiver clock offset from IGS final clock products is regarded as a reference.

Impact of multi-constellation products and ambiguity resolution in Precise Point Positioning for real-time measurements

Abstract Precise Point Positioning (PPP) has revolutionized Global Navigation Satellite Systems (GNSS) processing. This computation method achieves precise positioning with a single receiver and un-differenced observations. Its conceptual basis consists of solving the position with pseudo-range and carrier-phase GNSS measurements, with the application of external clock and orbit satellite corrections, previously estimated signal biases and atmospheric models computed in the International GNSS Service or Analysis Centers. However, in the case study of real-time PPP, the computation engine requires continuous streams of products that must meet certain availability requirements. In a case study of real-time measurements the technique is very sensitive to outliers in products and changes in the constellation geometry. As a result, there are long initialization periods, losses of convergence and a lack of accuracy in the results. This study shows how multi-constellation approaches for external products reduce loss of convergence and outliers in the real-time PPP solutions and also highlights the impact that ambiguity resolution has.

Rapid initialization of real-time PPP by resolving undifferenced GPS and GLONASS ambiguities simultaneously

Rapid initialization of real-time precise point positioning (PPP) has constantly been a difficult problem. Recent efforts through multi-GNSS and multi-frequency data, though beneficial indeed, have not proved sufficiently effective in reducing the initialization periods to far less than 10 min. Though this goal can be easily reached by introducing ionosphere corrections as accurate as a few centimeters, a dense reference network is required which is impractical for wi de-area applications. Leveraging the latest development of GLONASS PPP ambiguity resolution (PPP-AR) technique, we propose a composite strategy, where simultaneous GPS and GLONASS dual-frequency PPP-AR is carried out, and herein, the reliability of partial AR improves dramatically. We used 14 days of data from a German network and divided them into hourly data to test this strategy. We found that the initialization periods were shortened drastically from over 25 min when only GPS data were processed to about 6 min when GPS and GLONASS PPP-AR were accomplished simultaneously. More encouragingly, over 50% of real-time PPP solutions could be initialized successfully within 5 min through our strategy, in contrast to only 4% when only GPS data were used. We expect that our strategy can provide a promising route to overcoming the difficulty of achieving PPP initializations within a few minutes.

Precise Point Positioning Using Triple GNSS Constellations in Various Modes.

This paper introduces a new dual-frequency precise point positioning (PPP) model, which combines the observations from three different global navigation satellite system (GNSS) constellations, namely GPS, Galileo, and BeiDou. Combining measurements from different GNSS systems introduces additional biases, including inter-system bias and hardware delays, which require rigorous modelling. Our model is based on the un-differenced and between-satellite single-difference (BSSD) linear combinations. BSSD linear combination cancels out some receiver-related biases, including receiver clock error and non-zero initial phase bias of the receiver oscillator. Forming the BSSD linear combination requires a reference satellite, which can be selected from any of the GPS, Galileo, and BeiDou systems. In this paper three BSSD scenarios are tested; each considers a reference satellite from a different GNSS constellation. Natural Resources Canada’s GPSPace PPP software is modified to enable a combined GPS, Galileo, and BeiDou PPP solution and to handle the newly introduced biases. A total of four data sets collected at four different IGS stations are processed to verify the developed PPP model. Precise satellite orbit and clock products from the International GNSS Service Multi-GNSS Experiment (IGS-MGEX) network are used to correct the GPS, Galileo, and BeiDou measurements in the post-processing PPP mode. A real-time PPP solution is also obtained, which is referred to as RT-PPP in the sequel, through the use of the IGS real-time service (RTS) for satellite orbit and clock corrections. However, only GPS and Galileo observations are used for the RT-PPP solution, as the RTS-IGS satellite products are not presently available for BeiDou system. All post-processed and real-time PPP solutions are compared with the traditional un-differenced GPS-only counterparts. It is shown that combining the GPS, Galileo, and BeiDou observations in the post-processing mode improves the PPP convergence time by 25% compared with the GPS-only counterpart, regardless of the linear combination used. The use of BSSD linear combination improves the precision of the estimated positioning parameters by about 25% in comparison with the GPS-only PPP solution. Additionally, the solution convergence time is reduced to 10 minutes for the BSSD model, which represents about 50% reduction, in comparison with the GPS-only PPP solution. The GNSS RT-PPP solution, on the other hand, shows a similar convergence time and precision to the GPS-only counterpart.