Between-satellite Single-difference Research Articles

Land Vehicle Navigation Using Low-Cost Integrated Smartphone GNSS Mems and Map Matching Technique

Abstract The demand for smartphone positioning has grown rapidly due to increased positioning accuracy applications, such as land vehicle navigation systems used for vehicle tracking, emergency assistance, and intelligent transportation systems. The integration between navigation systems is necessary to maintain a reliable solution. High-end inertial sensors are not preferred due to their high cost. Smartphone microelectromechanical systems (MEMS) are attractive due to their small size and low cost; however, they suffer from long-term drift, which highlights the need for additional aiding solutions using road network that can perform efficiently for longer periods. In this research, the performance of the Xiaomi MI 8 smartphone’s single-frequency precise point positioning was tested in kinematic mode using the between-satellite single-difference (BSSD) technique. A Kalman filter algorithm was used to integrate BSSD and inertial navigation system (INS)-based smartphone MEMS. Map matching technique was proposed to assist navigation systems in global navigation satellite system (GNSS)-denied environments, based on the integration of BSSD–INS and road network models applying hidden Marcov model and Viterbi algorithm. The results showed that BSSD–INS–map performed consistently better than BSSD solution and BSSD–INS integration, irrespective of whether simulated outages were added or not. The root mean square error (RMSE) values for 2D horizontal position accuracy when applying BSSD–INS–map integration improved by 29% and 22%, compared to BSSD and BSSD–INS navigation solutions, respectively, with no simulated outages added. The overall average improvement of proposed BSSD–INS–map integration was 91%, 96%, and 98% in 2D horizontal positioning accuracy, compared to BSSD–INS algorithm for six GNSS simulated signal outages with duration of 10, 20, and 30 s, respectively.

Performance Evaluation of Triple-Frequency GPS/Galileo Techniques for Precise Static and Kinematic Applications.

The objective of this research was to develop new precise point positioning (PPP) processing models using triple-frequency GPS/Galileo observations. Different triple-frequency PPP models were developed including undifferenced, between-satellite single-difference (BSSD) and semi-decoupled PPP models. Additionally, a dual-frequency ionosphere-free undifferenced PPP model was developed. The performance of our developed PPP models was evaluated for both static and kinematic applications. To validate the proposed PPP models for static applications, triple-frequency GPS/Galileo observations spanning three successive days from eight globally distributed reference stations were acquired. Then, the observations were processed using the four static PPP solutions. It is found that the 3D positioning accuracy of the triple-frequency semi-decoupled, BSSD and undifferenced PPP models is enhanced after 10 min by about 50, 41 and 29%, respectively, compared with the dual-frequency undifferenced PPP model. After 20 min of processing, improvements in the 3D positioning accuracy by 40, 31 and 21% are obtained for the triple-frequency semi-decoupled, BSSD and undifferenced PPP models, respectively, with respect to the dual-frequency PPP model. The 3D positioning accuracy is also improved after 60 min, compared with the dual-frequency solution, by 40, 40 and 35% for the triple-frequency semi-decoupled, BSSD and undifferenced PPP solutions, respectively. For kinematic application validation, a vehicle trajectory was carried out. The collected triple-frequency GPS/Galileo observations were processed using the four kinematic PPP solutions. It is shown that the triple-frequency semi-decupled, BSSD and undifferenced PPP solutions enhance the 3D positioning accuracy by 31, 23 and 10%, respectively, in comparison with the dual-frequency undifferenced PPP solutions.

The Application of the BSSD Iono-Free Linear Combination Method in the Processing of Aircraft Positioning

Abstract The article presents the results of research into the use of the differentiation technique of BSSD (Between Satellite Single Difference) observations for the Iono-Free LC combination (Linear Combination) in the GPS system for the needs of aircraft positioning. Within the conducted investigations, a positioning algorithm for the BSSD Iono-Free LC positioning method was presented. In addition, an experimental test was conducted, in which raw observational data and GPS navigation data were exploited in order to recover the aircraft position. The examination was conducted for the Cessna 172 and the on-board dual-frequency receiver Topcon HiperPro. The experimental test presents the results of average errors of determining the position of the Cessna 172 in the XYZ geocentric frame and in the ellipsoidal BLh frame. Furthermore, the article presents the results of DOP (Dilution of Precision) coefficients, the test of the Chi square internal reliability test and the HPL and VPL confidence levels in GNSS precision approach (PA) in air transport. The calculations were performed in the original APS software (APS Aircraft Positioning Software) developed in the Department of Air Navigation of the Faculty of Aeronautics at the Polish Air Force University.

Between-satellite single-difference integer ambiguity resolution in GPS/GNSS network solutions

In various GNSS applications with high requirements for precision, integer ambiguity resolution (IAR) is of great significance for taking full advantage of precise carrier-phase observations. Until now, there are two approaches to achieving IAR in network solutions, i.e., to resolve double-difference (DD) integer ambiguities or to resolve zero-difference (ZD) integer ambiguities. In this paper, we will present an approach to resolving between-satellite single-difference (BSSD) integer ambiguities in network solutions. BSSD ambiguity fixing can be divided into two main steps: Firstly, WL satellite FCBs are estimated to help to fix WL BSSD ambiguities and then narrow-lane (NL) BSSD ambiguity resolution is performed in a bootstrapping mode: datum BSSD ambiguities are selected and compulsorily fixed to the nearest integers and then a standard sequential fixing procedure is employed for the remaining independent BSSD ambiguities. Network solutions with GPS data from about 130 stations were conducted to validate the proposed approach. Experimental results show that the quality of satellite orbits, station coordinates and satellite clocks obtained with the new approach was almost the same as that with the DD approach. It is also shown that the new approach enjoyed slightly higher fixing ratio for both WL and NL ambiguities and was superior in computation efficiency, e.g., an improvement of 60% on average was achieved in this study. As demonstrated by experiments of precise point positioning (PPP) with 30-min data, satellite clocks achieved with the new approach have the ability to support IAR in PPP, just like those achieved with ZD IAR approach.

Advanced receiver autonomous integrity monitoring using triple frequency data with a focus on treatment of biases

Most current Advanced Receiver Autonomous Integrity Monitoring (ARAIM) methods are designed to use dual-frequency ionosphere-free observations. These methods assume that receiver bias is absorbed in the common receiver clock offset and bound satellite biases by nominal values. However, most multi-constellation Global Navigation Satellite Systems (GNSS) can offer triple frequency data that can be used for civilian applications in the future, which can improve observation redundancy, solution precision and detection of faults. In this contribution, we explore the use of this type of observations from GPS, Galileo and BeiDou in ARAIM. Nevertheless, the use of triple frequency data introduces receiver differential biases that have to be taken into consideration. To demonstrate the significance of these additional biases we first present a method to quantify them at stations of known coordinates and using available products from the International GNSS service (IGS). To deal with the additional receiver biases, we use a between-satellite single difference (BSSD) observation model that eliminates their effect. A pilot test was performed to evaluate ARAIM availability for Localizer Performance with Vertical guidance down to 200feet (LPV-200) when using the triple-frequency observations. Real data were collected for one month at stations of known coordinates located in regions of different satellite coverage characteristics. The BSSD triple-frequency model was evaluated to give early indication about its feasibility, where the implementation phase still requires further comprehensive studies. The vertical position error was always found to be bounded by the protection level proven initial validity of the proposed integrity model.

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.

Performance analysis of precise point positioning using multi-constellation GNSS: GPS, GLONASS, Galileo and BeiDou

We developed a new GNSS PPP model, which combines the observations of GPS, GLONASS, Galileo and BeiDou satellite navigation systems for precise applications. Both undifferenced and between-satellite single-difference (BSSD) ionosphere-free GNSS PPP models are developed. The contribution of the new GNSS observations is assessed compared with the existing GPS and GPS/GLONASS PPP using three-hours GNSS static data positioning results for several GNSS stations and four consecutive days. Inter-system biases between GPS and other GNSS systems are obtained as additional unknowns in the developed PPP filter. The results indicate that both GPS and GPS/Galileo PPP present comparable positioning accuracy level, which is attributed to the limited number of Galileo satellites. The additional BeiDou observations enhances the positioning accuracy after 15 minutes by 5 cm, 4 cm and 9 cm in latitude, longitude and altitude, respectively compared with GPS only positioning accuracy. However, the BeiDou only PPP results present less accurate positioning accuracy compared with the GPS only PPP. The multi-constellation GNSS PPP enhances the positioning accuracy by 8 cm, 6 cm and 11 cm in latitude, longitude and altitude, respectively Compared with the GPS PPP results. Compared with the undifferenced PPP results, the BSSD model enhances the positioning accuracy after 15 minutes for the different GNSS constellations based PPP. The GPS/Galileo PPP positioning accuracy improves by 30%, 27% and 10% in latitude, longitude and altitude, respectively and the GPS/BeiDou PPP positioning accuracy, enhances by 17%, 22% and 15% in latitude, longitude and altitude, respectively while the multi-constellation GNSS PPP positioning accuracy improves by 22% and 15% in latitude and altitude, respectively over the undifferenced PPP technique. Additionally, the BSSD model is found to be superior with respect to the convergence times for the different GNSS combinations based PPP over the traditional undifferenced PPP model.

Improved Between-Satellite Single-Difference Precise Point Positioning Model Using Triple GNSS Constellations: GPS, Galileo, and BeiDou

This paper introduces a new dual-frequency precise point positioning (PPP) model, which combines the observations of three different GNSS constellations, namely GPS, Galileo, and BeiDou. Our model is based on between-satellite single-difference (BSSD) linear combination, which cancels out some receiver-related biases, including receiver clock error and non-zero initial phase bias of the receiver oscillator. The reference satellite can be selected from any satellite system GPS, Galileo, and BeiDou when forming BSSD linear combinations. Natural Resources Canada’s GPS Pace 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 at four IGS stations are processed to verify the developed PPP model. Precise satellite orbit and clock products from the IGS-MGEX network are used to correct both of the GPS and Galileo measurements. It is shown that using the BSSD linear combinations improves the precision of the estimated parameters by about 25% compared with the GPS-only PPP solution. Additionally, the solution convergence time is reduced to 10 minutes for both BSSD scenarios, which represent about 50% improvement in comparison with the GPS-only PPP solution.

Performance Analysis of Several GPS/Galileo Precise Point Positioning Models

This paper examines the performance of several precise point positioning (PPP) models, which combine dual-frequency GPS/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. We take advantage of the IGS-MGEX network products to correct for the satellite differential code biases and the orbital and satellite clock errors. Natural Resources Canada’s GPSPace PPP software is modified to handle the various GPS/Galileo PPP models. A total of six data sets of GPS and Galileo observations at six IGS stations are processed to examine the performance of the various PPP models. It is shown that the traditional un-differenced GPS/Galileo PPP model, the GPS decoupled clock model, and the semi-decoupled clock GPS/Galileo PPP model improve the convergence time by about 25% in comparison with the un-differenced GPS-only 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 precision of the estimated parameters by about 50% and 25% when the loose and the tight combinations are used, respectively, in comparison with the un-differenced GPS-only model. Comparable results are obtained through the tight combination when either a GPS or a Galileo satellite is selected as a reference.

An Improved Between-Satellite Single-Difference Precise Point Positioning Model for Combined GPS/Galileo Observations

AbstractThis article introduces a new model for precise point positioning (PPP), which combines dual-frequency GPS and Galileo observations. Our model is based on the between-satellite single-difference (BSSD) linear combination, which cancels out some receiver-related biases, including receiver clock error and non-zero initial phase bias of the receiver’s oscillator. Two different scenarios are considered when forming BSSD linear combinations. In the first scenario, either a GPS or a Galileo satellite is selected as a reference for both GPS and Galileo observables. The second scenario, on the other hand, selects two reference satellites: a GPS reference satellite for the GPS observables and a Galileo satellite for the Galileo observables. Natural Resources Canada’s GPSPace PPP software is modified to enable a combined GPS/Galileo PPP solution and to handle the newly introduced biases. A total of 12 data sets representing two-day GPS/Galileo measurements at six IGS stations are processed to verify the developed PPP model. Precise satellite orbit and clock products from the IGS-MGEX network are used to correct both of the GPS and Galileo measurements. It is shown that using one reference satellite to form the BSSD linear combinations improves the precision of the estimated parameters by about 25 % compared with the GPS-only PPP solution. When two reference satellites are used, however, the precision of the estimated parameters improves by about 50 % compared with the GPS-only PPP solution. Additionally, the solution convergence time is reduced to 10 min for both BSSD scenarios, which represents about 50 % improvement in comparison with the GPS-only PPP solution.

An Improved Model for Single-Frequency GPS/GALILEO Precise Point Positioning

This paper introduces a new precise point positioning (PPP) model, which combines single-fre- quency GPS/Galileo observations in between-satellite single-difference (BSSD) mode. In the absence of multipath, all receiver-related errors and biases are cancelled out when forming BSSD for a specific constellation. This leaves the satellite originating errors and atmospheric delays un- modelled. Combining GPS and Galileo observables introduces additional biases that have to be modelled, including the GPS to Galileo time offset (GGTO) and the inter-system bias. This paper models all PPP errors rigorously to improve the single-frequency GPS/Galileo PPP solution. GPSPace PPP software of Natural Resources Canada (NRCan) is modified to enable a GPS/Galileo PPP solution and to handle the newly introduced biases. A total of 12 data sets representing the GPS/Galileo measurements of six IGS-MEGX stations are processed to verify the newly developed PPP model. Precise satellite orbit and clock corrections from IGS-MEGX networks are used for both GPS and Galileo measurements. It is shown that sub-decimeter level accuracy is possible with single-frequency GPS/Galileo PPP. In addition, the PPP solution convergence time is improved from approximately 100 minutes for the un-differenced single-frequency GPS/Galileo solution to approximately 65 minutes for the BSSD counterpart when a single reference satellite is used. Moreover, an improvement in the PPP solution convergence time of 35% and 15% is obtained when one and two reference satellites are used, respectively.

Multiple Ambiguity Datum Precise Point Positioning Technique Using Multi-Constellation GNSS: GPS, GLONASS, Galileo and BeiDou

Precise Point Positioning (PPP) is traditionally based on dual-frequency observations of GPS or GPS/GLONASS satellite navigation systems. Recently, new GNSS constellations, such as the European Galileo and the Chinese BeiDou are developing rapidly. With the new IGS project known as IGS MGEX which produces highly accurate GNSS orbital and clock products, multi-constellations PPP becomes feasible. On the other hand, the un-differenced ionosphere-free is commonly used as standard precise point positioning technique. However, the existence of receiver and satellite biases, which are absorbed by the ambiguities, significantly affected the convergence time. Between-satellite-single-difference (BSSD) ionosphere free PPP technique is traditionally used to cancel out the receiver related biases from both code and phase measurements. This paper introduces multiple ambiguity datum (MAD) PPP technique which can be applied to separate the code and phase measurements removing the receiver and satellite code biases affecting the GNSS receiver phase clock and ambiguities parameters. The mathematical model for the three GNSS PPP techniques is developed by considering the current full GNSS constellations. In addition, the current limitations of the GNSS PPP techniques are discussed. Static post-processing results for a number of IGS MGEX GNSS stations are presented to investigate the contribution of the newly GNSS system observations and the newly developed GNSS PPP techniques and its limitations. The results indicate that the additional Galileo and BeiDou observations have a marginal effect on the positioning accuracy and convergence time compared with the existence combined GPS/GLONASS PPP. However, reference to GPS PPP, the contribution of BeiDou observations can be considered geographically dependent. In addition, the results show that the BSSD PPP models slightly enhance the convergence time compared with other PPP techniques. However, both the standard un-differenced and the developed multiple ambiguity datum techniques present comparable positioning accuracy and convergence time due to the lack of code and phase-based satellite clock products and the mathematical correlation between the positioning and ambiguity parameters.

Integration of Multi-Constellation GNSS Precise Point Positioning and MEMS-Based Inertial Systems Using Tightly Coupled Mechanization

We develop a new integrated navigation system, which integrates multi-constellations GNSS precise point positioning (PPP), including GPS, GLONASS and Galileo, with low-cost micro-electro-mechanical sensor (MEMS) inertial system, for precise positioning applications. To integrate GNSS and the MEMS-based inertial system, the process and measurement models are developed. Tightly coupled mechanism is adopted, which is carried out in the GNSS raw measurements domain. Both un-differenced and between-satellite single-difference (BSSD) ionosphere-free linear combinations of pseudorange and carrier phase GNSS measurements are processed. Rigorous models are employed to correct GNSS errors and biases. The GNSS inter-system biases are considered as additional unknowns in the integrated error state vector. The developed stochastic model for inertial sensors errors and biases are defined based on first order Gaussian Markov process. Extended Kalman filter is developed to integrate GNSS and inertial measurements and estimate inertial measurements biases and errors. Two field experiments are executed, which represent different real-world scenarios in land-based navigation. The data are processed by using our developed Ryerson PPP GNSS/MEMS software. The results indicate that the proposed integrated system achieves decimeter to centimeter level positioning accuracy when the measurement updates from GNSS are available. During complete GNSS outages the developed integrated system continues to achieve decimeter level accuracy for up to 30 seconds while it achieves meter-level accuracy when a 60-second outage is introduced.

Precise Point Positioning using Multi-Constellation GNSS Observations for Kinematic Applications

AbstractTraditional precise point positioning (PPP) is commonly based on un-differenced ionosphere-free linear combination of Global Positioning System (GPS) observations. Unfortunately, for kinematic applications, GPS often experiences poor satellite visibility or weak satellite geometry in urban areas. To overcome this limitation, we developed a PPP model, which combines the observations of three global navigation satellite systems (GNSS), namely GPS, GLONASS and Galileo. Both un-differenced and between-satellite single-difference (BSSD) ionosphere-free linear combinations of pseudorange and carrier phase GNSS measurements are processed. The performance of the combined GNSS PPP solution is compared with the GPS-only PPP solution using a real test scenario in downtown Kingston, Ontario. Inter-system biases between GPS and the other two systems are also studied and obtained as a byproduct of the PPP solution. It is shown that the addition of GLONASS observations improves the kinematic PPP solution accuracy in comparison with that of GPS-only solution. However, the contribution of adding Galileo observations is not significant due to the limited number of Galileo satellites launched up to date. In addition, BSSD solution is found to be superior to that of traditional un-differenced model.

PPP Accuracy Enhancement Using GPS/GLONASS Observations in Kinematic Mode

Commonly, kinematic PPP techniques employ un-differenced ionosphere-free linear combination of GPS observations. This, however, may not provide continuous solution in urban areas as a result of limited satellite visibility. In this paper, the traditional un-differenced as well as between-satellite single-difference (BSSD) ionosphere-free linear combinations of GPS and GLONASS measurements are developed. Except GLONASS satellite clock products, the final precise GPS and GLONASS satellites clock and orbital products obtained from the multi-GNSS experiment (MGEX) are used. The effects of ocean loading, earth tide, carrier-phase windup, sagnac, relativity, and satellite and receiver antenna phase-center variations are rigorously modeled. Extended Kalman filter (EKF) is developed to process the combined GPS/GLONASS measurements. A comparison is made between three kinematic PPP solutions, namely standalone GPS, standalone GLONASS, and combined GPS/ GLONASS solutions. In general, the results indicate that the addition of GLONASS observations improves the kinematic positioning accuracy in comparison with the standalone GPS PPP positioning accuracy. In addition, BSSD solution is found to be superior to that of the traditional un-diffe- renced model.

Tightly coupled integration of GPS precise point positioning and MEMS-based inertial systems

We develop a new integrated navigation system, which integrates GPS precise point positioning (PPP) with low-cost micro-electro-mechanical sensors (MEMS) inertial system, for precise positioning applications. Currently, most common GPS PPP techniques employ undifferenced ionosphere-free (IF) linear combination. In this work, both undifferenced and between-satellite single-difference (BSSD) IF linear combinations of pseudorange and carrier measurements are considered. IGS precise orbital and clock products are used to correct for satellite orbit and clock errors. Rigorous models are used to account for tropospheric delay, ocean loading, earth tide, carrier phase windup, relativity and satellite antenna phase-center variations. To integrate GPS PPP and MEMS-based inertial systems, the process and measurement models are developed. Tightly coupled mechanization is adopted, which is carried out in the raw measurements domain. Extended Kalman filter is developed to merge the corrected GPS satellite difference observations and inertial measurements and estimate inertial measurements biases and errors. A Matlab-based computer program is developed to carry out the tightly coupled integration. The performance of the proposed integrated system is analyzed using a real test situation. It is shown that decimeter-level positioning accuracy is achievable with both undifferenced and BSSD integrated systems. However, in general, better positioning accuracy is obtained with BSSD integrated system.

Single Frequency GPS/Galileo Precise Point Positioning Using Un-Differenced and Between-Satellite Single Difference Measurements

We develop a new precise point positioning (PPP) model for combined GPS/Galileo single-frequency observations. Both un-differenced and between-satellite single-difference (BSSD) modes are considered. Although it improves the solution availability and accuracy, combining GPS and Galileo observables introduces additional biases that must be modelled. These include the GPS-to-Galileo time offset and the inter-system bias. Additionally, to take full advantage of the Galileo E1 signal, it is essential that its stochastic characteristics are rigorously modelled. In this paper, various sets of GPS and Galileo measurements collected at two stations with short separation were used to investigate the stochastic characteristics of Galileo E1 signal. As a by-product, the stochastic characteristics of the legacy GPS P1 code were obtained and then used to verify the developed stochastic model of the Galileo signal. It is shown that sub-decimeter level accuracy is possible through our single-frequency GPS/Galileo PPP model. As well, the addition of Galileo improves the PPP solution convergence by about 30% in comparison with the GPS-only solution. Furthermore, the performance of BSSD GPS/Galileo PPP model was found comparable to that of the un-differenced counterpart.

Efficient Between-Satellite Single-Difference Precise Point Positioning Model

This paper describes a new model for precise point positioning (PPP), which overcomes the drawbacks of existing PPP models. This model is based on between-satellite single-difference (BSSD), which cancels out the receiver clock error, receiver initial phase bias, and receiver hardware delay. The decoupled clock (DC) corrections, which were provided by Natural Resources Canada (NRCan), were applied to account for code and carrier-phase satellite clock corrections, satellite hardware delay, and satellite initial phase bias. The results from three PPP models (namely, undifferenced-DC, BSSD, and BSSD-DC) were compared with the traditional (i.e., undifferenced) PPP solution. It is shown that the proposed BSSD models improves the PPP convergence time by up to 50% and improves the solution precision by more than 60% in comparison with the traditional PPP model.