scholarly journals An Improved Model For Precise Point Positioning With Modernized Glogbal Positioning System

2021 ◽  
Author(s):  
Mohamed E. Elsobeiey
Keyword(s):  
Initial Phase ◽  
Precise Point Positioning ◽  
Satellite Orbit ◽  
Second Order ◽  
Ionospheric Delay ◽  
Convergence Time ◽  
Single Difference ◽  
Phase Bias ◽  
Stochastic Characteristics ◽  
L2c Signal

Recent developments in GPS positioning show that a user with a standalone GPS receiver can obtain positioning accuracy comparable to that of carrier-phase-based differential positioning. Such a technique is commonly known as precise point positioning (PPP). A significant challenge of PPP, however, is that it typically requires a minimum of 30 minutes to achieve centimeter- to decimeter-level accuracy. This relatively long convergence time is the result of un-modeled GPS residual errors. This thesis addresses error mitigation techniques to achieve near real-time PPP. To explore the full advantage of the modernized GPS L2C signal, it is essential to determine its stochastic characteristics and code bias. GPS measurements were collected in order to study the stochastic characteristics of the modernized GPS L2C signal. As a byproduct, the stochastic characteristics of the legacy GPS signals, namely C/A and P2 codes, were also determined and then used to verify the developed stochastic model of the modernized signal. The differential code biases between P2 and C2, DCB P2-C2, were also estimated using the Bernese GPS software. A major residual error component, which affects the convergence of PPP solution, is the higherorder ionospheric delay. We rigorously modeled the second-order ionospheric delay, which represents the bulk of higher-order ionospheric delay, for our PPP model. First, we investigated the effect of second-order ionospheric delay on GPS satellite orbit and clock corrections. Second, we used the estimated satellite orbit and clock corrections to process the GPS data from several IGS stations after correcting the data for the effect of second-order ionospheric delay. The results demonstrated an improvement of up to 25% in the precision of the estimated coordinates with the second-order ionospheric delay, as well as reduction of the convergence time of the estimated parameters by about 15%, depending on the geographic location and ionospheric and geomagnetic conditions. Between-satellite single-difference PPP algorithms were developed to cancel out the receiver clock error, receiver initial phase bias, and receiver hardware delay. The decoupled clock corrections, provided by NRCan, were also applied to account for the satellite hardware delay and satellite initial phase bias. GPS data collected from several IGS stations were processed using the un-differenced model, un-differenced decoupled clock model, between-satellite singledifference (BSSD) model, and between-satellite single-difference using the decoupled clock (BSSD-DC) model. The results showed that the proposed BSSD model significantly improved the PPP convergence time by 50% and improved the solution precision by more than 60% over the traditional un-differenced PPP model.

scholarly journals An Improved Model For Precise Point Positioning With Modernized Glogbal Positioning System

2021 ◽  
Author(s):  
Mohamed E. Elsobeiey
Keyword(s):  
Initial Phase ◽  
Precise Point Positioning ◽  
Satellite Orbit ◽  
Second Order ◽  
Ionospheric Delay ◽  
Convergence Time ◽  
Single Difference ◽  
Phase Bias ◽  
Stochastic Characteristics ◽  
L2c Signal

Recent developments in GPS positioning show that a user with a standalone GPS receiver can obtain positioning accuracy comparable to that of carrier-phase-based differential positioning. Such a technique is commonly known as precise point positioning (PPP). A significant challenge of PPP, however, is that it typically requires a minimum of 30 minutes to achieve centimeter- to decimeter-level accuracy. This relatively long convergence time is the result of un-modeled GPS residual errors. This thesis addresses error mitigation techniques to achieve near real-time PPP. To explore the full advantage of the modernized GPS L2C signal, it is essential to determine its stochastic characteristics and code bias. GPS measurements were collected in order to study the stochastic characteristics of the modernized GPS L2C signal. As a byproduct, the stochastic characteristics of the legacy GPS signals, namely C/A and P2 codes, were also determined and then used to verify the developed stochastic model of the modernized signal. The differential code biases between P2 and C2, DCB P2-C2, were also estimated using the Bernese GPS software. A major residual error component, which affects the convergence of PPP solution, is the higherorder ionospheric delay. We rigorously modeled the second-order ionospheric delay, which represents the bulk of higher-order ionospheric delay, for our PPP model. First, we investigated the effect of second-order ionospheric delay on GPS satellite orbit and clock corrections. Second, we used the estimated satellite orbit and clock corrections to process the GPS data from several IGS stations after correcting the data for the effect of second-order ionospheric delay. The results demonstrated an improvement of up to 25% in the precision of the estimated coordinates with the second-order ionospheric delay, as well as reduction of the convergence time of the estimated parameters by about 15%, depending on the geographic location and ionospheric and geomagnetic conditions. Between-satellite single-difference PPP algorithms were developed to cancel out the receiver clock error, receiver initial phase bias, and receiver hardware delay. The decoupled clock corrections, provided by NRCan, were also applied to account for the satellite hardware delay and satellite initial phase bias. GPS data collected from several IGS stations were processed using the un-differenced model, un-differenced decoupled clock model, between-satellite singledifference (BSSD) model, and between-satellite single-difference using the decoupled clock (BSSD-DC) model. The results showed that the proposed BSSD model significantly improved the PPP convergence time by 50% and improved the solution precision by more than 60% over the traditional un-differenced PPP model.

On Modelling of Second-Order Ionospheric Delay for GPS Precise Point Positioning

2011 ◽  
Vol 65 (1) ◽  
pp. 59-72 ◽  
Author(s):  
Mohamed Elsobeiey ◽  
Ahmed El-Rabbany
Keyword(s):  
Precise Point Positioning ◽  
Higher Order ◽  
Second Order ◽  
Ionospheric Delay ◽  
Convergence Time ◽  
Electron Content ◽  
Data Sets ◽  
Satellite Clock ◽  
Precise Orbit ◽  
Point Positioning

Recent developments in GPS positioning show that a user with a standalone GPS receiver can obtain positioning accuracy comparable to that of carrier-phase-based differential positioning. Such technique is commonly known as Precise Point Positioning (PPP). A significant challenge of PPP, however, is that about 30 minutes or more is required to achieve centimetre to decimetre-level accuracy. This relatively long convergence time is a result of the un-modelled GPS residual errors. A major residual error component, which affects the convergence of PPP solution, is higher-order Ionospheric Delay (IONO). In this paper, we rigorously model the second-order IONO, which represents the bulk of higher-order IONO, for PPP applications. Firstly, raw GPS measurements from a global cluster of International GNSS Service (IGS) stations are corrected for the effect of second-order IONO. The corrected data sets are then used as input to the Bernese GPS software to estimate the precise orbit, satellite clock corrections, and Global Ionospheric Maps (GIMs). It is shown that the effect of second-order IONO on GPS satellite orbit ranges from 1·5 to 24·7 mm in radial, 2·7 to 18·6 mm in along-track, and 3·2 to 15·9 mm in cross-track directions, respectively. GPS satellite clock corrections, on the other hand, showed a difference of up to 0·067 ns. GIMs showed a difference up to 4·28 Total Electron Content Units (TECU) in the absolute sense and an improvement of about 11% in the Root Mean Square (RMS). The estimated precise orbit clock corrections have been used in all of our PPP trials. NRCan's GPSPace software was modified to accept the second-order ionospheric corrections. To examine the effect of the second-order IONO on the PPP solution, new data sets from several IGS stations were processed using the modified GPSPace software. It is shown that accounting for the second-order IONO improved the PPP solution convergence time by about 15% and improved the accuracy estimation by 3 mm.

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

2015 ◽  
Vol 9 (2) ◽  
Author(s):  
Akram Afifi ◽  
Ahmed El-Rabbany
Keyword(s):  
Precise Point Positioning ◽  
Satellite Orbit ◽  
Convergence Time ◽  
Dual Frequency ◽  
Linear Combinations ◽  
Estimated Parameters ◽  
Reference Satellite ◽  
Single Difference ◽  
Point Positioning ◽  
Galileo Satellite

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.

scholarly journals Research Article. Improved Dual Frequency PPP Model Using GPS and BeiDou Observations

2017 ◽  
Vol 7 (1) ◽  
pp. 1-8 ◽  
Author(s):  
A. Afifi ◽  
A. El-Rabbany
Keyword(s):  
Precise Point Positioning ◽  
Satellite Orbit ◽  
Convergence Time ◽  
Data Sets ◽  
Dual Frequency ◽  
Research Article ◽  
Solution Convergence ◽  
Satellite Geometry ◽  
System Bias ◽  
Time Offset

AbstractThis paper introduces a new dual-frequency precise point positioning (PPP) model, which combines GPS and BeiDou observations. Combining GPS and BeiDou observations in a PPP model offers more visible satellites to the user, which is expected to enhance the satellite geometry and the overall PPP solution in comparison with GPSonly PPP solution. However, combining different GNSS constellations introduces additional biases, which require rigorous modelling, including GNSS time offset and hardware delays. In this research, ionosphere-free linear combination PPP model is developed. The additional biases, which result from combining the GPS and BeiDou observables, are lumped into a new unknown parameter identified as the inter-system bias. Natural Resources Canada’s GPSPace PPP software is modified to enable a combined GPS/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 BeiDou measurements. It is shown that a sub-decimeter positioning accuracy level and 25% reduction in the solution convergence time can be achieved with combining GPS and Bei-Dou observables in a PPP model, in comparison with the GPS-only PPP solution.

scholarly journals Performance Analysis of Several GPS/Galileo Precise Point Positioning Models

2021 ◽  
Author(s):  
Akram Afifi ◽  
Ahmed El-Rabbany
Keyword(s):  
Precise Point Positioning ◽  
Convergence Time ◽  
Data Sets ◽  
Dual Frequency ◽  
Clock Model ◽  
Solution Convergence ◽  
Single Difference ◽  
Point Positioning ◽  
Galileo Satellite ◽  
Decoupled Clock Model

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.

scholarly journals Precise Point Positioning Using Triple GNSS Constellations in Various Modes

2021 ◽  
Author(s):  
Akram Afifi ◽  
Ahmed El-Rabbany
Keyword(s):  
Linear Combination ◽  
Real Time ◽  
Precise Point Positioning ◽  
Satellite Orbit ◽  
Convergence Time ◽  
Dual Frequency ◽  
Post Processing ◽  
Time Service ◽  
Reference Satellite ◽  
Point Positioning

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.

scholarly journals An improved precise point positioning model using GPS and Galileo observations

2021 ◽  
Author(s):  
Akram Afifi
Keyword(s):  
Urban Areas ◽  
Precise Point Positioning ◽  
Satellite System ◽  
Convergence Time ◽  
Clock Model ◽  
Solution Convergence ◽  
Single Difference ◽  
Point Positioning ◽  
Time Required ◽  
Decoupled Clock Model

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.

scholarly journals Precise Point Positioning Using Triple GNSS Constellations in Various Modes

2021 ◽  
Author(s):  
Akram Afifi ◽  
Ahmed El-Rabbany
Keyword(s):  
Linear Combination ◽  
Real Time ◽  
Precise Point Positioning ◽  
Satellite Orbit ◽  
Convergence Time ◽  
Dual Frequency ◽  
Post Processing ◽  
Time Service ◽  
Reference Satellite ◽  
Point Positioning

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.

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

GEOMATICA ◽  
2014 ◽  
Vol 68 (3) ◽  
pp. 195-205 ◽  
Author(s):  
Akram Afifi ◽  
Ahmed El-Rabbany
Keyword(s):  
Stochastic Model ◽  
Full Advantage ◽  
Precise Point Positioning ◽  
Single Frequency ◽  
Solution Convergence ◽  
Single Difference ◽  
System Bias ◽  
Stochastic Characteristics ◽  
Point Positioning ◽  
Time Offset

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.

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