Performance Analysis of Several GPS/Galileo Precise Point Positioning Models

Convergence Time ◽

Data Sets ◽

Dual Frequency ◽

Clock Model ◽

Solution Convergence ◽

Single Difference ◽

Point Positioning ◽

Galileo Satellite ◽

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 precise point positioning model using GPS and Galileo observations

10.32920/ryerson.14662089.v1 ◽

2021 ◽

Author(s):

Akram Afifi

Keyword(s):

Urban Areas ◽

Satellite System ◽

Convergence Time ◽

Clock Model ◽

Solution Convergence ◽

Single Difference ◽

Point Positioning ◽

Time Required ◽

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.

An improved precise point positioning model using GPS and Galileo observations

10.32920/ryerson.14662089 ◽

2021 ◽

Author(s):

Akram Afifi

Keyword(s):

Urban Areas ◽

Satellite System ◽

Convergence Time ◽

Clock Model ◽

Solution Convergence ◽

Single Difference ◽

Point Positioning ◽

Time Required ◽

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.

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

Journal of Applied Geodesy ◽

10.1515/jag-2014-0030 ◽

2015 ◽

Vol 9 (2) ◽

Cited By ~ 3

Author(s):

Akram Afifi ◽

Ahmed El-Rabbany

Keyword(s):

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.

An Innovative Dual Frequency PPP Model for Combined GPS/Galileo Observations

Journal of Applied Geodesy ◽

10.1515/jag-2014-0009 ◽

2015 ◽

Vol 9 (1) ◽

Cited By ~ 7

Author(s):

Akram Afifi ◽

Ahmed El-Rabbany

Keyword(s):

Unknown Parameter ◽

Satellite System ◽

Convergence Time ◽

Dual Frequency ◽

Solution Convergence ◽

Accuracy Level ◽

Satellite Geometry ◽

Galileo Satellite ◽

Time Offset

AbstractThis paper develops a new dual-frequency precise point positioning model, which combines GPS and Galileo observables. The addition of Galileo satellite system offers more visible satellites to the user, which is expected to enhance the satellite geometry and the overall PPP solution in comparison with GPS-only PPP solution. However, combining GPS and Galileo observables introduces additional biases, which require rigorous modelling, including the GPS to Galileo time offset, and Galileo satellite hardware delay. In this research, a GPS/Galileo ionosphere-free linear combination PPP model is developed. The additional biases of the GPS/Galileo combination are lumped and accounted for through the introduction of a new unknown parameter, inter-systems bias, in the PPP mathematical model. It is shown that a subdecimeter positioning accuracy level and 25% reduction in the solution convergence time can be achieved with the developed GPS/Galileo PPP model.

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

Journal of Geodetic Science ◽

10.1515/jogs-2017-0001 ◽

2017 ◽

Vol 7 (1) ◽

pp. 1-8 ◽

Author(s):

A. Afifi ◽

A. El-Rabbany

Keyword(s):

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.

ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences ◽

Enhanced model for precise point positioning with single and dual frequency GPS/Galileo observables

10.5194/isprsarchives-xl-2-173-2014 ◽

2014 ◽

Vol XL-2 ◽

pp. 173-177 ◽

Author(s):

A. Afifi ◽

A. El-Rabbany

Keyword(s):

Urban Areas ◽

Convergence Time ◽

Dual Frequency ◽

Estimation Model ◽

Solution Convergence ◽

Satellite Geometry ◽

System Bias ◽

Point Positioning ◽

Time Offset

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.

Single-Frequency Precise Point Positioning Using Multi-Constellation GNSS: GPS, GLONASS, Galileo and BeiDou

GEOMATICA ◽

10.5623/cig2016-203 ◽

2016 ◽

Vol 70 (2) ◽

pp. 113-122 ◽

Author(s):

Mahmoud Abd Rabbou ◽

Ahmed El-Rabbany

Keyword(s):

Urban Areas ◽

Cost Effective ◽

Convergence Time ◽

Single Frequency ◽

Dual Frequency ◽

Positioning Accuracy ◽

Point Positioning ◽

Beidou Satellites ◽

Gnss Observations

Single-frequency precise point positioning (PPP) presents a cost-effective positioning technique for a large number of users. However, it possesses low positioning accuracy and convergence time compared with the dual-frequency PPP. Single-frequency PPP commonly employs GPS satellite systems that suffer from poor satellite geometry, especially in dense urban areas. We develop a new single-frequency PPP model that combines the observations of current GNSS constellations, including GPS, GLONASS, Galileo and Beidou. The MGEX IGS final precise products are utilized to account for the orbital and clock errors, while the IGS final global ionospheric maps (GIM) model is used to correct for the ionospheric delay. The GNSS inter-system biases are treated as additional unknowns in the estimation process. The con tri bution of the additional GNSS observations to single-frequency PPP is assessed through solution comparison with its traditional GPS-only counterpart. Various GNSS combinations are considered in the assessment, including GPS/GLONASS, GPS/Galileo, GPS/BeiDou and all-constellation GNSS. It is shown that the additional GNSS observations enhance the PPP solution accuracy and convergence time in comparison with the tra di tional GPS-only solution. Except for stations with a sufficient number of tracked BeiDou satellites, both Galileo and BeiDou have marginal effects on the positioning accuracy due to their limited number of satel lites. However, for stations with a sufficient number of visible BeiDou satellites, an average of 40% PPP accuracy improvement is obtained. The major contribution to the PPP accuracy enhancement is obtained from GLONASS satellite observations.

Precise Point Positioning Model Using Triple GNSS Constellations: GPS, Galileo and BeiDou

Journal of Applied Geodesy ◽

10.1515/jag-2016-0010 ◽

2016 ◽

Vol 10 (4) ◽

Author(s):

Akram Afifi ◽

Ahmed El-Rabbany

Keyword(s):

Real Time ◽

Urban Areas ◽

Convergence Time ◽

Dual Frequency ◽

Post Processing ◽

International Gnss Service ◽

Time Service ◽

System Bias ◽

Point Positioning

AbstractThis paper introduces a comparison between dual-frequency precise point positioning (PPP) post-processing model, which combines the observations of three different GNSS constellations, namely GPS, Galileo, and BeiDou and real-time PPP model. A drawback of a single GNSS system such as GPS, however, is the availability of sufficient number of visible satellites in urban areas. Combining GNSS observations offers more visible satellites to users, which in turn is expected to enhance the satellite geometry and the overall positioning solution. However, combining several GNSS observables introduces additional biases, which require rigorous modelling, including the GNSS time offsets and hardware delays. In this paper, a GNSS post-processing PPPP model is developed using ionosphere-free linear combination. The additional biases of the GPS, Galileo, and BeiDou combination are accounted for through the introduction of a new unknown parameter, which is identified as the inter-system bias, in the PPP mathematical model. Natural Resources Canada’s GPSPace PPP software is modified to enable a combined GPS / Galileo / BeiDou PPP solution and to handle the newly inter-system bias. 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 of the GPS, Galileo and BeiDou measurements. For the real-time PPP model the corrections of the satellites orbit and clock are obtained through the international GNSS service (IGS) real-time service (RTS). GPS and Galileo Observations are used for the GNSS RTS-IGS PPP model as the RTS-IGS satellite products are not available for BeiDou satellites. This paper provides the GNSS RTS-IGS PPP model using different satellite clock corrections namely: IGS01, IGC01, IGS01, and IGS03. All PPP models results of convergence time and positioning precision are compared to the traditional GPS-only PPP model. It is shown that combining GPS, Galileo, and BeiDou observations in a PPP model reduces the convergence time by 25 % compared with the GPS-only PPP model.

Approaching Global Instantaneous Precise Positioning with the Dual- and Triple-Frequency Multi-GNSS Decoupled Clock Model

Remote Sensing ◽

10.3390/rs13183768 ◽

2021 ◽

Vol 13 (18) ◽

pp. 3768

Author(s):

Nacer Naciri ◽

Sunil Bisnath

Keyword(s):

Ambiguity Resolution ◽

Ar Model ◽

Convergence Time ◽

Dual Frequency ◽

Clock Model ◽

Precise Positioning ◽

Triple Frequency ◽

Positioning Technique ◽

Carrier Phase Ambiguity ◽

Precise Point Positioning (PPP), as a global precise positioning technique, suffers from relatively long convergence times, hindering its ability to be the default precise positioning technique. Reducing the PPP convergence time is a must to reach global precise positions, and doing so in a few minutes to seconds can be achieved thanks to the additional frequencies that are being broadcast by the modernized GNSS constellations. Due to discrepancies in the number of signals broadcast by each satellite/constellation, it is necessary to have a model that can process a mix of signals, depending on availability, and perform ambiguity resolution (AR), a technique that proved necessary for rapid convergence. This manuscript does so by expanding the uncombined Decoupled Clock Model to process and fix ambiguities on up to three frequencies depending on availability for GPS, Galileo, and BeiDou. GLONASS is included as well, without carrier-phase ambiguity fixing. Results show the possibility of consistent quasi-instantaneous global precise positioning through an assessment of the algorithm on a network of global stations, as the 67th percentile solution converges below 10 cm horizontal error within 2 min, compared to 8 min with a triple-frequency solution, showing the importance of having a flexible PPP-AR model frequency-wise. In terms of individual datasets, 14% of datasets converge instantaneously when mixing dual- and triple-frequency measurements, compared to just 0.1% in that of dual-frequency mode without ambiguity resolution. Two kinematic car datasets were also processed, and it was shown that instantaneous centimetre-level positioning with a moving receiver is possible. These results are promising as they only rely on ultra-rapid global satellite products, allowing for instantaneous real-time precise positioning without the need for any local infrastructure or prior knowledge of the receiver’s environment.