Papers by Mahmoud Abd Rabbou
Second order ionospheric delay results from the interaction of the ionospheric layer and the magn... more Second order ionospheric delay results from the interaction of the ionospheric layer and the magnetic field of the Earth. It can reach up to centimeters in range error during the periods of high total electron content (TEC) values, which adversely affect the accuracy of precise point positioning (PPP). Traditionally, the second order ionospheric delay has been computed numerically as a function of the geomagnetic field, the characteristics of the electron (electron mass, power, and others) and total electron content (TEC). The model, however, is computationally expensive, which limits its application to post-mission GPS PPP. The introduction of a third civil signal (L5), as part of the GPS modernization program, allows for the estimation of second order ionospheric delay through triple-frequency combination. In this poster, the second order ionospheric delay computed from triple-frequency linear combination is examined and compared with the geomagnetic-based model. It is shown that ...
This research investigates the performance of linear and nonlinear estimation filtering for GPS P... more This research investigates the performance of linear and nonlinear estimation filtering for GPS PPP/MEMS- based inertial system. Although integrated GPS/INS system involves nonlinear motion state and measurement models, extended Kalman filter (EKF) is by far the most common estimation filter employed. In this paper, we examine the performance of two nonlinear filtering techniques, namely the unscented Kalman filter (UKF) and the particle filter (PF), for GPS PPP/MEMS-INS integration. Tightly coupled mechanization is adopted, which is developed in the raw measurements domain. Un-differenced ionosphere-free linear combination of pseudorange and carrier-phase measurements PPP technique is employed. The performance of the proposed nonlinear filters is analyzed using a real test scenario. It is shown that the performance of both UKF and PF is comparable to that of EKF, as long as GPS updates from are available.
Traditionally, dual frequency ionosphere free linear combination PPP technique is employed to can... more Traditionally, dual frequency ionosphere free linear combination PPP technique is employed to cancel out the first order ionospheric delay for precise applications. However, geodetic-grade dual-frequency receivers may not provide cost effective solutions in many instances. Single-frequency GPS PPP has been proposed as an alternative solution, which overcomes the high cost. Unfortunately, however, GPS often experiences poor satellite visibility or weak satellite geometry in urban areas. To overcome this limitation, we develop a multi- constellation single frequency PPP technique, which combines the measurements of four GNSS systems, namely GPS, GLONASS, Galileo and BeiDou. The global ionospheric maps are used to account for the ionospheric delay. It is shown that the newly developed technique is superior to the GPS-only counterpart.
Precise Point Positioning (PPP) is traditionally based on dual-frequency observations of GPS or G... more 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.
In this paper, the contribution of Galileo observations to GPS precise point positioning (PPP) is... more In this paper, the contribution of Galileo observations to GPS precise point positioning (PPP) is assessed for both static and kinematic applications. As well, the performance of Galileo-only PPP is investigated in static mode using the existing four operational Galileo satellites. Un-differenced ionosphere-free linear combinations of pseudorange and carrier phase measurements are considered herein. Rigorous models are used to account for tropospheric delay, satellite clock error, ocean loading, Earth tide, carrier phase windup, relativity, and satellite antenna phase-center variations. The accuracy of combined GPS/ Galileo PPP solution is assessed in static mode using data from a number of GNSS stations within the multi-GNSS experiment (MGEX). To assess the accuracy of kinematic GPS/Galileo PPP, we use data from a real test scenario in downtown Kingston, Ontario. The results indicate that Galileo-only PPP achieves decimetre to metre-level positioning accuracy. However, the solution convergence time exceeds the one-hour level due to the presence of code biases. The addition of Galileo observations slightly enhances the PPP accuracy and convergence time in comparison with the GPS-only PPP solution.
Integration of Global Positioning System (GPS) and Inertial Navigation System (INS) integrated sy... more Integration of Global Positioning System (GPS) and Inertial Navigation System (INS) integrated system involves nonlinear motion state and measurement models. However, the extended Kalman filter (EKF) is commonly used as the estimation filter, which might lead to solution divergence. This is usually encountered during GPS outages, when low-cost micro-electro-mechanical sensors (MEMS) inertial sensors are used. To enhance the navigation system performance, alternatives to the standard EKF should be considered. Particle filtering (PF) is commonly considered as a nonlinear estimation technique to accommodate severe MEMS inertial sensor biases and noise behavior. However, the computation burden of PF limits its use. In this study, an improved version of PF, the unscented particle filter (UPF), is utilized, which combines the unscented Kalman filter (UKF) and PF for the integration of GPS precise point positioning and MEMS-based inertial systems. The proposed filter is examined and compared with traditional estimation filters, namely EKF, UKF and PF. Tightly coupled mechanization is adopted, which is developed in the raw GPS and INS measurement domain. Un-differenced ionosphere-free linear combinations of pseudorange and carrier-phase measurements are used for PPP. The performance of the UPF is analyzed using a real test scenario in downtown Kingston, Ontario. It is shown that the use of UPF reduces the number of samples needed to produce an accurate solution, in comparison with the traditional PF, which in turn reduces the processing time. In addition, UPF enhances the positioning accuracy by up to 15% during GPS outages, in comparison with EKF. However, all filters produce comparable results when the GPS measurement updates are available.
Traditional precise point positioning (PPP) is commonly based on un-differenced ionosphere-free l... more Traditional 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.
We develop a new integrated navigation system, which integrates GPS precise point positioning (PP... more 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.
Commonly, kinematic PPP techniques employ un-differenced ionosphere-free linear combination of GP... more 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-satel- lite single difference (BSSD) ionosphere-free linear combinations of GPS and GLONASS measure- ments 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 im- proves 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.
This research investigates the performance of non-linear estimation filtering for GPS-PPP/MEMS-ba... more This research investigates the performance of non-linear estimation filtering for GPS-PPP/MEMS-based inertial system. Although integrated GPS/INS system involves nonlinear motion state and measurement models, the most common estimation filter employed is extended Kalman filter. In this paper, both unscented Kalman filter and particle filter are developed and compared with extended Kalman filter. Tightly coupled mechanization is adopted, which is developed in the raw measurements domain. Un-differenced ionosphere-free linear combination of pseudorange and carrier-phase measurements is employed. The performance of the proposed non-linear filters is analyzed using real test scenario. The test results indicate that comparable accuracy-level are obtained from the proposed filters compared with extended Kalman filter in positioning, velocity and attitude when the measurement updates from GPS measurements are available.
In this paper, an improved Precise Point Positioning GPS/MEMS-based integrated system is introduc... more In this paper, an improved Precise Point Positioning GPS/MEMS-based integrated system is introduced for precise positioning applications. Un-differenced ionosphere-free linear combinations of carrier phase and code measurements are processed. Tropospheric delay, satellite clock, ocean loading, Earth tide, carrier-phase windup, relativity, and satellite and receiver antenna phase-center variations are accounted for using rigorous modeling. Tightly coupled mechanism is adopted, which is carried out in the raw measurements domain. Both Extended Kalman filter (EKF) and Unscented Kalman filter (UKF) are developed to merge the GPS and inertial measurements. The performance of integrated system is analyzed using a real test scenario in downtown Kingston. It is shown that both Extended Kalman and Unscented Kalman filters have comparable performance. The positioning results of the integrated system show that decimeter-level accuracy is achievable. During the GPS outages, the integrated system showed meterlevel accuracy when a 60-second outage was introduced. However, the positioning accuracy was improved to sub-decimeter and centimeter level when 30- and 10-second GPS outages were introduced, respectively.
Geodetic-grade dual-frequency GPS receivers are typically used for precise point positioning (PPP... more Geodetic-grade dual-frequency GPS receivers are typically used for precise point positioning (PPP). Unfortunately, these receiver systems are expensive and may not provide a cost-effective solution in many instances. The use of low-cost single-frequency GPS receivers, on the other hand, are limited by the effect of ionospheric delay. A number of mitigation techniques have been proposed to account for the effect of ionospheric delay for single-frequency GPS users. Unfortunately, however, those mitigation techniques are not suitable for PPP. More recently, the U.S. Total Electron Content (USTEC) product has been developed by the National Oceanic and Atmospheric Administration (NOAA), which describes the ionospheric total electron content in high resolution over most of North America. This paper investigates the performance of USTEC and studies its effect on single-frequency PPP solution. A performance comparison with two widely-used ionospheric mitigation models is also presented.
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Papers by Mahmoud Abd Rabbou
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.
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.