Un-differenced precise point positioning model using triple GNSS constellations

Abstract. 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.

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.

With the full operation of the global BeiDou navigation satellite system (BDS-3), positioning performance can be further enhanced by BDS-3 combined with the regional BeiDou navigation satellite system (BDS-2). However, due to satellite signals being out of lock and the limited visibility of satellites, the traditional multi-frequency BDS-2/3 precise point positioning (PPP) model is unable to maintain great positioning performance under urban environmental conditions. In this study, a mixed multi-frequency undifferenced and uncombined (UDUC) BDS-2/3 PPP model is presented to improve the positioning performance under urban environmental conditions by making full use of B1I, B1C, B2I, B2a, and B3I signals from all visible BDS satellites. In this model, BDS satellites with single-, dual-, triple- and quad-frequency observations all can participate in PPP. The static and kinematic experiments were carried out using the mixed multi-frequency UDUC BDS-2/3 PPP model to fully assess the positioning performance under urban environmental conditions with comparisons to the multi-frequency model. The static experiments indicated that the mixed multi-frequency UDUC BDS-2/3 PPP could continuously achieve decimeter-level positioning accuracy at a cut-off elevation angle of 40°, but part of the BDS-3 PPP would lose resolution due to limited visible satellites. Furthermore, the initial kinematic vehicle experiment showed that mixed multi-frequency UDUC BDS-2/3 PPP had better satellite geometry and more observation redundancy than the traditional multi-frequency model. Compared with the traditional multi-frequency BDS-2/3 model, the positioning accuracy of the mixed multi-frequency model was improved by 51.6, 35.5, and 39.1%, respectively, in east, north, and up directions. The convergence time was shortened by 40%.

The availability of multiple signals from different Global Navigation Satellite System (GNSS) constellations provides opportunities for improving positioning accuracy and initial convergence time. With dual-frequency observations from the four constellations (GPS, GLONASS, Galileo, and BeiDou), it is possible to investigate combined GNSS precise point positioning (PPP) accuracy and stability. The differences between GNSS systems result in inter-system biases (ISBs). We consider several ISB values such as GPS-GLONASS, GPS-Galileo, and GPS-BeiDou. These biases are compliant with key parameters defined in the multi-GNSS PPP processing. In this study, we present a unified PPP method that sets ISB values as fixed or constant. A comprehensive analysis that includes satellite visibility, position dilution of precision, position accuracy is performed to evaluate a unified PPP method with constrained cut-off elevation angles. Compared to the conventional PPP solutions, our approach shows more stable positioning at a constrained cut-off elevation angle of 50 degrees.

It is anticipated that the performance of real‐time (RT) GNSS meteorology can be further improved by incorporating observations from multiple Global Navigation Satellite System (GNSS), including GPS, GLONASS, Galileo, and BeiDou. In this paper, an operational RT system for extracting zenith troposphere delay (ZTD) using a modified version of the Precise Point Positioning With Integer and Zero‐difference Ambiguity Resolution Demonstrator (PPP‐WIZARD) was established. GNSS, including GPS, GLONASS, and Galileo, observation streams were processed using RT Precise Point Positioning (PPP) strategy based on RT satellite orbit/clock products from the Centre National d'Etudes Spatiales. An experiment covering 30 days was conducted, in which the observation streams of 20 globally distributed stations were processed. The initialization time and accuracy of the RT troposphere results using single‐system and multisystem observations were evaluated. The effect of PPP ambiguity resolution was also evaluated. Results reveal that RT troposphere estimates based on single‐system observations can both be applied in weather nowcasting, in which the GPS‐only solution is better than the GLONASS‐only solution. The performance can also be improved by PPP ambiguity resolution and utilizing GNSS observations. Specifically, we notice that ambiguity resolution is more effective in improving the accuracy of ZTD, whereas the initialization process can be better accelerated by GNSS observations. Combining all techniques, the RT troposphere results with an average accuracy of about 8 mm in ZTD can be achieved after an initialization process of approximately 8.5 min, which demonstrates superior results for applying GNSS observations and ambiguity resolution for RT meteorological applications.

Carrier phase-based ionospheric observables using PPP models

Differential code bias estimation based on uncombined PPP with LEO onboard GPS observations

For precise positioning in arctic regions with Global Navigation Satellite Systems (GNSS), such as GPS and Glonass, there are a number of issues to be resolved or taken into account. The most important ones are satellite geometry, ionospheric effects and distribution of correction data. Precise Point Positioning (PPP) is currently the standard for precise offshore positioning. PPP requires a sparse global network of GNSS reference stations to estimate precise satellite orbit and clock parameters in real-time. These parameters are transmitted to users, who can compute their position with an accuracy of 0.1 m using code and carrier observations. The main disadvantage of PPP is that in general it takes a long time to converge to this accuracy, about 30–45 minutes. GNSS carrier observations are similar to pseudo ranges, but have an additional bias which needs to be estimated. Under certain conditions, these biases are integer. This property is used in what is generally referred to as Real-Time Kinematic (RTK) positioning, a technique which uses corrections generated at reference stations to make sure these ambiguities are integer. Integer Ambiguity Resolution (IAR) results in RTK accuracies of 0.01–0.03 m or better and short convergence times, ranging from instantaneous to several minutes for long inter-station distances. The disadvantage is the limited area of applicability, because RTK in general does not use precise orbits and clocks. Current research focuses on the combination of PPP and RTK techniques. The main goal is to achieve cm accuracy with a sparse network of reference stations. Another goal is to reduce convergence time. Applications are in the field of precise real-time offshore positioning in general, and subsidence monitoring and tidal estimation in particular. Results will be presented from standard PPP and PPP combined with IAR for arctic regions and from a test bed in the Gulf of Mexico. These results, although preliminary, indicate centimeter level accuracy is indeed possible, also in the arctic. We will also look at further improvements, mainly in convergence time, using all operational satellites and signals from current and future navigation systems.

Global Navigation Satellite System (GNSS) based Precise Point Positioning (PPP) has become the de facto standard for precise real-time offshore positioning applications. Current precision is of the order of 3−5 cm horizontally and twice this value for the vertical. However, this may not yet be good enough for tidal applications. In this contribution we will discuss new developments at Fugro, one of the world’s main providers of precise offshore real-time GNSS positioning services, to further improve PPP precision to the 2−3 cm level in the vertical component worldwide. For demanding applications, it is possible to even further improve this precision. These developments are based on merging PPP techniques (use of precise satellite orbits and clocks) with Integer Ambiguity Resolution (IAR), known from GNSS Real-Time Kinematic (RTK) positioning techniques. PPP IAR requires the generation and distribution to mobile users of Uncalibrated Phase Delays (UPDs) a network of reference stations. The network can be as small as one station or cover the entire globe. Once applied to the data of a mobile receiver, the carrier ambiguities should be integer. Fixing of these ambiguities to their proper integer value will result in significantly improved positioning performance. The infrastructure used to generate precise orbits, clocks and UPDs will be discussed. PPP IAR results will be shown from regional and global test beds, based on Fugro’s precise orbits and clocks for all currently available GNSSs. In addition, it will be shown that the introduction of new systems and signals, like triple-frequency GPS, Galileo and BeiDou, will help to significantly reduce the time required for PPP IAR solutions to converge to this centimeter level of accuracy.

PPP-RTK which takes full advantages of both Real-Time Kinematic (RTK) and Precise Point Positioning (PPP), is able to provide centimeter-level positioning accuracy with rapid integer Ambiguity Resolution (AR). In recent years, with the development of BeiDou Navigation Satellite System (BDS) and Galileo navigation satellite system (Galileo) as well as the modernization of Global Positioning System (GPS) and GLObal NAvigation Satellite System (GLONASS), more than 140 Global Navigation Satellite System (GNSS) satellites are available. Particularly, the new-generation GNSS satellites are capable of transmitting signals on three or more frequencies. Multi-GNSS and multi-frequency observations become available and can be used to enhance the performance of PPP-RTK. In this contribution, we develop a multi-GNSS and multi-frequency PPP-RTK model, which uses all the available GNSS observations, and comprehensively evaluate its performance in urban environments from the perspectives of positioning accuracy, convergence and fixing percentage. In this method, the precise atmospheric corrections are derived from the multi-frequency and multi-GNSS observations of a regional network, and then disseminated to users to achieve PPP rapid AR. Furthermore, a cascade ambiguity fixing strategy using Extra‐Wide‐Lane (EWL), Wide-Lane (WL) and L1 ambiguities is employed to improve the performance of ambiguity fixing in the urban environments. Vehicle experiments in different scenarios such as suburbs, overpasses, and tunnels are conducted to validate the proposed method. In suburbs, an accuracy of within 2 cm in the horizontal direction and 4 cm in the vertical direction, with the fixing percentage of 93.7% can be achieved. Compared to the GPS-only solution, the positioning accuracy is improved by 87.6%. In urban environments where signals are interrupted frequently, a fast ambiguity re-fixing can be achieved within 5 s. Moreover, multi-frequency GNSS signals can further improve the positioning performance of PPP-RTK, particularly in the case of small amount of observations. These results demonstrate that the multi-frequency and multi-GNSS PPP-RTK is a promising tool for supporting precise vehicle navigation.

Smartphones typically compute position using duty-cycled Global Navigation Satellite System (GNSS) L1 code measurements and Single Point Positioning (SPP) processing with the aid of cellular and other measurements. This internal positioning solution has an accuracy of several tens to hundreds of meters in realistic environments (handheld, vehicle dashboard, suburban, urban forested, etc.). With the advent of multi-constellation, dual-frequency GNSS chips in smartphones, along with the ability to extract raw code and carrier-phase measurements, it is possible to use Precise Point Positioning (PPP) to improve positioning without any additional equipment. This research analyses GNSS measurement quality parameters from a Xiaomi MI 8 dual-frequency smartphone in varied, realistic environments. In such environments, the system suffers from frequent phase loss-of-lock leading to data gaps. The smartphone measurements have low and irregular carrier-to-noise (C/N0) density ratio and high multipath, which leads to poor or no positioning solution. These problems are addressed by implementing a prediction technique for data gaps and a C/N0-based stochastic model for assigning realistic a priori weights to the observables in the PPP processing engine. Using these conditioning techniques, there is a 64% decrease in the horizontal positioning Root Mean Square (RMS) error and 100% positioning solution availability in sub-urban environments tested. The horizontal and 3D RMS were 20 cm and 30 cm respectively in a static open-sky environment and the horizontal RMS for the realistic kinematic scenario was 7 m with the phone on the dashboard of the car, using the SwiftNav Piksi Real-Time Kinematic (RTK) solution as reference. The PPP solution, computed using the YorkU PPP engine, also had a 5–10% percentage point more availability than the RTK solution, computed using RTKLIB software, since missing measurements in the logged file cause epoch rejection and a non-continuous solution, a problem which is solved by prediction for the PPP solution. The internal unaided positioning solution of the phone obtained from the logged NMEA (The National Marine Electronics Association) file was computed using point positioning with the aid of measurements from internal sensors. The PPP solution was 80% more accurate than the internal solution which had periodic drifts due to non-continuous computation of solution.

The study of climate change is an important field of research. Monitoring of atmospheric variability especially the tropospheric precipitable water vapor (PWV) is a powerful way to investigate climate change. Global navigation satellite systems (GNSS) provide a good tool for studying atmospheric parameters as GNSS signals along its path from the satellites to the ground based receivers suffer a significant delay due to the refractivity of earth’s atmosphere. GNSS signals are not only delayed but also refracted in the neutral atmosphere. The zenith wet delays (ZWD) caused by the troposphere can be estimated during the geodetic processing of GNSS signals. Since the ZWD is tightly correlated to the PWV, GNSS observations can be used to study the changes of PWV. In this study GNSS data from the Egyptian permanent GNSS network (EPGN), International GNSS Service (IGS), EUREF Permanent Network (EPN) and Scripps Orbit and Permanent Array Center (SOPAC), for the years 2013 and 2014, were used. These GNSS stations provided a good geometrical coverage over the respective region. All GNSS data were processed using Bernese V 5.2 software. The needed product from GNSS data processing is the tropospheric zenith total delay (ZTD) over each GNSS site. The ZTD is divided based on physical parameters into zenith hydrostatic delay (ZHD) and zenith wet delay (ZWD). The ZWD is the basic observable used to calculate PWV. The values of the PWV were calculated and its variation over the study area was investigated. The quality of calculated PWV values from GNSS data evaluated against traditional Radiosonde (RS) measurements. The results of GNSS PWV showed good agreement with RS PWV when the PWV values were low, but this agreement became worse at high PWV values as the differences between the two techniques increased. The correlation coefficient between RS PWV and GNSS PWV varied from 0.31 to 0.84. Standard deviation of the differences between RS PWV and GNSS PWV ranged from 2.369 to 5.973 mm. The PWV estimated from GNSS observations had annual cycle, and its cycle in 2013 was different from that in 2014. The PWV differences between the 2 years clarified that the water vapor content over the east Mediterranean in most of 2014 days was higher than that in 2013. Furthermore, PWV variations were noted on both temporal and spatial scales. The highest temporal variation value was 25.41 mm whereas the maximum value of the spatial variation was 19.67 mm. The present study illustrated the importance of using geodetic networks to provide atmospheric information.

Atmospheric wet delay caused by Precipitable Water Vapor (PWV) significantly impacts the performance of many geodetic surveying systems such as Global Navigation Satellite System (GNSS). In this study, we use wet delay corrections forecast by the Weather Research and Forecasting (WRF) model to enhance GNSS Precise Point Positioning (PPP) during two observation periods with two different weather conditions, that is, period 1: March 01 to 14, 2020 (average PWV: 23.5 kg/m2) and period 2: June 02 to 15, 2020 (flooding weather with average PWV: 55.6 kg/m2), over the South China. PWV data from 277 to 263 GNSS stations are assimilated into WRF model to enhance the WRF water vapor forecasting capability for period 1 and period 2, respectively. Wet delay corrections from two different WRF configurations, that is, WRF no data assimilation and WRF with assimilation of GNSS PWV, are used to augment the PPP. Totally, eight WRF‐enhanced PPP schemes are tested. The results show that WRF‐enhanced PPP schemes generally have a better positioning performance in the up component than traditional PPP. After using WRF wet delay corrections, for static mode, the vertical positioning accuracy is improved by 14.6% and 33.7% for period 1 and period 2, respectively. The corresponding convergence time are reduced by 41.8% and 25.0% for period 1 and period 2, respectively. For kinematic mode, the positioning accuracy improvements in the up component reach 13.8% and 19.0% for period 1 and period 2, respectively. The kinematic PPP convergence time is reduced by up to 8.2% for period 1.

Unmanned Aerial Vehicles (UAVs) have been used for accurate orthophoto generation based on advanced Global Navigation Satellite System (GNSS) techniques. In recent years, the UAV systems have become an effective tool for fast monitoring of damages caused by disasters such as the earthquake hazards. The conventional orthophoto generation based on ground control points takes too much time during emergency situations. In the study, different methodologies for the processing of the acquired GNSS Positioning data for direct georeferencing of UAVs were investigated in terms of various orbit products. Evaluating the fitness for emergency response applications, the ground control points (GCPs) also used for validation of the generated orthophoto without using GCPs and based on Precise Point Positioning (PPP) approach. In this study, Ultra-Rapid, Rapid and Final PPP methods based on GNSS observations were used for direct geo-referencing. Thirteen GCPs were located at the study area for the validation of the orthophoto accuracy generated by direct geo-referencing.

Precipitable water vapor (PWV) is an important component of atmospheric spatial parameters and plays a vital role in meteorological studies. In this study, PWV retrieval by real-time precise point positioning (PPP) technique is validated by using global navigation satellite system (GNSS) observations and four real-time products from different analysis centers, which are Centre National d’Etudes Spatiales (CNES), Internation GNSS Service (IGS), Japan Aerospace Exploration Agency (JAXA), and Wuhan University (WHU). To comparatively analyze the performance of each scenario, the single-system (GPS/Galileo/BDS3), and multi-system (GPS + Galileo + BDS) PPP techniques are applied for zenith tropospheric delay (ZTD) and PWV retrieval. Then, the ZTD and PWV are evaluated by comparison with the IGS final ZTD product, the European Centre for Medium-Range Weather Forecasts (ECMWF) Reanalysis v5 (ERA5) data, and radiosondes observations provided by the University of Wyoming. Experimental results demonstrate that the root mean squares error (RMS) of ZTD differences from multi-system solutions are below 11 mm with respect to the four-product series and the RMS of PWV differences are below 3.5 mm. As for single-system solution, the IGS real-time products lead to the worst accuracy compared with the other products. Besides the scenario of BDS3 observations with IGS real-time products, the RMS of ZTD differences from the GPS-only and Galileo-only solutions are all less than 15 mm compared to the four-product series, as well as the RMS of PWV differences is under 5 mm, which meets the accuracy requirement for GNSS atmosphere sounding.