Precise Point Positioning Approach Research Articles

Comparative performance analysis of precise point positioning technique in the UAV − based mapping

Uncrewed Aerial Vehicle (UAV) photogrammetry is a very efficient, low-cost approach for mapping small or medium-sized local areas. This approach is adequate for achieving the needed accuracy in many applications, and onboard positioning sensors have made this technique more feasible by decreasing the need for ground control stations (GCPs). When real-time positioning strategies are used, photogrammetric mapping can also be performed instantaneously in the field. This is especially crucial in applications like disaster management, where current situation must be detected rapidly. It is critical to choose a georeferencing approach in applications that is appropriate for the physical parameters of the mapping area, the intended use of the photogrammetric mapping, and the needed accuracy. In order to accurately georeference the photogrammetric outputs, this study assesses the real-time and post-processed performances of absolute and relative GNSS positioning approaches. Finally, it compares these strategies in terms of the position accuracy of the created models. In the evaluations, the 3D models of the study area were created utilizing network-based Real Time Kinematic (n-RTK), Post-Processed Kinematic (PPK) Positioning, and Precise Point Positioning (PPP) approaches, with direct georeferencing of the UAV-based photogrammetric images. These models were then compared to models developed using traditional indirect georeferencing with GCPs and aided indirect georeferencing. According to the findings, direct georeferencing using the n-RTK and PPK techniques provided a horizontal position accuracy in terms of root mean square errors (rms2D = 1.6 cm and 1.9 cm) almost equal to indirect georeferencing using GCPs (rms2D = 1.9 cm). In terms of vertical position accuracies, the n-RTK and PPK approaches in direct georeferencing (rmsh = 3.7 cm and 3.9 cm, respectively) produced rather different results than the GCPs-based conventional strategy (rmsh = 1.6 cm), although the discrepancies were within acceptable error limits. Direct georeferencing with the PPP approach produced the lowest horizontal and vertical position accuracies (rms2D = 5.9 cm, rmsh= 5.7 cm). However, this level of accuracy was deemed adequate for use in large-scale mapping in Turkey's authorized regulation.

EVALUATION OF THE PERFORMANCE OF MULTI-GNSS ADVANCED ORBIT AND CLOCK AUGMENTATION – PRECISE POINT POSITIONING (MADOCA-PPP) IN JAPAN REGION

For users of Precise Point Positioning (PPP), Multi-GNSS Advanced Orbit and Clock Augmentation PPP signals provide corrective data. When using the PPP approach and/or PPP-Ambiguity Resolution (AR) method, the QZSS signal provides globally applicable error corrections on satellite orbit, clock offset, and code/phase biases. In addition, from FY2024, as a part of the MADOCA-PPP technology demonstration, wide-area ionospheric correction data will be provided for the Asia-Oceania region. A software estimator of precise satellite information developed by JAXA, Multi-GNSS Advanced Demonstration Tool for Orbit and Clock Analysis (MADOCA), allows u-blox CO99-ZED-F9P and MSJ 3008-GM4-QZS utilizing MADOCA-PPP to be used in GNSS applications that need sub-decimetre precision but don’t have to be expensive. Errors caused by positioning satellites are computed by using observation data from domestic and overseas GNSS monitoring station networks such as IGS and MIRAI, and obtained correction data is transmitted from QZSS signal to provide highly precise positioning augmentation services that can be used in the Asia-Oceania Region. Users may utilize the PPP technique for high-precision locating by employing a GNSS receiver that supports the QZSS signals. This paper describes an experiment carried out with the static method to combine GPS, GLONASS, and QZSS signals in the project site (ISHI, USUD and MIZU stations in Japan). This paper examines the GPS/GLONASS/QZSS obtainable accuracy. These obtained results indicate that integrating GPS system with GLONASS and QZSS is favoured for surveying applications. It appears that integrating GPS/GLONASS/QZSS (MADOCA precise ephemeris file) static measurements in the study area between 0–4 millimetres accuracy can be guaranteed on all occasions.

Assessing seismic displacements and early warning using kinematic PPP with MADOCA real-time products: A case study of 2023 Kahramanmaraş (Türkiye) earthquakes

Early warning and emergency hazard response studies in large earthquakes require rapid and reliable determination of earthquake magnitude. The magnitude of an earthquake can be estimated based on peak ground displacement (PGD) values captured from high-rate GNSS records. In this study, two major earthquakes that hit Kahramanmaraş Province on February 6, 2023, were investigated by using the real-time Global Navigation Satellite System (GNSS) Precise Point Positioning (PPP) technique to confirm the usability of GNSS in early warning. Data from high-rate (1-Hz) GNSS stations were evaluated with the real-time kinematic PPP approach utilizing the multi-GNSS advanced demonstration tool for orbit and clock analysis (MADOCA) products and JPL's GipsyX software. In addition, static PPP was also used to identify the permanent displacements caused by earthquakes. Static PPP results demonstrated that significant displacements were detected at stations close to the epicenters, particularly the 446.86 cm horizontal displacement in the EKZ1 station. Considering the kinematic PPP results revealed that when PGD values calculated from seismic waves, functional model, and updated coefficients were implemented, the moment magnitude of the Pazarcık earthquake was estimated as Mw 7.78, which was reported as Mw 7.8 by USGS and Mw 7.7 by AFAD, whilst the magnitude of the Elbistan earthquake was computed as Mw 7.56, which was reported as Mw 7.5 by USGS and 7.6 by AFAD. Overall, this study validates the effectiveness of the real-time GNSS PPP as an attractive alternative for analyzing coseismic events and supporting early warning.

A Rapid-Convergence Precise Point Positioning Approach Using Double Augmentations of Low Earth Orbit Satellite and Atmospheric Information

The precise point positioning (PPP) technique generally takes tens of minutes to converge, severely limiting its use. This longer convergence time is mainly due to the slower variation of satellite geometry in space and the stronger correlation of unknown parameters to be estimated. Fortunately, the lower orbit altitude of Low Earth Orbit (LEO) satellites contributes to the fast variation of the satellites’ spatial geometry. In addition, high-precision atmospheric delay information has become readily available, which can help decrease unknown parameters’ correlation. This study proposes a double-augmentation PPP approach with accelerated convergence by tightly integrating the LEO/atmosphere-augmented information. The GNSS observations in both mid-latitude and low-latitude areas, and simulated LEO observations under a Walker/polar mixed constellation, are used to validate the double-augmentation PPP approach. Test results in both areas indicate that the double-augmentation PPP can converge within 0.8 min, improving the convergence time by over 73%, and over 83% compared to the LEO-only augmented PPP and atmosphere-only augmented PPP.

An open-source software package for Precise Point Positioning: raPPPid

Precise Point Positioning (PPP) has proven to be a powerful GNSS positioning method used for various scientific and commercial applications nowadays. We present a flexible and user-friendly software package named raPPPid suitable for processing single to triple-frequency GNSS observations in various PPP approaches (e.g., ionospheric-free linear combination, uncombined model), available under https://github.com/TUW-VieVS/raPPPid. To tune the PPP procedure, the user can select from many satellite products, models, options, and parameters. This way, the software raPPPid can handle high-to-low quality observation data ranging from geodetic equipment to smartphones. Despite significant improvements, the convergence time of PPP is still a major topic in scientific research. raPPPid is specially designed to reduce the convergence period with diverse implemented approaches, such as PPP-AR or ionospheric pseudo-observations, and to offer the user multiple plots and statistics to analyze this critical period. Typically, raPPPid achieves coordinate convergence times of around 1 min or below with high-quality observations and ambiguity fixing. With smartphone data and a simplified PPP approach, a 2D position accuracy at the one-meter level or below is accomplished after two to three minutes.

Shipborne GNSS acquisition of sea surface heights in the Baltic Sea

Abstract For determining precise sea surface heights, six marine GNSS (global navigation satellite system) survey campaigns were performed in the eastern Baltic Sea in 2021. Four GNSS antennas were installed on the vessel, the coordinates of which were computed relative to GNSS–CORS (continuously operating reference stations). The GNSS–CORS results are compared to the PPP (precise point positioning)-based results. Better accuracy is associated with the GNSS–CORS postprocessed points; however, the PPP approach provided more accurate results for longer than 40 km baselines. For instance, the a priori vertical accuracy of the PPP solution is, on average, 0.050 ± 0.006 m and more stable along the entire vessel’s survey route. Conversely, the accuracy of CORS-based solutions decreases significantly when the distances from the GNSS–CORS exceed 40 km, whereas the standard deviation between the CORS and PPP-based solutions is up to 0.075 m in these sections. Note that in the harbor (about 4 km from the nearest GNSS–CORS), the standard deviation of vertical differences between the two solutions remains between 0.013 and 0.024 m. In addition, the GNSS antennas situated in different positions on the vessel indicated different measurement accuracies. It is suggested for further studies that at least one GNSS antenna should be mounted above the mass center of the vessel to reduce the effects of the dominating pitch motion during the surveys.

A Novel GNSS Single-Frequency PPP Approach to Estimate the Ionospheric TEC and Satellite Pseudorange Observable-Specific Signal Bias

As the significant error sources influencing the Global Navigation Satellite System (GNSS) positioning, navigation, and timing (PNT) services, ionospheric delay and satellite hardware delay should be properly calibrated. Particularly, the pseudorange observable-specific signal bias (OSB) is convenient and can be directly corrected in the raw pseudorange measurement. In this work, we present a novel single-frequency ionospheric-free-half precise point positioning (PPP) (SFPPP2) approach for ionospheric studies, in which the ionospheric vertical total electron content (VTEC) and satellite OSB are isolated from the slant ionospheric observables by means of the ionospheric multilayer mapping function (MF). The computation and parameterization methods of the ionospheric VTEC and satellite pseudorange OSB are present. To validate the effectiveness and reliability of the novel method, we investigate and compare the performance of the single-frequency ionospheric-float PPP (SFPPP1), SFPPP2, and dual-frequency ionospheric-float PPP (DFPPP1) solutions for ionosphere sensing. The analytical results indicate that the novel approach can extract the slant ionospheric observables with the accuracy of submeters. The accuracy of the estimated ionospheric VTEC by the single-frequency PPP approaches is in the submeter level, which exhibits a slightly worse accuracy than that from the dual-frequency PPP solution. The estimated ionospheric VTEC accuracy is improved with the multilayer MF compared with the single-layer MF. The estimated BeiDou Navigation Satellite System (BDS) pseudorange OSB with the proposed SFPPP2 approach is stable, reliable, and of the high accuracy, and the rms’s with respect to Chinese Academy of Sciences (CAS) product for C2I and C6I signals with single-layer and multilayer MFs are 0.40, 0.41, 0.60, and 0.63 ns, respectively. The proposed PPP approach can retrieve the VTEC and satellite pseudorange OSB by mass-market receivers for the GNSS users.

Estimation of the ocean tide loading displacements by GPS and GLONASS kinematic Precise Point Positioning

Ocean Tide Loading Displacement (OTLD) parameters, derived by Global Positioning System (GPS) approach, need more time to converge to a stable state and show poor precision of K1 and K2 constituents. Combining multi-system Global Navigation Satellite System (GNSS) data can greatly improve the positioning accuracy and significantly reduce the convergence time compared to single GPS PPP, combined GPS+GLONASS with ambiguity resolved in kinematic Precise Point Positioning (PPP) is improved on the basis of the algorithm of GPS kinematic PPP. We collected eight years of continuous observations of 11 worldwide sites from International GNSS Service to generate three dimensional OTLD parameters of eight constituents using GPS with ambiguity fixed, GLONASS with ambiguity free and combined GPS+GLONASS with ambiguity fixed kinematic PPP approach. The results show the eight constituents derived by GPS_FX and GPS+GLONASS_FX solution need four years and three years to converge to stable values, respectively. GLONASS can significantly improve the convergence rate of K1 and K2 constituents which needs only two years to converge to stable values, and S2 and P1 constituents which need three years to stable values. The results also show the GPS+GLONASS/reference misfits are the smallest for the most constituents in three components (less than 2mm) except for K2 and K1 in vertical and north directions. GLONASS can improve more than 40% in vertical and north components over GPS and GPS+GLONASS for K2 and K1 constituents and show very close agreement with GPS_FX solution in vertical and north component for S2 and P1 constituents. Ambiguity resolved in OTLD estimation can significantly accelerate the convergence and improve the accuracy for eight constituents, especially for combined GPS+GLONASS kinematic PPP mode, but no single constellation mode solution for all eight major constituents exists.

NRTK, PPP or Static, That Is the Question. Testing Different Positioning Solutions for GNSS Survey

Worldwide, the determination of the coordinates from a Global Navigation Satellite System (GNSS) survey (in Network Real Time Kinematic, Precise Point Positioning, or static mode) has been analysed in several scientific and technical applications. Many of those have been carried out to compare Precise Point Positioning (PPP), Network Real Time Kinematic (NRTK), and static modes’ solutions, usually, using the latter as the true or the most plausible solution. This approach is not always possible as the static mode solution depends on several parameters (baseline length, acquisition time, ionospheric, and tropospheric models, etc.) that must be considered to evaluate the accuracy of the method. This work aims to show the comparison among the GNSS survey methods mentioned above, using some benchmark points. The tests were carried out by comparing the survey methods in pairs to check their solutions congruence. The NRTK and the static solutions refer to a local GNSS CORS network’s analysis. The NRTK positioning has been obtained with different methods (VRS, FKP, NEA) and the PPP solution has been calculated with two different software (RTKLIB and CSRS-PPP). A statistical approach has been performed to check if the distribution frequencies of the coordinate’s residual belong to the normal distribution, for all pairs analysed. The results show that the hypothesis of a normal distribution is confirmed in most of the pairs and, specifically, the Static vs. NRTK pair seems to achieve the best congruence, while involving the PPP approach, pairs obtained with CSRS software achieve better congruence than those involving RTKLIB software.

Assessment of NRCAN PPP online service in determination of crustal velocity: case study Northern Egypt GNSS Network

Precise point positioning (PPP) has the ability to give precise positioning with high accuracy. That may be an alternative to precise Deferential GNSS (DGNSS), in addition to being a low-cost alternative among all processing strategies of Global Navigation Satellite System (GNSS), especially when online services are used. To see the assessment study of PPP in the determination of crustal velocity, 66 days of GNSS data distributed in the period 2013–2015 were used. Composing a network of eight stations called the Northern Egyptian Permanent GNSS Network (N-EPGN) with nine IGS stations was processed. Scientific software GAMIT/GLOBK and Bernese used to calculate the final precise coordinate and the associated velocity of each station in the International Terrestrial Reference Frame (ITRF 2008). Each campaign consists of 3 days. These data were processed by PPP approach. The final precise coordinate and the associated velocity of each EPGN station estimated. The final results compare to those different methods of analysis and programs refer to high level of agreement between the coordinates and velocity which confirm that PPP approach can be applied for the investigation of crustal deformation.

Modeling and assessment of real-time precise point positioning timing with multi-GNSS observations

Real-time precise point positioning (PPP) method is of great interest for global navigation satellite systems (GNSS) time application with multi-GNSS observations. In this study, a multi-GNSS precise timing approach using Centre National d’Etudes Spatiales (CNES) real-time products was presented to improve the reliable of precise timing. Users can obtain the difference between the local time (time of rover receiver) and UTC(k) directly using a GNSS receiver, once the CNES products are aligned to UTC(k) by a multi-GNSS PPP approach. In other words, the reference times of the realigned products for GPS, GLONASS, BDS-2 and Galileo are UTC (k). Then, users can obtain the difference between the local time and UTC(k) directly using any single-system or multi-GNSS combination. Note that the receiver hardware delay needs to be calibrated before timing application. Numerical analyses clarify how the multi-GNSS precise timing approach performs. First, the standard deviation (STD) of the difference between the multi-GNSS timing results and the clock difference from the IGS final products is shown to be less than 0.5 ns. The multi-GNSS solutions outperform that of a single system. Furthermore, GPS-only PPP timing solutions perform better than that of GLONASS and Galileo-only. In addition, the maximum reductions of STD values are up to 33.6%, 11.6%, 14.6%, 25.6% for GPS-only, GLONASS-only, Galileo-only and multi-GNSS timing, respectively, using a receiver clock model. Second, the frequency stability of the multi-GNSS scheme is slightly better than GPS-only. For single-system PPP timing, GLONASS-only performs worst, while GPS-only performs best. The maximum improvements of frequency stability are up to 61.9%, 67.1%, 90.6%, 65.8% for GPS-only, GLONASS-only, Galileo-only and multi-GNSS timing, respectively, with a receiver clock model using the realigned products. More interestingly, we found that the performance Galileo-only was improved with the observations on 2019 as compared to Galileo with the observations on 2018.

BDS Satellite-Based Augmentation Service Correction Parameters and Performance Assessment

BDS (Beidou Navigation Satellite System) integrates the legacy PNT (Positioning, Navigation, Timing) service and the authorized SBAS (Satellite-Based Augmentation Services) service. To support the requirement of decimeter-level positioning, four types of differential corrections are developed in the BDS SBAS, including the State Space Representation (SSR)-based satellite orbit/clock corrections, the Observation Space Representation (OSR)-based ionospheric grid corrections, and the partition comprehensive corrections. In this study, we summarize the features of these differential corrections, including their definition and usages. The function model of precise point positioning (PPP) for dual- and single-frequency users using the four types of BDS SBAS corrections are proposed. Datasets are collected from 34 stations over one month in 2019, and PPP is performed for all the datasets. Results show that the root mean square (RMS) of the positioning errors for static/kinematic dual-frequency (DF) PPP are of 12 cm/16 cm in horizontal and 18 cm/20 cm in vertical component, while for single-frequency (SF) PPP are of 14 cm/32 cm and 22 cm/40 cm, respectively. With regard to the convergence performance, the horizontal and vertical positioning errors of kinematic DF-PPP can converge to 0.5 m in less than 15 min and 20 min, respectively. As for the kinematic SF-PPP, it could converge to 0.8 m in horizontal and 1.0 m in vertical within 30 min, where the ionosphere-constrained PPP performs better than the UofC PPP approach, owing to the contribution of the ionospheric grid corrections.

Improved kinematic Precise Point Positioning performance with the use of map constraints

Abstract A positioning approach combining satellite measurements with a map representing the ground-truth trajectory is developed with the main objective of improving the availability of solutions for a mobile vehicle. For the positioning model, the Precise Point Positioning (PPP) technique is augmented with an alternative map-matching to find a probable space where the true vehicle or platform position is located. Then, by using a selection criterion based on the precise carrier phase residuals, the best candidate position within the space can be determined. This process provides an accurate initial position to the PPP filter, different from the standard PPP approach that relies on a point position using the less accurate pseudorange observables. A controlled experiment of a mobile receiver navigating over a pre-defined trajectory was conducted. The results show that the approach offers an instantaneous initial convergence, eliminating the re-convergences during two GNSS obstructions of 32 and 17 seconds, while constantly keeping the solution on the correct trajectory, even when tracking 3 to 2 satellites. This approach outperforms the standard PPP and RTK solutions in terms of convergences and re-convergences. These results are corroborated when comparing the average and standard deviation of residuals to the standard PPP model. For the pseudorange residuals, improvements of 17.5 cm and 24.3 cm in the average and standard deviation respectively were achieved. The carrier phase residuals standard deviation of the proposed approach was 3 cm better than that of the standard PPP.

A new approach to real-time precise point-positioning timing with International GNSS Service real-time service products

Real-time precise timing with the precise point-positioning (PPP) technique is of great interest for scientists. However, real-time precise products are not aligned to a unified time scale. Hence, real-time precise products can only be utilized for time transfer not for timing. Furthermore, if the reference time changes frequently, the receiver clock offset cannot be modelled to further improve the accuracy of timing. In this work, we present a precise satellite timing approach using International GNSS Service (IGS) real-time service products, obtaining the difference between the local time of the user and UTC(k) directly using a global navigation satellite systems (GNSS) receiver. This approach is based on three steps: (1) receiving real-time data streams and receiver observations connected to UTC(k); (2) aligning the reference time of the new precise products to UTC(k) by a PPP approach, with the new precise products then being broadcast via NTRIP (networked transport of RTCM via internet protocol); and (3) obtaining the difference between local time and UTC(k) directly using a GNSS receiver, which can be done by users anywhere on the Earth. Our numerical analyses clarify how our precise timing approach performs using IGS real-time service products. First, the standard deviation (STD) of the difference between the timing results and the receiver clock results released by the IGS final products is approximately 0.2 ns. The STD values of the difference are reduced by approximately 2.76%–25.66% using the between-epoch constraint model. Second, the frequency stability of the timing has a good consistency with the receiver clock offset from the IGS final products with regard to long-term stability, while the short-term stability of the timing with the between-epoch constraint model is better than that of IGS final products. Third, the real-time kinematic positioning accuracy obtained using the new products and CLK93 products is of a similar level when the clock offset is estimated with the white noise model. By using the new products, the positioning accuracy of the between-epoch constraint model is improved by 0.91%, 2.54% and 23.21% over the result without the clock model in three coordinate components.

Performance of Selected Ionospheric Models in Multi-Global Navigation Satellite System Single-Frequency Positioning over China

Ionospheric delay as the major error source needs to be properly handled in multi-GNSS (Global Navigation Satellite System) single-frequency positioning and the different ionospheric models exhibit apparent performance difference. In this study, two single-frequency positioning solutions with different ionospheric corrections are utilized to comprehensively analyze the ionospheric delay effects on multi-frequency and multi-constellation positioning performance, including standard point positioning (SPP) and ionosphere-constrained precise point positioning (PPP). The four ionospheric models studied are the GPS broadcast ionospheric model (GPS-Klo), the BDS (BeiDou Navigation Satellite System) broadcast ionospheric model (BDS-Klo), the BDS ionospheric grid model (BDS-Grid) and the Global Ionosphere Maps (GIM) model. Datasets are collected from 10 stations over one month in 2019. The solar remained calm and the ionosphere was stable during the test period. The experimental results show that for single-frequency SPP, the GIM model achieves the best accuracy, and the positioning accuracy of the BDS-Klo and BDS-Grid model is much better than the solution with GPS-Klo model in the N and U components. For the single-frequency PPP performance, the average convergence time of the ionosphere-constrained PPP is much reduced compared with the traditional PPP approach, where the improvements are of 11.2%, 11.9%, 21.3% and 39.6% in the GPS-Klo-, BDS-Klo-, BDS-Grid- and GIM-constrained GPS + GLONASS + BDS single-frequency PPP solutions, respectively. Furthermore, the positioning accuracy of the BDS-Grid- and GIM-constrained PPP is generally the same as the ionosphere-free combined single-frequency PPP. Through the combination of GPS, GLONASS and BDS, the positioning accuracy and convergence performance for all single-system single-frequency SPP/PPP solutions can be effectively improved.

Sub-hourly precise point positioning accuracy analysis – case study for selected ASG-EUPOS stations

Precise Point Positioning (PPP) is still considered a new technique of GNSS measurements intensively developed in recent years. One of the main advantages of this method is the autonomous mode of measurement, requiring only one receiver, which ensures the high accuracy of the measured position. The accuracy, in some modes of measurement and processing, is similar to the results obtained with the use of Relative GNSS technique (RGNSS). The main disadvantages of PPP include the need to introduce a set of corrections, which in the RGNSS are reduced using differential equations and a relatively long time (about 20 min or more) needed for ambiguity resolution. The analysis conducted so far concerning the determination of the PPP accuracy focused mainly on the results obtained from long (daily) static observation. The results obtained from the sub-daily observation, less often analysed, involved longer time intervals (1–8 h). In this paper, time series of position components derived from sub-hourly (30 min) PPP solutions were analysed. The analysis was based on 30 days of observations performed at 8 ASG-EUPOS system stations. For processing the collected GNSS observations (in different variants) the NAvigation Package for Earth Orbiting Satellites (NAPEOS) software was chosen. If it will be assumed that standard deviation (SD) can be a good measure of the accuracy of the obtained results, the conducted analyzes prove that the sub-hourly PPP technique can provide accuracy in the order of 0.5 cm (SD below 0.5 cm) for the horizontal position components and 1 cm (SD below 1 cm) for the vertical position component. The above accuracy was obtained in the multi-station PPP approach (fixed ambiguity solution). In float ambiguity solution scenarios the standard deviation increases up to 1 cm for horizontal components and up to 2 cm for the vertical component. The periodicity, in the obtained position components time series, were analysed using the Lomb-Scargle periodogram. Spectral analysis showed clear periodicity in the obtained results (especially for GPS-only fixed and float solutions). For GPS or GPS/GLONASS processing strategies 73% of detected periodic signals correspond to a multiple of the orbital periods of the satellites.

Effect analysis of higher-order ionospheric corrections on quad-constellation GNSS PPP

With the development of global navigation satellite system (GNSS) precise point positioning (PPP) technology, higher positioning accuracy is required in some applications. An important error source in PPP is the residual higher-order (i.e. second- and third-order) ionospheric error after the first-order ionospheric error has been removed by dual-frequency observation combinations. Generally, higher-order ionospheric errors are negligible; but at high ionospheric activities, higher-order ionospheric errors can reach a few centimeters, which must be considered in high-precision positioning. In this study, a quad-constellation PPP approach with higher-order ionospheric corrections is proposed. The temporal variations of the higher-order ionospheric errors for GPS, GLONASS, BDS and Galileo are analyzed and their effects on quad-constellation PPP are evaluated. The GNSS observations collected at different solar activities are used to analyze the effect of the higher-order ionospheric errors and the results indicate that their magnitudes can reach almost 2 cm for their first frequency signals at high solar activity. The occurrence of geomagnetic storms further increases the higher-order ionospheric errors by a few millimeters. Multi-GNSS datasets collected at low, middle and high latitude stations at different ionospheric activities are processed and the results indicate that the higher-order ionospheric delay can affect the 3D position solutions of the quad-constellation PPP at a maximum of 6 mm.

PPP-based Swarm kinematic orbit determination

Abstract. The Swarm mission of the European Space Agency (ESA) offers excellent opportunities to study the ionosphere and to provide temporal gravity field information for the gap between the Gravity Recovery and Climate Experiment (GRACE) and its follow-on mission (GRACE-FO). In order to contribute to these studies, at the Institut für Erdmessung (IfE) Hannover, a software based on precise point positioning (PPP) batch least-squares adjustment is developed for kinematic orbit determination. In this paper, the main achievements are presented. The approach for the detection and repair of cycle slips caused by ionospheric scintillation is introduced, which is based on the Melbourne–Wübbena and ionosphere-free linear combination. The results show that around 95 % of cycle slips can be repaired and the majority of the cycle slips occur on L2. After the analysis and careful preprocessing of the observations, 1-year kinematic orbits of Swarm satellites from September 2015 to August 2016 are computed with the PPP approach. The kinematic orbits are validated with the reduced-dynamic orbits published by the ESA in the Swarm Level 2 products and SLR measurements. The differences between IfE kinematic orbits and ESA reduced-dynamic orbits are at the 1.5, 1.5 and 2.5 cm level in the along-track, cross-track and radial directions, respectively. Remaining systematics are characterized by spectral analyses, showing once-per-revolution period. The external validation with SLR measurements shows RMSEs at the 4 cm level. Finally, fully populated covariance matrices of the kinematic orbits obtained from the least-squares adjustment with 30, 10 and 1 s data rate are discussed. It is shown that for data rates larger than 10 s, the correlation between satellite positions should be taken into account, for example, for the recovery of gravity field from kinematic orbits.

Real-Time Precise Point Positioning Using Tomographic Wet Refractivity Fields

The tropospheric wet delay induced by water vapor is a major error source in precise point positioning (PPP), significantly influencing the convergence time to obtain high-accuracy positioning. Thus, high-quality water vapor information is necessary to support PPP processing. This study presents the use of tomographic wet refractivity (WR) fields in PPP to examine their impacts on the positioning performance. Tests are carried out based on 1-year of 2013 global navigation satellite system (GNSS) observations (30 s sampling rate) from three stations with different altitudes in the Hong Kong GNSS network. Coordinate errors with respect to reference values at a 0.1 m level of convergence is used for the north, east, and up components, whilst an error of 0.2 m is adopted for 3D position convergence. Experimental results demonstrate that, in both static and kinematic modes, the tomography-based PPP approach outperforms empirical tropospheric models in terms of positioning accuracy and convergence time. Compared with the results based on traditional, Saastamoinen, AN (Askne and Nordis), and VMF1 (Vienna Mapping Function 1) models, 23–48% improvements of positioning accuracy, and 5–30% reductions of convergence time are achieved with the application of tomographic WR fields. When using a tomography model, about 35% of the solutions converged within 20 min, whereas only 23%, 25%, 25%, and 30% solutions converged within 20 min for the traditional, Saastamoinen, AN, and VMF1 models, respectively. Our study demonstrates the benefit to real-time PPP processing brought by additional tomographic WR fields as they can significantly improve the PPP solution and reduce the convergence time for the up component.

Multi-GNSS precise point positioning for precision agriculture

The main objective of this research was to examine the feasibility of Multi-GNSS precise point positioning (PPP) in precision agriculture (PA) through a series of experiments with different working modes (i.e. stationary and moving) under different observation conditions (e.g. open sky, with buildings or with canopy). For the stationary test carried out in open space in the UK, the positioning accuracy achieved was 13.9 mm in one dimension by a PPP approach, and the repeatability of positioning results was improved from 19.0 to 6.0 mm by using Multi-GNSS with respect to GPS only. For the moving test carried out in similar location in the UK, almost the same performance was achieved by GPS-only and by Multi-GNSS PPP. However, for a moving experiment carried out in China with obstruction conditions, Multi-GNSS improved the accuracy of baseline length from 126.0 to 35.0 mm and the repeatability from 110.0 mm to 49.0 mm, The results suggested that the addition of the BeiDou, Galileo and GLONASS systems to the standard GPS-only processing improved the positioning repeatability, while a positioning accuracy was achieved at about 20 mm level in the horizontal direction with an improvement against the GPS-only PPP results. In space-constrained and harsh environments (e.g. farms surrounded with dense trees), the availability and reliability of precise positioning decreased dramatically for the GPS-only PPP results, but limited impacts were observed for Multi-GNSS PPP. In addition, compared to real time kinematic (RTK) GNSS, which is currently most commonly used for high precision PA applications, similar accuracy has been achieved by PPP. In contrast to RTK GNSS, PPP can provide high accuracy positioning with higher flexibility and potentially lower capital and running costs. Hence, PPP might be a great opportunity for agriculture to meet the high accuracy requirements of PA in the near future.