The Galileo for Science Project (G4S_2.0) is an ongoing project funded by the Italian Space Agency that has several goals in the field of Fundamental Physics by exploiting the Galileo-FOC Constellation and, in particular, GSAT0201 (E18) and GSAT0202 (E14), the two satellite in elliptical orbit. By exploiting the accuracy of the atomic clocks on board the satellites, in particular of the clock-bias estimated in the process of data reduction of the tracking observations during a Precise Orbit Determination (POD), it allows on the one hand to measure the gravitational redshift, constraining the Local Position Invariance (LPI) and, on the other hand, to place constraints on the possible presence of dark matter in our galaxy in the form of Domain Walls. A fundamental point is obtaining a suitable satellite orbit solution by performing an accurate POD. In this context, the activities carried out with the Bernese code will be presented.

How to cite: Cinelli, M., Sapio, F., Lucchesi, D., Visco, M., Di Marco, A., Fiorenza, E., Lefevre, C., Loffredo, P., Lucente, M., Magnafico, C., Peron, R., Santoli, F., and Vespe, F.: The Galileo for Science project: Bernese GNSS Software applications for Fundamental Physics, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-13425, https://doi.org/10.5194/egusphere-egu24-13425, 2024.

To achieve the 1 mm accuracy and 0.1 mm/year stability of Terrestrial Reference Frame (TRF) required by Global Geodetic Observing System (GGOS), various surface displacements have to be precisely modeled. Non-tidal atmosphere, ocean, and hydrology loading displacements are major sources causing stochastic and systematic effects in station coordinates estimated by space geodetic techniques such as Global Navigation Satellite Systems (GNSS). Studies show that the correction of non-tidal loading displacements in GNSS station coordinate time series reduces coordinate repeatability and thereby improves stability. Currently, non-tidal loading displacements are corrected on the observation level in Very Long Baseline Interferometry (VLBI) data analysis for standard IVS (International VLBI Service for Geodesy and Astrometry) products, but not in GNSS data analysis. We applied the ESMGFZ non-tidal atmosphere and ocean loading displacements (NTAOL) on the observation, normal equation, and parameter levels for global GNSS network solutions in 2005-2019. We demonstrate that the station coordinate repeatability can be significantly improved when correcting NTAOL displacements, especially in the up component where a reduction of 20-30% can be observed at middle and high latitudes. Whereas for other geodetic parameters, such as satellite orbits, Earth Rotation Parameters (ERP), and geocenter motion, however, the impact of NTAOL displacements is insignificant. The difference between applying NTAOL displacements on the observation to that on the normal equation level is on sub-daily scales and we show that most of these differences are absorbed by receiver clocks. As for the differences of applying NTAOL on the observation and on the parameter levels, small but systematic effects on the horizontal components of station coordinates appear, which are mainly due to network alignment. We also demonstrate that the a priori tropospheric delay modeling affects the non-tidal atmosphere loading signals in station coordinates, i.e., when applying empirical tropospheric delay models, e.g., GPT3, NTAL correction introduces a significantly smaller improvement of station coordinate repeatabilities (below 5% in up component). Hence, we recommend always using discrete tropospheric delay products from Numerical Weather Model (NWM) as a priori values when NTAL corrections are applied.

How to cite: Wang, J., Dobslaw, H., Balidakis, K., Glaser, S., Männel, B., Ge, M., Heinkelmann, R., and Schuh, H.: Applying non-tidal atmosphere and ocean loading corrections on the observation, normal equation, and parameter levels in GNSS data analysis, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-12883, https://doi.org/10.5194/egusphere-egu24-12883, 2024.

Annual signals derived from GNSS position time series have become a very important source of information on a variety of geophysical phenomena occurring in the closer or farther vicinity of the antennas. In this research, we investigated the vertical position time series obtained from the International GNSS Service (IGS) third reprocessing (repro3) and PPP times series from the Nevada Geodetic Laboratory (NGL). We selected 1019 globally distributed stations with good quality data and time spans longer than 5 years. First, we pre-processed them for outliers and identified the epochs of offsets using manual inspection. Then, we inspected the differences between the annual signals contained in both sets of time series. We noticed from the map of annual signal differences that there is a worldwide annual common mode in the series of “IGS-NGL” station position differences, with a median amplitude of the order of 2 mm, and a maximum around August. We hypothesized that those differences could be explained by different strategies of alignment to the reference frame, and in particular by the alignment of the NGL series to the scale of the ITRF. To investigate this, we produced additional series by applying different types of constraints to the daily repro3 normal equations. Namely, we compared four sets of time series: “IGS” which are the official repro3 solutions, aligned by no-net-rotation nor translation (NNR+NNT) constraints to the IGSR3 reference frame via the well-distributed IGSR3 core network; “IGa” which are repro3 solutions aligned by no-net-rotation, translation nor scale (NNR+NNT+NNS) constraints to IGSR3 via the same core network; “IGb” which are repro3 solutions aligned by NNR+NNT+NNS constraints to IGSR3 via the same daily sets of reference stations as used by Jet Propulsion Laboratory (JPL) to align their orbit and clock products; and “IGc” which are repro3 solutions aligned by NNR+NNT+NNS constraints to the IGb14 reference frame via the same set of reference stations as used by JPL. A comparison of these four sets of time series with the NGL PPP time series reveals that c.a. half of the systematic differences in vertical annual signals between IGS and NGL comes from the alignment of the NGL solutions in scale to the reference frame, and another half comes from the use of different station networks for the alignment to the reference frame.

How to cite: Bogusz, J., Rebischung, P., and Klos, A.: Differences in annual signals between IGS- and NGL-derived position time series: testing different strategies of alignment to the reference frame, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-5351, https://doi.org/10.5194/egusphere-egu24-5351, 2024.

We present a neural network optimized for producing GNSS displacements to explore machine learning capabilities in forecasting ground motions for earthquake early warning and to improve our understanding of ground motion in real-time. For earthquake early warning, displacements at GNSS receivers are currently being incorporated into the ShakeAlert system, but displacements in real-time are problematic due to issues with phase ambiguity fixing, cycle slips, and loss of satellite lock as well as dilution of precision from satellite network geometry. These errors can lead to anomalous motions of up to a meter. Raw GNSS observations for velocities can utilize orbits (relative positions) and remove uncertainties caused by path errors, leading to a higher precision observation than the displacements. In general, peak ground velocity is diagnostic of earthquake damage and displacement is diagnostic of total moment release, so obtaining these observations at the highest fidelity is crucial for rapid earthquake source estimation. Since processing raw GNSS velocities gives a higher precision observation, we aim to derive displacements from velocities using a machine learning approach. We use a Long Short-Term Memory (LSTM) network, a recurrent neural network (RNN) with the ability to remember values for an arbitrary amount of time, for time series prediction of the GNSS displacements. The input variables for the model are three-component GNSS velocities derived from the SNIVEL software package, with the possibility of including signal to noise and phase observables, and the output variable is the GNSS displacement time series. The GNSS displacement is validated against the displacements computed with the precise point positioning code GipsyX. With over 2250 1-Hz observations from 82 different events ranging from M4.9 to M9, we have ample data to train, validate, and test the network on. We train several neural network instances on random selection of train/validation/test split for redundancy and shuffle data input order for each instance. By computing the GNSS displacement from GNSS velocities, we produce a higher precision observation, a low-cost method for monitoring deformation without the traditionally high overhead associated with real-time GNSS processing, and the possibility of direct onboard receiver transmission of displacements.

How to cite: DeGrande, J. and Crowell, B.: Evaluating a Long Short-Term Memory(LSTM) network for real-time high-rate GNSS time series analysis, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-309, https://doi.org/10.5194/egusphere-egu24-309, 2024.

With the continuous development and updates of GNSS systems, an increasing number of satellites now emit triple-frequency signals. Currently, research on triple-frequency positioning is predominantly focused on the Asian region, with limited attention given to the multi-frequency positioning performance in Europe. This study utilizes triple-frequency signals from BDS-3/GPS/Galileo satellites and employs observations from EUREF Permanent GNSS Network (EPN) to evaluate the performance of Precise Point Positioning Ambiguity Resolution (PPP-AR) and Atmosphere-augmented Real-Time Kinematics (PPP-RTK) modes in the European region. We calculate Uncalibrated Phase Delay (UPD) using 46 EPN stations and perform PPP-AR on all 138 stations to derive ionospheric and tropospheric delays. The fixing residuals of EWL/WL/NL UPD achieve 99.9%/98.2%/84.9% for BDS, 100.0%/97.1%/89.9% for Galileo, and 99.9%/94.9%/88.7% for GPS satellites within 0.15 cycles, respectively. Double and triple-frequency PPP-AR 68^th percentile results achieve 7.0/3.5 and 7.0/6.0 minutes for horizontal and vertical components using GPS/Galileo/BDS constellations. Additionally, the ionospheric delays derived from double and triple frequencies show only slight differences, measured at the centimeter-level among GPS/Galileo/BDS constellations. Relying on atmospheric delay augmentation, i.e., PPP-RTK, we further analyze the positioning performance under varying inter-station distances from 100 km to 400 km. The triple-frequency brings about a 5% improvement in convergence for BDS and Galileo satellites with respect to double-frequency solutions, while only slightly enhancing GPS satellites. Combining GPS/BDS/Galileo achieves nearly instantaneous convergence even at distances up to 400 km. Overall, the European region using GPS/Galileo/BDS constellations can achieve rapid positioning by triple-frequency signals, and instantaneous convergence can be achieved for double and triple-frequency solutions when atmosphere delays are implemented.

How to cite: Cui, B., Du, S., Jiang, X., Wang, L., Huang, G., Ge, M., and Schuh, H.: Multi-GNSS double/triple-frequency PPP-AR/RTK performance evaluation in the European region, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-7066, https://doi.org/10.5194/egusphere-egu24-7066, 2024.

Using LEO satellites for positioning and navigation has been a research hotspot in the GNSS community in recent years. As the LEO satellites are much closer to earth and move much faster relative to earth than GNSS, precise point positioning (PPP) convergence time can be substantially improved. Various simulation studies on LEO augmentation have been carried out, but its performance with real LEO observations in a real-world environment is rarely reported. The CENTISPACE^TM system, which is developed by Beijing Future Navigation Tech Co., Ltd., has launched four experimental satellites in the last two years, providing a good opportunity for studying LEO augmentation. We collect real LEO navigation observations from two CENTISPACE^TM satellites using a regional network. Before conducting LEO-augmented PPP, orbit determination and time synchronization (ODTS) for the experimental LEO satellites are first investigated, and a data-processing framework is established using the space-borne GNSS observations from LEO satellites and the LEO augmentation observations from ground stations. The LEO-augmented PPP algorithm is then derived, with a focus on the LEO relativistic effect. With these bases, we analyze the LEO-augmented PPP performance with different GNSS systems (including GPS, BDS, and Galileo) combined with LEO satellites. The static PPP tests using one (G/C/E), two (GC/GE/CE), and three (GCE) GNSS systems show that the average convergence time is significantly reduced with the participation of the two LEO satellites, from 32.7, 17.9, and 14.2 min to 16.7, 8.9, and 5.7 min, respectively. This indicates that adding only two LEO satellites improves the convergence times of static PPP with one, two, and three GNSS systems by 48.9%, 50.2%, and 59.8%, respectively. For PPP precision evaluation, the GNSS-only 3D positioning errors are 6.1, 4.6, and 4.6 cm with one, two, and three systems, respectively. They are reduced to 5.2, 3.9, and 3.8 cm by adding two LEO satellites, respectively. The corresponding improvements are 13.9%, 16.4%, and 18.8%, respectively. The above study not only validates the customized processing framework and strategy for LEO augmentation processing but also demonstrates the great potential of LEO augmentation. With more LEO satellites to be deployed in the future, much larger improvements can be achieved.

How to cite: Li, W., Li, M., Huang, T., Chang, C., and Zhao, Q.: Precise point positioning with LEO augmentation: results from two experimental satellites, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-3726, https://doi.org/10.5194/egusphere-egu24-3726, 2024.

Reliable integer ambiguity resolution is the key to the global navigation satellite system (GNSS)-based precise positioning applications. In many scenarios, it is a common setup that more than one antenna is mounted on the moving platform. The integer ambiguity resolution can therefore be improved if the constant baseline information between the antennas is used reasonably. In this contribution, the baseline information, which can be measured a prior  as the constraint and has been successfully used to improve the GNSS-based attitude determination, is now extended to relative positioning. The baseline length is fully integrated into the ambiguity objective function of the relative positioning model, thus improving the reliability of relative positioning resolution. In experimental validation, both simulated and real datasets are tested to demonstrate the benefits brought by the baseline length constraint. The results show that the constraint ensures a higher ambiguity resolution success rate, and the improvement is more obvious when the observable condition is weaker.

How to cite: Wu, S., Fan, B., Ding, Y., Jiang, Z., Ran, Y., and Cao, K.: Improving ambiguity resolution success rate in GNSS-based relative positioning with moving-baseline length constraint, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-23, https://doi.org/10.5194/egusphere-egu24-23, 2024.

To achieve highest precision in positioning and navigation, frequency transfer, ionosphere monitoring, etc. with global navigation satellite system (GNSS) data, the technique of uncombined precise point positioning (PPP) ambiguity resolution holds great potential. Unified data processing and reliable ambiguity resolution for multi-GNSS are essential prerequisites. Consequently, we propose a refined approach for quality control of multi-GNSS uncombined PPP ambiguity resolution employing a sequential Kalman filter. In addition to addressing the implementation of uncombined PPP ambiguity resolution, our focus extends to the selection of the reliable ambiguity datum, computational efficiency and refining the ambiguity resolution strategy. When quad-constellation GNSS data are processed, the results demonstrate that employing the sequential Kalman filter with OpenMP can enhance computational efficiency by approximately three times compared to the standard filter. Additionally, the sequential Kalman filter is also convenient to incorporate the ambiguity datum or the fixed ambiguity as a strong constraint and complete the post-residuals check for further validating the ambiguity resolution. Following the consideration of a set of indicators, e.g., arc length, cutoff angle, ratio value and success rate, for controlling reliable ambiguity resolution, the incorrect ambiguity fixing rate can be effectively reduced, especially during the convergence stage.

How to cite: Cao, X. and Soja, B.: Quality control for multi-GNSS uncombined PPP ambiguity resolution using a sequential Kalman filter, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-5099, https://doi.org/10.5194/egusphere-egu24-5099, 2024.

With the release of Android 7.0 in 2016, it became possible to retrieve raw GNSS measurement data from Android smartphones. The capability of directly accessing the GNSS measurements allows, among other things, a more reliable estimation of the user’s position by applying external correction data and sophisticated algorithms. However, the GNSS hardware in smartphones is simple and cost-effective, clearly impacting the quality of the measurements. This results in higher levels of noise and frequently occurring effects like outliers, cycle slips, and multipath.

Precise Point Positioning (PPP) is an excellent technique for smartphone positioning due to its features and flexibility. PPP is characterized by applying precise satellite products (orbits, clocks, and biases) and complex models and algorithms to estimate the user's position. Due to this concept, PPP does not require nearby reference stations because these precise satellite products are globally valid. Furthermore, the concept of PPP allows the development of resilient and flexible algorithms, providing a remarkable advantage considering the challenging nature of GNSS measurements from smartphones.

The Galileo High Accuracy Service (HAS) started its service in January 2023. This service is free of charge and provides real-time corrections to the broadcasted navigation message for GPS and Galileo over signal-in-space (E6 frequency) and the internet. The design of the Galileo HAS makes it particularly interesting for low-cost GNSS and smartphone applications. According to the system operator, the Galileo HAS enables position accuracies at the decimeter level, depending on the PPP processing algorithms and the GNSS hardware of the user.

This contribution addresses challenges originating from the ultra-low-cost smartphone equipment and suggests suitable solutions (e.g., data-cleaning algorithms). Furthermore, PPP results with state-of-the-art smartphones (e.g., Google Pixel 7) and the Galileo HAS are presented. The corresponding PPP calculations are performed with our open-source software raPPPid using the uncombined PPP model with ionospheric constraint in quasi-real-time settings. The results demonstrate that it is possible to achieve position accuracies down to the decimeter level with the Galileo HAS under good conditions.

How to cite: Wareyka-Glaner, M. F. and Möller, G.: Smartphone PPP with the Galileo High Accuracy Service, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-9332, https://doi.org/10.5194/egusphere-egu24-9332, 2024.

Before 2016, the users had access only to the position-velocity-time (PVT) information from the GNSS chipsets, and the raw GNSS observations were not available. The GNSS module's positioning accuracy on smartphones typically ranged from 3 to 5 meters under favorable multipath conditions, but over 10 meters in challenging environments. This level of accuracy was not sufficient for some applications. Fortunately, in May 2016, during the "Google I/O" conference, Google announced that the raw GNSS measurements, i.e., the pseudorange, carrier-phase, Doppler shift and carrier-to-noise density ratio (C/N0) observations, would be accessible through the Android Nougat (version 7) operating systems. Google has officially released Android 7 (Nougat) on August 22, 2016, marking a breakthrough for the GNSS community. Since then, research has been conducted to develop new algorithms to improve GNSS positioning performance using these mass-market devices. In 2021 and 2022, the Android GPS team of Google hosted two Google smartphone decimeter challenges (GSDC), where various smartphone GNSS datasets of real vehicular applications were used to determine smartphone positioning accuracies. As has been revealed, meter-level accuracy is generally achieved by the leading participants, which is still not enough to enable smartphone precise positioning. This indicates an ongoing demand to enhance the positioning accuracy with smartphones.

Different positioning algorithms, such as absolute or relative positioning methods can be applied to the smartphone observations as well. Precise point positioning (PPP) is a powerful method for conducting accurate real-time positioning using a single receiver. Research papers have reported PPP smartphone positioning accuracy ranging from decimeter to sub-meter accuracy, depending on different factors such as the environment and positioning mode (static and kinematic). Most studies have so far focused on utilizing the GNSS only observations obtained from the smartphone's API. However, incorporating additional information as constraints can enhance accuracy and overall stability (for example height information).

The Android operating system incorporates a set of functions known as APIs, allowing the users to use the system's features. Each Android version has distinct types of APIs. Among these, the android.location API is dedicated to the location-related services, with the "Location" class being one of them. This class consists of parameters such as latitude, longitude, altitude, timestamp, accuracy, bearing and velocity. The "AltitudeMeters" from this class provides the height above the WGS84 ellipsoid in meters, serving as supplementary information in this research. Although the vertical positioning accuracy of GNSS is generally lower than the horizontal accuracy, utilizing recorded height from the smartphone GNSS chipset can still be beneficial. This incorporation increases the degree of freedom and strengthens the geometry of the receiver and satellites. In this study, we assess the effectiveness of the uncombined PPP model in the presence of height constraints. We will utilize both pedestrian walking and vehicular datasets collected by a dual-frequency Xiaomi Mi8 device to evaluate the effect of adding height constraint to PPP model. We expect an improvement on the root-mean-square (RMS) of horizontal positioning, the 50th percentile error, and the convergence time when employing the height constraints.

How to cite: Zangenehnejad, F. and Gao, Y.: Height-constrained uncombined PPP for enhanced pedestrian and vehicular positioning with an Android smartphone, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-4153, https://doi.org/10.5194/egusphere-egu24-4153, 2024.

Smartphone-based positioning, navigation, and timing applications have been among the most popular topics within the GNSS community since 2016 when Google announced that raw GNSS observations are publicly available. However, achieving high positioning accuracy with smartphones is troublesome because of their specific limitations, such as the high noise level of observations, low protection against multipath, and discontinuities in carrier phase observations. Due to considerable discontinuities in carrier phase observations, code observations still play a crucial role in smartphone-based positioning applications. Subsequently, a realistic stochastic approach is mandatory to obtain the utmost positioning performance. This is especially true since the stochastic behavior of code observations for geodetic receivers and Android smartphones are quite different i.e., GNSS observations obtained from a smartphone are much noisier. The signal strength of GNSS signals collected from Android smartphones is also not very stable and is significantly lower when compared with geodetic receivers. Unlike observations obtained from geodetic receivers, no significant dependency between observation noise and elevation angle can be observed in smartphone observations. Therefore, conventional stochastic models, mainly based on the satellite elevation angle, are not enough to represent the stochastic behavior of smartphone observations. In this context, this study provides an enhanced stochastic approach for code observations obtained from Android smartphones. The corresponding approach includes a weighting scheme based on carrier-to-noise ratio (C/N0) values representing the signal strength of GNSS code observations. Besides, depending on their observation noises, this approach assigns different model coefficients for each constellation, which means differences between the navigation systems can be considered in adequate observation weighting. This approach also uses a robust Kalman filter method based on the IGG (Institute of Geodesy and Geophysics) III function to compensate for the effects of outliers and incorrectly weighted observations on the filtering performance. In this study, GPS, GLONASS, Galileo, and BeiDou code observations collected from a Xiaomi Mi 8 are processed to evaluate the performance of the proposed stochastic model. Firstly, observation noises are analyzed utilizing code-minus-phase observations, and the results show that GLONASS observations are considerably noisier than observations from other systems. Following, probability distributions of observation noises are evaluated to determine a realistic stochastic model, and the SIGMA- model with different coefficients for each constellation is adopted in this study. The Standard Point Positioning (SPP) method is also used to analyze the positioning performance of the proposed model. The results indicate that the proposed model can provide a 3D positioning accuracy of 1.5 m with the smartphone in static mode, which means the model improves the positioning accuracy by 36.9% compared to the conventional elevation-dependent stochastic approach. From these results, it can be said that the enhanced stochastic approach, based on C/N0 values and computing model coefficients for each constellation differently, can better reflect the stochastic behavior of code observations collected by Android smartphones.

How to cite: Bahadur, B. and Schön, S.: An enhanced stochastic approach for code observations collected from Android smartphones, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-5540, https://doi.org/10.5194/egusphere-egu24-5540, 2024.

The last decade has brought us rapid developments in low-cost GNSS receiver technology. The performance level of such receivers can be unexpectedly close to that offered by high-grade geodetic ones. Nevertheless, the further growth of applicability for these types of devices still needs a more detailed analysis of observations.

Motivated by such developments, we focused on the quality of multi-GNSS pseudorange data acquired by three low-cost receivers: u-blox ZED-F9P, Septentrio Mosaic-X5, and Skytraq PX1122R and its comparison with reference values adopted from the geodetic receiver - Trimble Alloy. We investigated two main characteristics of code data – observation noise and correlation in the time domain. In contrast to a typical pseudorange data analysis based on a single-receiver scenario performed with multipath combinations, we extended our tests with data acquired at zero-baseline formed of homogeneous receiver pairs. Such an approach allowed us to analyze the quality of more realistic data, i.e., affected by multipath, and data with multipath removed through between-receiver differencing.

The investigations revealed significant discrepancies in data quality between selected low-cost receivers and recorded signals. Generally, the pseudorange noise was the lowest for Septentrio Mosaic-X5, whereas the noisiest observations were found for Skytraq PX1122R. More interestingly, considering the deviation of code data, Septentrio Mosaic-X5 outperformed the geodetic receiver. On the other, we noted that the low-cost receivers' measurements are noticeably correlated in the time domain, even for between-receiver differences of multipath combinations. 

How to cite: Sieradzki, R., Paziewski, J., Stepniak, K., and Banach, J.: Quality analysis of the low-cost GNSS receiver pseudorange data. , EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-7563, https://doi.org/10.5194/egusphere-egu24-7563, 2024.

The Global Navigation Satellite System (GNSS) carrier phase and pseudorange measurements exhibit different levels of accuracy, and there are differences in observation accuracy among different observation systems, satellites and receivers. A reasonable stochastic model is crucial for improving Precise Point Positioning (PPP) results. We propose a method for constructing stochastic models in PPP using triple-frequency observations. By forming geometry-free and ionosphere-free (GFIF) combinations and subtracting inter-frequency clock biases (IFCB), the accuracies of phase and pseudorange observations are evaluated using residuals to determine weights. Data from 278 International GNSS Service (IGS) stations on September 1, 2023 are processed to calculate the accuracies of carrier phase and pseudorange observations in GPS, Galileo, and BDS-3 systems. The results show that the accuracies of carrier phase observations among different receivers are relatively close, while there are obvious disparities in pseudorange observation accuracies. The average Root Mean Square (RMS) of Galileo carrier phase and pseudorange observations is the smallest among three systems. In BDS-3 system, there are certain disparities in carrier phase observation accuracies among different types of satellites. Specifically, for LEICA and SEPT receivers, the average RMS of IGSO satellites is greater than that of MEO satellites. To validate the effectiveness of the proposed model, the static and dynamic PPP solutions are conducted using 80 IGS stations. The results demonstrate that compared to the empirical model, the proposed model shortens the average convergence time by 22.5%, 31.5%, and 24.1% in static PPP for GPS, Galileo, and BDS-3 systems, respectively. At 0.5h, the average three dimensions (3D) positioning accuracies improve by 2.1, 3.5 and 2.9 cm, respectively. For dynamic PPP within the range of 0.5 to 1 hour, the average RMS of the 3D positioning are reduced by 2.6, 4.7 and 3.0 cm, respectively. Furthermore, for multi-system PPP of GPS+Galileo+BDS-3, the average convergence time and positioning accuracy are also improved with the proposed stochastic model.

How to cite: Xiao, J. and Li, H.: Construction and Evaluation of the Stochastic Model in Precise Point Positioning based on Triple-Frequency Geometry-Free Combination, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-10780, https://doi.org/10.5194/egusphere-egu24-10780, 2024.

Global Navigation Satellite System (GNSS) plays an increasingly important role in all walks of life. In order to meet the demands of different users, it is crucial to establish corresponding correct mathematical models, especially in the field of precise positioning and navigation. However, due to the spatiotemporal complexity of and limited knowledge on GNSS errors, some residual errors would inevitably remain even after being corrected with differencing and linear combination, empirical model correction, and traditional parameterization. These residual observation errors are referred to as unmodeled errors. In fact, the unmodeled errors have adverse impacts on high-precision GNSS positioning. However, most existing studies mainly focus on handling the part of systematic errors that can be adequately modeled and then simply ignore the part of unmodeled errors that may actually exist. To make a breakthrough in the precision and reliability of GNSS applications currently, this study focuses on the theory and method for processing the GNSS unmodeled errors based on the mathematical model compensation, including resilient functional model adjustment and resilient stochastic model optimization. Specifically, according to the significance and properties of unmodeled errors, the unmodeled-error-ignored model, unmodeled-error-corrected model, unmodeled-error-fixed model, unmodeled-error-float model, and unmodeled-error-weighted model are proposed, where the approaches of significance testing, geometry-free/based/fixed models, hemispherical/hierarchy maps, composite stochastic model, multi-epoch partial parameterization, and inequality and equality constraints are adopted. Ultimately, an unmodeled error processing flow that can adaptively adjust as the external conditions change is proposed, then one can obtain high-precision GNSS positioning solutions.

How to cite: Zhang, Z. and Li, B.: GNSS unmodeled error processing based on the resilient mathematical model compensation in high-precision GNSS positioning, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-4504, https://doi.org/10.5194/egusphere-egu24-4504, 2024.

To ensure an accurate and precise position in GNSS applications, phase center corrections (PCC) have to be taken into account. PCC are antenna and frequency dependent correction values. They describe the distance along the line-of-sight direction between the electrical phase center, where the GNSS signal is received, and the antenna reference point. In Melbourne-Wübenna or code-minus-carrier linear combinations, which are often used in highly precise GNSS applications, the codephase of the GNSS signal plays a key role. Similar to the PCC, also correction values for the codephase observation exist, called codephase center corrections (CPC), also known as group delay variations (GDV). The definition of CPC as well as their estimation process with a robot in the field is similar as for PCC.

The team at Institut für Erdmessung is optimizing the established absolute antenna calibration approach for estimating CPC and PCC for multi GNSS signals in terms of repeatability, noise reduction and multipath impact. In this calibration process, an antenna under test (AUT) is precisely tilted and rotated around a fixed point in space by using a robot. A nearby reference station allows the calculation of time differenced single differences (dSD), which are used to estimate absolute CPC and PCC with spherical harmonics of degree and order 8. The pattern quality and also the repeatability of this approach depends, among other effects, on the observation noise of the GNSS signals.

In this contribution, a detailed study about the influence of observation noise on the estimated patterns is presented. To this end, dSD are simulated based on an existing pattern and the robot positioning. The dSD are modified before the estimation process by polluting them with different kind and magnitude of noise. The estimated patterns are compared using e.g. the root-mean-square or the absolute difference between two runs. Our analysis shows, that 18% of the white noise magnitude is reflected in the repeatability of the pattern estimation in terms of absolute differences between two calibration runs. 

How to cite: Breva, Y., Kröger, J., Kersten, T., and Schön, S.: How Observation Noise impacts the Estimation of Codephase- and Phase-Center Correction with a Robot in the Field, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-9080, https://doi.org/10.5194/egusphere-egu24-9080, 2024.

Troposphere mapping function plays a very important role in space geodetic tropospheric correction, estimation, and application in meteorology. In the past decades, a series of mapping functions, such as NMF, GMF, VMF1 and VMF3, were successively developed for pursuing better mapping function performance. However, limited by modeling data source of numerical weather model, the mapping functions temporal-spatial resolutions are stuck in 6 h and 1°×1°, existing problems of bad applicability in extreme weather and regions with complex terrains. As the release of the generally acknowledged best global reanalysis ERA5, we have a chance to improve current mapping function modeling by taking full advantage of accuracy and temporal-spatial resolution (1h and 0.25°×0.25) of ERA5. In this contribution, we used the ERA5 reanalysis to establish the hourly site-wise Wuhan University Mapping Function (WMF) covering 1583 GNSS, VLBI and DORIS stations, and compared the accuracy and GNSS PPP performance of WMF with VMF3 at globally distributed stations. We found the significant accuracy improvements of WMF to VMF3 as well as the non-negligible vertical coordinate and ZTD difference biases between the two mapping functions.

How to cite: Zhou, Y., Lou, Y., Zhang, W., Gong, X., and Chen, G.: Improving troposphere mapping function by ERA5 for better space geodetic estimates, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-5179, https://doi.org/10.5194/egusphere-egu24-5179, 2024.

GNSS real-time PPP have been demonstrated to be applicable to PWV retrieval effectively. The GNSS real-time satellite clock error is one of the essential factors that affects the accuracy of PPP, and its estimation method is usually considered to be white noise random processes which ignore the stable periodic variation characteristics of GNSS atomic clocks. In addition, the GNSS satellite clock offsets real-time service have low timeliness due to the time consumption of clock offsets series estimation and fitting of quadratic polynomial coefficients, even when communication is interrupted for a short period of time, RTS cannot be obtained. Thus, we developed a method that directly estimate satellite clock model coefficients simultaneously with tropospheric wet delay, receiver clock error, and phase ambiguity parameters from global GNSS code and phase measurements. The difference from traditional RTS is that the satellite clock model coefficients can be delivered to PPP users once estimated process is completed without the step of fitting. Several satellite clock models composed of polynomial and harmonic-based functions are applied to the parameter estimation of real-time satellite clock error, we compared the accuracy of estimated model parameters to IGS real-time satellite clock offsets, and discussed its performance of PPP positioning and PWV retrieval. Finally, we simulated the performance of proposed parameter estimation scheme of satellite clock error and PWV retrieval for different update interval in case of communication interruption for several minutes.

How to cite: Li, X. and Li, H.: Parameter estimation of GNSS real-time satellite clock error and its application in PWV retrieval, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-1303, https://doi.org/10.5194/egusphere-egu24-1303, 2024.

Multi-GNSS techniques are continuously improving themselves and strengthening their infrastructures. In response, companies producing GNSS hardware and software are enhancing their products with refined techniques, leading to improved positioning precision. In line with these advancements, efforts are being made to enhance algorithms which predict the accuracy of GNSS positioning. Following these improvements, users who conduct field works or optimize networks would want to know about the improved accuracy of GNSS positioning. After GPS, the new members of the GNSS are continually improving their infrastructure. To achieve the desired coordination in terms of a common processing ground among these techniques remains a challenge. This is particularly crucial for organizations developing GNSS software. For instance, NASA JPL has been making efforts to produce a PPP-AR solution. The transition from GIPSY OASIS II to GIPSY-X allowed for the processing of combined GPS, GLONASS, and GALILEO data in a JPL experiment in 2019. However, today, there is yet no AR infrastructure for the combined solution of all techniques beyond the float solution. In this study, we investigated whether JPL's 2019 AR solution is still applicable to current research. Initial attempts yielded promising results as we conducted experiments with 50 points from the IGS MGEX network's shared data. By comparing the differences between the 2019 PPP-AR solution and the 2019 and 2023 float solutions, we found that the discrepancies are not significantly large in today's GNSS accuracy. We concluded that an accuracy model generated from the 2019 AR solution could provide a satisfactory estimate for today's users. Initial findings indicate that GPS performs well with the combination of three techniques, while the synergy of techniques significantly contributes to the improvement of the vertical positioning. The accuracy produced by the combination is witnessed to be dependent on the observation period, emphasizing the need for attention from those conducting campaign measurements in this context.

How to cite: Çetin, D., Sanli, D. U., and Ogutcu, S.: An attempt to model the accuracy of GNSS Positioning from GIPSY-X PPP-AR Referring to  JPL’s 2019 Experiment, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-14958, https://doi.org/10.5194/egusphere-egu24-14958, 2024.