GPS Solutions

Satellite phase center variations need to be pre-eliminated in GNSS precise point positioning to ensure the best positioning precision and efficiency. To address the missing satellite antenna phase center corrections of GPS BLOCK IIF L5 signal, this study implements the estimation of satellite antenna Phase Center Offset (PCO) and Phase Center Variation (PCV) of BLOCK IIF and BLOCK III. One year of daily PCO and PCV solutions are estimated based on 118 globally distributed GPS stations. The x-offset, y-offset and z-offset PCO estimates yield a mean standard deviation of 2.3, 2.1 and 19.5 mm respectively. The mean differences between BLOCK III L5 PCO estimates and ground-based calibrated corrections are 1.8, 0.9 and 9.9 mm on the three components. Nadir-dependent PCVs are calculated with a precision better than 1.2 mm. Utilizing the antenna center corrections determined in this study, the convergence time of triple-frequency GPS kinematic PPP-AR can be shortened by 13.3%. Dual-frequency L1/L5 static PPP-AR validations show that L5 PCO corrections have no significant contribution to the positioning while 70% of globally distributed stations show improvements on the up component after applying L5 PCV corrections. By introducing L5 PCO/PCV corrections, the positioning precision of L1/L5 static PPP-AR are improved from 6.1, 3.2, 9.6 mm for the east, north and up components, respectively, to 6.2, 3.2 and 8.2 mm. The improvements of positioning precision are mainly for the up component, reaching 15%.

Accurate estimation of atmospheric delays and reliable ambiguity resolution (AR) are major challenges in implementing network real-time kinematic (NRTK) positioning technology. Previous studies on NRTK positioning have focused on using a double-differenced (DD) model, which restricts the flexibility of interpolated atmospheric delays and lacks a rigorous strategy for GLONASS AR due to the frequency-division multiple access (FDMA) regime. In this contribution, the ionosphere-weighted single-differenced RTK (IW-SD-RTK) model is proposed to obtain more accurate and flexible interpolation of SD atmospheric delays. Then, the influence of the short-term variation in the receiver hardware biases on the estimation of SD ionospheric delays is analyzed by comparing the common clock (CC) and decoupled clock (DC) IW-SD-RTK models, where the receiver hardware biases are treated as constant in the CC-IW-SD-RTK model and as white noise in the DC-IW-SD-RTK model. Furthermore, to improve the compatibility and interoperability of code division multiple access (CDMA) and FDMA in NRTK positioning, a novel integer-estimable (IE) FDMA model is employed for GLONASS AR. The results demonstrate that the DC-IW-SD-RTK model obtains more accurate and stable ionospheric delays than the CC-IW-SD-RTK model, and the DC-IW-SD-RTK model also outperforms the CC-IW-SD-RTK model in NRTK user positioning performance. Additionally, compared to standalone GPS, the incorporation of GPS and GLONASS observations improves the ADOP by approximately 42%, 45%, and 49% and the user 3-dimensional positioning precision by approximately 10%, 34%, and 19% for small-, medium-, and large-scale networks, respectively. The mean time to first fix (TTFF) is also improved by 36%.

As the 25th solar cycle is approaching its peak, the Real-time Kinematic (RTK) positioning performance is significantly affected by solar activity and the ionosphere. This study focuses on a triangulation network in the Hong Kong region with baseline lengths ranging from 10 to 20 km. The rover station is located at a distance of 16 km from the nearest reference station. A complete dataset spanning the entire solar activity cycle from 2013 to 2023 was collected for analysis. Virtual observations of the rover station’s position were generated using Network RTK (NRTK) processing mode. The results show that during years of low solar activity, the overall fixing rate exceeds 80%. However, in years of high solar activity, the fixing rate exhibits a noticeable correlation with local time, reaching its lowest point at around 16:00 local time, dropping to approximately 66%. In years of low solar activity, the horizontal and vertical accuracy, with a 95% confidence level, remain below 5 cm and 10 cm, respectively. In contrast, during years of high solar activity, the accuracy deteriorates to 7.5 cm and 13 cm in the horizontal and vertical direction. In addition, as the Vertical Total Electron Content (VTEC) increases, the RTK positioning performance gradually declines. On the other hand, with the increase of Rate of TEC Index (ROTI), the RTK positioning performance deteriorates rapidly.

Factor graph optimization has been widely used for state estimation in robotic SLAM community. Extensive algorithms have been proposed for camera/LiDAR/INS based SLAM. However, GNSS positioning based on factor graph optimization is limited, which prevents the introduction of high precise GNSS to robotic SLAM community. The current implementations are focused on pseudorange or RTK based positioning. PPP with ambiguity resolution (AR) is the state-of-the-art positioning technique for the past decade. Therefore, the PPP AR based on factor graph optimization is proposed, in which the pseudorange and carrier phases factors are constructed from the error equations of raw observations, while the ambiguity resolution factor is built from the ambiguity resolution. Results from 80 MGEX stations show that the average accuracy of static PPP is improved from 1.25, 0.61 and 2.29 cm to 0.81, 0.5 and 2.1 cm, corresponding to improvements of 35.1%, 18.7% and 8.7% in east, north, and up directions, respectively. As for kinematic PPP, the average accuracy is improved from 2.62, 2.21 and 5.8 cm to 1.64, 1.74 and 5.37 cm, corresponding to improvements of 37.5%, 21.6% and 7.4% in east, north, and up directions, respectively. The kinematic PPP was also verified with real-world data collected from a moving vehicle. After the first ambiguity fixing, the accuracy of PPP is improved from 3.7, 2.1 and 10.1 cm to 1.6, 2.0 and 9.0 cm for east, north and up component, respectively, corresponding to improvements of 32%, 5% and 11%. The above results confirm the efficiency of the proposed algorithm.

This paper proposes a 2D notch generator algorithm based on frequency-invariant (FI)-shaped beampattern synthesis for the Global Navigation Satellite System (GNSS) space–time anti-jamming blind null-steering mode. Unlike conventional blind null-steering anti-jamming algorithms based on the power inversion (PI) algorithm, the developed method treats the blind null-steering spatial filter as a 2D spatial notch filter. The beampattern synthesis method is used to solve the value of the space–time filter. With the jamming direction as prior information, constraints are applied to the flat-top (FT) and nulling (NL) regions, and FI-shaped constraints are added to the FT region to establish the objective function. NL and FI enhancement coefficients are introduced to ensure the convergence speed of the objective function and the depth of nulling. The optimization method based on the alternating direction multiplier method is employed to solve the objective function. This synthesis method is applicable to arbitrary antenna arrays. The simulation shows that compared with the PI-based algorithms, the proposed algorithm ensures undistorted reception of GNSS signals, considerably improves the receiver’s signal-to-jamming-noise ratio in different jamming scenes, enhances anti-jamming ability, and achieves an improvement of better than 20 dB in multiple three-jamming scenes.

Spoofing is becoming a prevalent threat to the users of Global Navigation Satellite Systems (GNSS). It is important to deepen our understanding of spoofing attacks and develop resilient techniques to effectively combat this threat. Detecting and mitigating these attacks requires thorough testing, typically conducted in a laboratory environment through the establishment of a spoofing test-bed. The complexity, cost and resource demands of creating such a test-bed underscore the necessity of utilizing openly available datasets. To address this need, this paper introduces a new GNSS spoofing data repository from Finnish Geospatial Research Institute (FGI) named hereafter as ‘FGI-SpoofRepo’. This data repository consists of raw In-phase and Quadrature (I/Q) data of live recordings of GPS L1 C/A, Galileo E1, GPS L5, and Galileo E5a signals. These datasets encompass three distinct types of spoofing characteristics (synchronous, asynchronous, and meaconing), making them very useful example candidates of open data for testing the performance of any anti-spoofing techniques (be it detection or mitigation). The inclusion of live signals in multiple GNSS frequencies and the presence of cryptographic signatures in Galileo E1 signal make these datasets potential benchmarks for assessing the resilience performance of multi-frequency multi-constellation receivers. The analysis of the datasets is carried out with an open-source MATLAB-based software-defined receiver, FGI-GSRx. An updated version of FGI-GSRx, equipped with the necessary modifications for processing and analyzing the new datasets, is released alongside the datasets. Therefore, the GNSS research community can utilize the open-source FGI-GSRx or any third-party SDR to process the publicly available raw I/Q data for implementation, testing and validation of any new anti-spoofing technique. The results show that time-synchronous spoofing seamlessly takes over positioning solution, while time-asynchronous spoofing acts as noise or in some cases, completely prevent the receiver from providing a positioning solution. Signal re-acquisition during an ongoing spoofing attack (cold start), the receiver tends to lock onto the spoofing signal with the highest peak, posing a potential threat to GNSS receivers without assisted information. Overall, this research aims to advance the understanding of complex spoofing attacks on GNSS signals, providing insight into enhancing resilience in navigation systems.

The tropospheric delay is difficult to be modeled accurately resulting from the high variability of atmospheric water vapor, especially under the conditions of sparse station distribution and large elevation differences, which poses challenges for real-time precise positioning. In this contribution, a real-time high-resolution (0.01° × 0.01°) zenith tropospheric delay (ZTD) model considering sparse stations and topography variations (named GFNSS) is established by integrating the information from the Global Forecast System (GFS) and Global Navigation Satellite System (GNSS). GNSS observations and GFS forecasts in the Hong Kong area are selected for the experiments. The performance of ZTDs derived from GFNSS is assessed and validated with the real-time GNSS ZTDs obtained by the precise point positioning method and the IGS post-processed ZTD products. Results show that the root mean square error (RMSE) of GFNSS ZTDs is 5.5 mm and 12.8 mm when validated with real-time and post-processed ZTD, while those for ZTD derived from the low-order surface model (LSM) are 8.8 mm and 19.0 mm, presenting a reduction of 37.5% and 32.6%, respectively. The sensitivity of model performance to the number of modeling stations and elevation differences is also evaluated. The results reveal that the GFNSS model is resistant to station number and presents high accuracy and stability with the RMSE values varying between 4.0 and 6.0 mm as the modeling station number decreases from 13 to 4, while the RMSE for the LSM model increases dramatically from 4.0 to 27.4 mm. Meanwhile, the GFNSS model achieves an RMSE value of 5.8 mm when the elevation differences are over 300 m, indicating a notable 84.9% reduction compared to that of LSM (RMSE of 38.5 mm).

The Solution INdependent EXchange (SINEX) file format, an international standard for the exchange of information, is essential in the Global Navigation Satellite System (GNSS) processing strategies that integrate different software applications. GNSS data processing using Jet Propulsion Laboratory’s (JPL) GipsyX software, which employs the Precise Point Positioning (PPP) technique, generates positions and covariance matrices in gdcov files, a GipsyX file format specific for storing this information. GipsyX software provides a tool, named mkDailySinex.py, to convert from gdcov file to SINEX file, but it is designed specifically for creating daily JPL SINEX files and does not function properly for non-JPL GipsyX users. I have developed a Python 3 program, named gdcov2sinex.py, which solves this problem, enabling any user to perform the SINEX conversion and, therefore, apply the processing strategies that integrate GipsyX with other software, such as GAMIT/GLOBK. The new python tool presented herein takes advantage of the capabilities of mkDailySinex.py and provides all its default options, but also expands the number of selectable options, which can be useful to the user. The source code, user manual, and a sample dataset of gdcov2sinex.py are provided as electronic supplementary material of this paper.

The Inter-Satellite Link (ISL) technology plays a vital role in BeiDou Navigation Satellite System (BDS), and it’s a developmental trend of the future GNSS. However, ISL is insensitive to both the Earth’s rotation and the constellation’s overall rotation, which has resulted in persistent overall constellation drift issues for autonomous navigation. Due to technical limitations, the current method for autonomous navigation requires adding ground anchor stations in order to connect the satellite constellation to Earth’s surface, thereby minimizing the drift of constellation. Nevertheless, this approach is not a fully autonomous navigation as we expected. This paper proposes an autonomous navigation scheme based on ISL utilizing a lunar satellite as a spatial anchor point and leveraging lunar gravity to establish an inertial space direction reference for the satellite constellation. The feasibility and effectiveness of this scheme are validated through theoretical analysis and simulation experiments. After 120 days of precise orbit determination simulation, the accuracy of result is improved from 408.56 m to 7.78 m, which shows a 98% improvement for all GNSS orbit by adding a lunar satellite into ISL net. This improvement is primarily observed in terms of tangent and normal directions, which experience enhancements of 89.6% and 98.6%, respectively. Specifically, we achieve an improvement of approximately 89% in the accuracy of the inclination angle, around 99% in the right ascension of ascending node, and about 89% in the sum of the argument of perigee and mean anomaly.

Low Earth Orbit (LEO) satellites can augment the traditional GNSS-based positioning, navigation and timing services, which require real-time high-precision LEO satellite clock products. As the complicated systematic effects contained in the LEO satellite clock estimates limit their high-precision mid- to long-term prediction, high-frequency LEO satellite clocks need to be estimated within a Kalman filter, resulting in a short prediction time for real-time applications. Compared to the clock estimation using Batch Least-Squares (BLS) adjustment, filter-based clock estimation experiences a lower precision. Increasing the model strength by introducing external orbital information, thus, de-correlating the orbital and clock parameters, will benefit real-time clock precision. In this contribution, reduced-dynamic LEO satellite orbits are first estimated using BLS adjustment in near real-time and predicted in the short term. The predicted orbits are then constrained during the Kalman-filter-based clock estimation process. The variance–covariance matrix of the introduced orbital errors is tested for different sets of values in the radial, along-track and cross-track directions when constraining orbits of different prediction times. One week of GPS data from the Sentinel-3B satellite in 2018 was used for validation of the proposed method. When weakly constraining high-accuracy predicted orbits within a prediction time of 20 min, i.e., with a standard deviation of the constraint set to 2–3 dm in the radial and cross-track directions, and 4–6 dm in the along-track direction, the estimated clock accuracy can be improved from about 0.27 to 0.23 ns, with a 13.4% improvement. Depending on the prediction period of the introduced orbits, the Signal-In-Space Range Error (SISRE) of the LEO satellite to Earth can also be improved, from about 9.59 cm without constraints, to 7.38–8.07 cm after constraining the predicted orbits, with an improvement of 16–23%. The improvements in the SISRE also indicate a better consistency between the real-time clock and orbital estimates.

The radio navigation satellite system (RNSS) timing has been widely used in crucial power systems. However, the problem of RNSS service vulnerability to interference and spoofing significantly affects its application. The phasor measurement unit can effectively detect timing spoofing that exceeds the maximum allowable error, but there has been less research on small-offset timing spoofing. We propose a joint timing spoofing detection method of the radio determination satellite system (RDSS) and RNSS in BDS for small-offset timing spoofing. The RDSS service uses an authentication mechanism in the master station, making it challenging to be spoofed, and it has the same time and space references as the RNSS service. We obtain the RNSS and RDSS timing signal counts and performs dynamic time wrapping to measure the similarity metric of two-time series as a detection quantity. Then, the proposed method is verified by actual experiments. The experiment results show that the detection probability of the RDSS-assisted method is significantly higher than that of the method only using the RNSS variance. The detection probability of the proposed method can reach 90% at a false alarm probability of 0.1, which verifies the accuracy and reliability of the proposed method.

Galileo supports global precise point positioning (PPP) service by delivering precise products via satellites, which is known as high accuracy service (HAS). To improve reception efficiency, the Galileo HAS employs a high-parity vertical reed-solomon encoding scheme, increasing the complexity of HAS corrections recovery. To promote research and application of the HAS, an open-source C/C + + decoding package, HASPPP, has been developed for seamless embedding into the prevalent C/C++-based software, such as RTKLIB. HASPPP provides interfaces for effortless decoding support of raw HAS binary data from various manufacturers. The HASPPP manual offers code analysis along with simple to complex examples to aid users in swiftly mastering decoding. HASPPP has undergone rigorous validation of its decoding accuracy and reliability.

This study proposes a new concept of carrier-phase-based satellite augmentation system named “Compact Real-time Kinematic for Expanded Area (COREA),” which provides centimeter-level positioning services across nationwide coverage. The proposed system’s architecture is very similar to that of the satellite-based augmentation system (SBAS), a meter-level aviation safety service. While network real-time kinematic and precise-point-positioning-RTK (PPP-RTK) rely on several densely positioned reference stations, COREA provides carrier-phase-based corrections using a few reference stations with a distance of 400–1000 km. Furthermore, the COREA corrections can be transmitted by satellite signals with extremely low-speed data links of 250 bps, similar to SBAS. This study focused on the generation method for satellite code/phase clock (CPC) corrections, which is the most significant part of the system. We analyzed the user performance of the COREA system constructed in the Midwest and South of the United States with six reference stations. Consequently, satellite CPC corrections are resilient to communication failures and highly accurate in identifying user integer ambiguity. The 95% position accuracy is approximately 1.8 cm horizontally and 7.1 cm vertically, with an average convergence time of 1–3 min using only GPS triple-frequency signals. In summary, the COREA system preserves the hardware architecture of the legacy SBAS while providing centimeter-level services with fast convergence times by utilizing extremely low-speed satellite data links across the country.

The global navigation satellite system’s signals are frequently obstructed in complex environments, and the carrier phase is prone to experiencing large cycle slips; hence, phase prediction becomes necessary. However, the current phase prediction theory presents flaws in the prediction preparation stage. The existing prediction methods merely resort to the error threshold to determine the start time of prediction, which may give rise to significant initial prediction errors. We tackle this problem and its corresponding solution for deeply coupled systems: the multistage threshold discrimination method. This method analyzes the phase error information of the cache in the prediction preparation stage to accurately determine the start time of prediction and minimize the initial prediction error. The performance of the proposed method is evaluated with static and dynamic data. In predicting for 20 s under static conditions and 10 s under dynamic conditions, the predicted pass rates are 92.6% and 52.4%, respectively, 10.4% and 11.0% higher than those of the original method. The average prediction error is reduced by 36.6% and 33.9% under static and dynamic conditions. In the scenario where the signal is interrupted multiple times, the root mean square of positioning error is reduced by 30.2%, 53.0%, and 58.7% in the east, north, and up directions. These results suggest that the proposed method is effective and constitutes a complement to the phase prediction theory.

In recent years, Global Navigation Satellite Systems (GNSSs) have become integral to our daily lives because of their precise positioning and navigation capabilities. Widespread use of smartphones equipped with GNSS receivers results in the generation of a huge amount of positioning data. Therefore, real-time cloud computing has emerged as a promising approach to effectively leverage this wealth of location information. In this study, we developed an Android app that captures raw GNSS data from smartphones, leverages cloud computing resources, calculates the position of the device, and returns the computed solution to the user. Integration of cloud-based processing not only conserves the device resources but also enables real-time position calculation, paving the way for enhanced location-based applications and services.

An open source software package has been developed for Global Navigation Satellite Systems (GNSS) interferometric reflectometry. The gnssrefl package is written in python; it can be installed from the source code, the python packaging index website, or via a docker. It includes modules that download GNSS data and orbit data from global archives. A periodogram is used to retrieve the height of the GNSS antenna over the reflecting surface using signal to noise ratio data. Signals from the Global Positioning System, Glonass, Galileo, and Beidou constellations are supported. Modules are provided to estimate volumetric water content of soil, snow depth/accumulation, and water level. Utilities for mapping and assessing reflection zones and determining the maximum resolvable height are available.

Unmodeled errors materially affect the float solutions of both ambiguities and coordinates in global navigation satellite systems (GNSS), and thus also the fixed solution. Recently, extensive attempts have been made to guarantee the reliability of integer ambiguity or reject observation faults for improving the fixed solution in real-time kinematic positioning (RTK), while far too little studies have achieved this by processing the unmodeled errors in long baselines. This contribution is therefore set out to address the unmodeled errors in GNSS RTK long baseline fixed solution. At first, we establish an equation using the quadratic form of the float ambiguity to estimate the float ambiguity bias. Then, based on the estimated float ambiguity bias, a procedure for processing the unmodeled errors in the fixed solution is proposed. Finally, a simulation experiment and a real-measured experiment are conducted, respectively. By applying the proposed procedure, the improvements in the mean and RMSE of the fixed solution bias are found to be approximately 1.11–6.17 cm and 1.06–5.73 cm in three dimensions.

This work evaluates the capability of a low-cost smartphone to measure variations in water level caused by astronomical tide and storm surges along the coast of Buenos Aires, Argentina, over a period of 27 months, employing the GNSS-IR technique. To achieve this, the smartphone Signal to Noise Ratio-derived heights are contrasted with the heights acquired from a co-located tide gauge of the Argentine Naval Hydrographic Service. A novel methodology is applied to obtain the water levels from the smartphone observations by identifying density maximums in reflections calculated using the Lomb-Scargle periodogram. The density maximums are obtain using LOWESS regression, generating a water level series sampled every 5 min referenced to the Chart Datum. Water levels were calculated for 97.7% of the time, exhibiting a standard deviation of 0.042 m against tide gauge observations. Differences between the daily (monthly) mean levels of the analyzed series showed a standard deviation of 0.016 m (0.007 m), and the amplitude differences for the tidal harmonic constituents were smaller than 0.011 m. While the results found in this work show that these devices cannot compete with traditional tide gauges, they can complement them or be used independently to monitor water level changes in regions where installing and maintaining conventional tide gauges is challenging.

Sea surface salinity (SSS) is crucial to the marine ecosystem. Soil Moisture and Ocean Salinity (SMOS) establishes a geophysical modeling function (GMF) between sea surface brightness temperature (BT) and SSS, which incorporates sea surface wind speed and significant wave height (SWH) to retrieve the SSS. However, the relationship between sea surface BT and SSS is complex and influenced by a variety of factors, making it challenging to accurately characterize this relationship using GMF. Spaceborne Global Navigation Satellite System Reflectometry (GNSS-R) observations directly respond to sea surface roughness and offer low cost and high spatiotemporal resolution advantages. Therefore, in this study, for the first time, spaceborne GNSS-R observations from the Cyclone GNSS (CYGNSS) have been incorporated into the SMOS SSS retrieval. Additionally, an empirical model between SMOS BT and Argo SSS was developed using an artificial neural network (ANN). Compared to the conventional SMOS SSS retrieval method, the proposed method in this study reduces the root mean square error (RMSE) of the retrieved SSS from 1.17 to 0.76 psu and increases the correlation coefficient (R) from 0.55 to 0.66. Furthermore, comparisons were made with ground truth measurements from the National Data Buoy Center (NDBC) buoys, which indicated that the proposed method decreases the RMSE of the retrieved SSS from 0.87 to 0.62 psu and reduces the absolute mean deviation from 0.66 to 0.48 psu. These provide references for the future application of spaceborne GNSS-R in SSS retrieval.