GPS Solutions

A growing threat for Global Navigation Satellite System (GNSS) service is Radio Frequency Interference (RFI). An important class of GNSS RFI signatures is time dependent frequency pattern signals, generically termed here as chirp signals radiated by Personal Privacy Devices which are jammers with a continuously growing (and illegal) use. The analysis of the impact of chirp signals on GNSS receivers is of the utmost importance in civil aviation. Civil aviation spectrum regulations characterize the Radio Frequency environment of the Safety-of Life GNSS service at signal processing level by comparing the effective carrier-to-noise power density ratio (C/N0,eff), calculated from a degradation of the nominal C/N0, to a C/N0 threshold. Therefore, in this work the mathematical model of the theoretical C/N0 degradation of the received useful signal in presence of a chirp signal is derived from the traditional calculation of the Spectrum Separation Coefficient (SSC) and the theoretical RFI chirp signal power spectrum density, whihc is also developed in this work. Moreover, the impact of the chirp signal characteristics on the SSC and C/N0 degradation are commented. Finally, the applicability of the proposed model based on the SSC is also analyzed from the GNSS signal, receiver local replica and RFI chirp signal characteristics.

The Receiver Autonomous Integrity Monitoring (RAIM) technique is very important for the GNSS receiver to detect faulty measurement sources before they mislead the positioning solution. Based on the parity RAIM method, a simple algorithm to detect and eliminate one fault is provided. However, there is no such a simple algorithm to detect and eliminate two faults. A general approach is traversing all possible fault cases and calculate the sum of the squares of the residual errors (SSE) of each case by solving the observation equation. However, solving the observation equation takes a lot of computation. This paper proposes a detection and elimination algorithm that can deal with no more than 2 faults, based on the least-squares-residual method. The new algorithm avoids solving the observation equation for each possible fault cases, and has very low computational complexity. Simulations are done to evaluate the performance of the algorithm, and the effect of the satellite geometry conditions on the algorithm is also discussed.

Global Navigation Satellite Systems (GNSS) tropospheric tomography is a commonly used technique for the reconstruction of three-dimensional water vapour field, and a priori vertical constraint models are required for water vapour density (WVD) determination which plays a critical role in the quality of tomographic results. However, generalised exponential models were routinely used for vertical constraints and limited research was carried out in the GNSS tomography by taking epoch-by-epoch variations into consideration. In this study, an adaptive four-dimensional (4-D) WVD model for the vertical constraints in GNSS tropospheric tomography was developed based on both ERA5 and surface meteorological data in Hong Kong for each month during the period of 2015–2019, and the back-propagation neural network technique was used to develop the fitting model. Then, the WVD model was used to obtain the WVD of adjacent voxels in the vertical direction to alleviate the mis-representation of the generalised exponential model. The newly developed WVD model used in GNSS tropospheric tomography was validated using GNSS data from the Hong Kong region in the year 2020 and two tomographic epochs (00:00–00:30 UTC and 12:00–12:30 UTC) were evaluated each day. For each topographic epoch, the WVDs of the tomographic voxels including radiosonde profile are evaluated (10 voxels over 10 height layers) using radiosonde data as the reference and the WVDs of all tomographic voxels are evaluated (300 voxels over 10 height layers) using ERA5 data as the reference. Results showed that when radiosonde/ERA5 data were utilized as the references, corresponding monthly mean values of the root mean square errors (RMSEs) in the entire year reduced from 1.97/1.94 g/m3 of the traditional tomographic method to 1.56/1.36 g/m3 of the new method which showed approximately 21/30% improvements. These results suggest a better performance of the tomographic approach using the new WVD model for the vertical constraints proposed by this study by taking epoch-by-epoch information.

The CentipedeRTK network is a collaborative Global Navigation Satellite System (GNSS) network launched in 2019, consisting mainly of low-cost GNSS receivers and antennas. This network enables free Real-Time Kinematic (RTK) positioning with centimeter accuracy for all users. The raw GNSS measurements from the CentipedeRTK network are routinely archived by the French scientific network RÉseau NAtional GNSS permanent, with the aim of exploiting raw GNSS measurements for geoscience applications. This paper presents a first assessment of the use of this dataset for tropospheric monitoring. We considered all the data provided in 2023 by more than 400 low-cost GNSS stations in mainland France. After selecting the stations with dual-frequency observations over the period, the data of 331 stations were analyzed using precise point positioning , resulting in a set of 265 stations satisfying our screening procedure and providing data covering more than 50% of the year 2023. A first indication of the quality of the analysis is given by the repeatability of the stations, of the order of \(2.2\pm 1.1\) , \(2.1\pm 0.8\) and \(6.9\pm 2.6\)  mm respectively on the East, North and Up components. These values are slightly higher than those obtained for nearby conventional stations, especially for the vertical component ( \(5.4\pm 0.8\)  mm). The tropospheric delays were compared with those retrieved from nearby GNSS reference stations (less than 30 km away) belonging to conventional networks (186 stations considered). The comparison shows a good agreement between low-cost and conventional stations, with a root mean square of differences of \(7.4\pm 3.0\)  mm; a mean bias of 2.7 mm is highlighted and shown to be stable over time; its origin has not yet been determined but its magnitude seems related to the antenna type of the CentipedeRTK stations. In a second step, the integrated water vapor content were derived from the tropospheric delays and compared with those of the European Centre for Medium-range Weather Forecasts fifth reanalysis (ERA5). Only stations located at an altitude less than 100 m around the ERA5 orography were considered (240 stations). The differences between the two techniques are similar to those reported in the literature for traditional networks, with a mean bias of \(0.06\pm 0.82\)  kg m \(^{-2}\) and a mean standard deviation of \(1.48\pm 0.18\)  kg m \(^{-2}\) . This again confirms the quality of the dataset. Finally, the value of such low-cost stations for monitoring and describing meteorological phenomena is illustrated by the study of an atmospheric river affecting the central–western part of France in December 2023. All these results underline the considerable potential of low-cost GNSS networks in geoscience applications, especially in regions with limited instrumentation. Their role could be particularly important in meteorological or climatological contexts, where GNSS-based water vapor monitoring is widely used.

Slow Slip Events (SSEs) are like long-duration slow earthquakes during which stress is gradually released over several days to months, and a comprehensive catalog of SSEs is essential for a better understanding of the earthquake cycle. However, SSEs usually only produce mm to cm surface deformations, making them a challenge to identify from raw Global Navigation Satellite System (GNSS) time series, which are often obscured by low-frequency background noise. We devise an approach that first employs variational Bayesian Independent Component Analysis to improve the signal-to-noise ratio of GNSS time series and then utilizes deep learning combining bidirectional Long Short-Term Memory and two different attention mechanisms to identify SSEs. We apply this new method to the GNSS three-component time series at 240 stations along the Cascadia subduction zone from 2012 to 2022. A total of 56 SSEs are detected, 18 more than the number in the existing SSEs catalogs during the same period. The starting time, duration, spatial and propagation pattern of the 56 SSEs are consistent with the tremor catalog, which helps to gain new insights into the slip behavior in the Cascadia subduction zone. In general, our work provides an effective framework for extracting subtle signals hidden in GNSS time series.

Multipath effect is one of the major challenges for Global Navigation Satellite Systems (GNSS) to achieve millimeter-level high-precision positioning and orbit determination. Wavelet Transform (WT) and Sidereal Filtering (SF) can effectively extract and mitigate multipath errors. Therefore, they are widely used in ground deformation monitoring and high precise GNSS applications. In view of this, the selection of refined wavelet decomposition levels and thresholds is critical for better extraction and mitigation of multipath errors. In this paper, we systematically analyze the performance of multipath error mitigation in Single-Difference (SD) and Double-Difference (DD) residuals based on different wavelet decomposition levels, thresholds and threshold functions. The results show that both DD SF and SD SF can effectively mitigate multipath errors. Compared to the traditional positioning, the positioning accuracy using the adopted SD SF in the east, north and up direction are improved by about 30.42%, 8.54% and 12.49%, respectively, which is slightly better than DD SF. For wavelet decomposition levels, the RMS of the rigrsure (Stein unbiased risk estimate), heursure (universal threshold, square root log), sqtwolog (combination of sqtwolog and rigrsure methods) and minimax (minimize the maximum mean squared error) thresholds at level 6 is the smallest among levels 1–10 of wavelet decomposition. For wavelet thresholds, the positioning performance of the heursure and sqtwolog thresholds is better that that of the rigrsure and minimax thresholds. For threshold functions, the positioning performance of four thresholds in the soft threshold function is slightly better than that in the hard threshold function.

The application of global navigation satellite system in vehicle navigation imposes high requirements on its safety, which makes it extremely important to detect deceptive interference (DI). The integration of prior road position information is usually necessary for the vehicle navigation, but it requires extensive learning and data collection, resulting in high implementation costs. We focus on efficient and practical research on DI detection by utilizing the most traditional wheel speed sensor auxiliary information. The classical pseudorange consistency detection method avoids the use of absolute position information, and overcomes the limitation of clustering algorithms caused by the number of spoofing interferences. Hypothesis test statistics are constructed by using the differencing method in the east and north directions, and the probability distributions of detection values under normal and spoofing conditions are theoretically derived. A comprehensive deception detection scheme is introduced to enhance the detection probability, catering to both single and multiple satellite deception situations, with a central focus on the contribution change factor of positioning satellites. Experimental results demonstrate that within a time scale of several tens of seconds, effective identification and correction of DI involving more than one code chip bias can be achieved.

The ionosphere shows regular changes such as daily, 27 days, seasonal, semi-annual, annual, and 11 years. These changes can be modeled and their effects largely determined. However, in addition to regular changes, irregular changes occur in the ionosphere due to space weather conditions, natural disasters, and human-induced irregularities. GNSS is one of the instruments along with many others that can give a piece of information on the ionospheric state. Various indices/parameters are used to determine the effect of space weather conditions. The well-known ones are solar activity indices, geomagnetic storm indices, magnetic field components, proton density, and proton flux parameters. It is important to take all of these indices into consideration when investigating the source of the anomaly. Considering only some of them may lead to incorrect inferences about the source of possible anomalies. To carry out comprehensive research in this field, it is necessary to analyze a very large data set. This indicates the requirement for an automatic system. With the Global and Regional Ionosphere Monitoring System (GRIMS) designed within the scope of this study, the ionosphere can be monitored globally and regionally. The GRIMS is online at https://www.online-grims.com/. By using Global ionospheric maps and GNSS receiver data, global, regional, and station-specific anomalies can be detected regularly through methods such as HDI (Highest Density Interval) and ARIMA (Autoregressive Integrated Moving Average). GRIMS gathers space weather-related parameters from ionospheric data centers to help users interpret the situation, and it allows users to download the results and request data for specific days. The details of the experimental results and output products of the system designed during the geomagnetic active days of March 17, 18, 2015 are given in this paper. Moreover, geomagnetic active days that occurred between 2000 and 2023 are given in the GRIMS.

Global Navigation Satellite System fast precise positioning can be achieved with accurate ionospheric corrections computed from an adequate number of GNSS stations in a local region. In low-latitude regions, the presence of electron density gradients over short distances can lead to outliers in the map of ionospheric corrections and decrease its accuracy. In this study, we explored outlier detection in ionospheric correction mapping through statistical residuals during a four-month test in 2021. Our findings indicate that the residuals of the local ionospheric model conform to the Laplace distribution. To determine outliers, we use an empirical rule for the Laplace distribution, setting thresholds at μ ± 3b, μ ± 3.5b, and μ ± 5.8b for data retention rates of 95%, 97%, and 99.7%, respectively. Here, μ represents the location parameter, which corresponds to the median of data, and b is the scale parameter, calculated as the medium absolute deviation. We found that while removing outliers can improve model accuracy, it may result in unavailable prediction due to a lack of data in a spare network. For example, applying a μ ± 3.5b threshold for outlier removal led to approximately 2.5% of recording time having no ionospheric corrections map in low-latitude regions, however, the local model has the potential to improve its mean accuracy by up to 50% for both low and mid-latitudes. Therefore, choosing the appropriate percentile threshold depends on the network configuration and the desired accuracy. Removing erroneous satellite data to improve ionospheric accuracy brings positive impacts on precise positioning.

The modernization of the Global Navigation Satellite Systems (GNSS) has brought many new features and capabilities, one of which is programmable power output capability, also known as flex power. Flex power capability allows for an increase in the signal strength of the individual signals to better fulfil operational constraints, but it may also cause biases in the pseudorange and carrier phase observations. This study focuses on the flex power capability characteristics of the second-generation Beidou Navigation and Positioning System (Beidou-2). We summarized the Beidou-2 flex power activation periods from January 2021 to April 2024 and analyzed the impact of flex power on phase biases and precise point positioning with ambiguity resolution (PPP-AR). The results show that Beidou-2 flex power would affect both pseudorange and phase observations on the B3I signals simultaneously. In addition, Hatch–Melbourne–Wübbena (HMW) combinations with single-epoch exhibit obvious discontinuities due to this mode of Beidou-2 flex power. Furthermore, the differences in estimated wide-lane (WL) biases can reach up to approximately 0.4 cycles when the Beidou-2 flex power is switched on or off. During this time, regarding the WL biases estimation with the daily constant strategy, the WL ambiguity residuals of Beidou-2 PPP-AR users are only approximately 70% within ± 0.25 cycles. In contrast, with the piecewise constant strategy, the WL ambiguity residuals above the threshold can reach approximately 90%. Considering flex power in kinematic PPP-AR, the position biases root mean square (RMS) values of 0.8, 0.8 and 2.5 cm can be achieved for the east, north and up components, respectively, while the corresponding position biases RMS without careful consideration of flex power are 1.0, 0.9 and 2.8 cm. Therefore, to achieve more reliable positioning results, it is advisable to incorporate flex power into high-precision GNSS data processing, especially for bias products of PPP-AR.

To address the lack of publicly available inter-frequency clock bias (IFCB) products and the impact of IFCB on real-time or near-real-time multi-frequency precision positioning, a MATLAB-based software for multi-GNSS IFCB estimation and forecast (M_IFCB) was produced for multi-frequency users. This software can estimate the IFCB of GPS, BDS-2, Galileo and BDS-3 satellites and provide three alternative forecast models for GPS satellites with large IFCB amplitude variations. To verify the availability of M_IFCB, 194 and 41 globally evenly distributed MGEX continuous tracking stations were used for IFCB estimation and GPS triple-frequency uncombined precise point positioning (PPP) performance evaluation, respectively. The results show that the precision of the static solutions of the triple-frequency uncombined PPP increased by about 20.4% in the horizontal direction and 18.5% in the vertical direction, respectively. Incorporating the predicted IFCB correction, the precision of the static solutions increased by about 19.9% in the horizontal direction and 17.6% in the vertical direction, respectively.

In the third reprocessing campaign (repro3) initiated by the International GNSS Service (IGS), 11 analysis centers (ACs) reanalyzed GPS/GLONASS/Galileo observations spanning 1994–2020 for station coordinates, satellite orbits, clocks, biases and attitudes. To improve the robustness of satellite products, the IGS AC Coordinator (ACC) carried out the satellite orbit combination, and the reference satellite attitudes were computed by the Technical University of Graz (TUG). The clock/bias combination was performed by Wuhan University via the IGS “Precise Point Positioning with Ambiguity Resolution” (PPP-AR) Pilot Project using the PRIDE ckcom software. This article aims at reporting the clock/bias combination results in the repro3. In particular, the consistencies for the combined GPS P1–P2/Galileo C1–C5 differential code biases (DCBs) and the GPS/Galileo uncalibrated phase delays (UPDs) among contributing ACs are all better than 0.1 ns and 0.05 cycles, respectively. As a result, the consistencies for the combined GPS/Galileo satellite clocks/biases are better than 10 ps, equating about 3 mm which is very close to the nominal precision of carrier-phase. In general, the Hadamard deviation and PPP-AR results confirm the higher robustness of the combined satellite clock/bias products over their original AC-specific counterparts. This is because the combined satellite clock/bias products harvest the merits of AC-specific contributions by identifying and excluding outlier solutions from the combination process.

In recent years, there has been increasing attention to positioning, navigation, and timing applications with smartphones. Because of frequently disrupted carrier phase observations, code observations remain critical for smartphone-based positioning. Considering a realistic stochastic model is mandatory to obtain the utmost positioning performance, this study proposes a sound stochastic approach for code observations from Android smartphones. The proposed approach includes a modified version of the SIGMA-ɛ variance model with different coefficients for each GNSS constellation and a robust Kalman filter method. First the noise characteristics of observations from the Xiaomi Mi 8 smartphone are analyzed utilizing code-minus-phase combinations to estimate the coefficients for each GNSS constellation. This includes the determination of a variance model as well as a check of the probability distribution. Finally, the proposed approach is validated in the positioning domain using single-frequency code observation-based real-time standalone positioning. The results show that more than 95% of observations follow the normal distribution when the proposed approach is applied. Compared with the conventional stochastic approach, including a C/N0-dependent model and standard Kalman filter, it improves the positioning accuracy by 45.8% in a static experiment, while its improvement is equal to 26.6% in a kinematic experiment. For the static and kinematic experiments, in 50% of the epochs, the 3D positioning errors are smaller than 3.0 m and 3.4 m for the proposed stochastic approach. The results exhibit that the stochastic properties of code observations from smartphones can be successfully represented by the proposed approach.

Over the past two decades, low-cost single-frequency Global Navigation Satellite System (GNSS) receivers have been used in numerous engineering fields and applications due to their affordability and practicality. However, their main drawback has been the inability to track satellite signals in multiple frequencies, limiting their usage to short baselines only. In recent years, low-cost dual-frequency GNSS receivers equipped with Real-Time-Kinematic (RTK) engines entered the mass market, addressing many of the limitations of single-frequency GNSS receivers. This review article aimed to analyze the observations and positioning quality of low-cost GNSS receivers in different positioning methods. To provide answers to defined research questions, relevant studies on the topic were selected and investigated. From the analyzed studies, it was found that GNSS observations obtained from low-cost GNSS receivers have lower quality compared to geodetic counterparts, however, they can still provide positioning solutions with comparable accuracy in static and kinematic positioning modes, particularly for short baselines. Challenges persist in achieving high positioning accuracy over longer baselines and in adverse conditions, even with dual-frequency GNSS receivers. In the upcoming years, low-cost GNSS technology is expected to become increasingly accessible and widely utilized, effectively meeting the growing demand for positioning and navigation.

The inter-satellite link (ISL) has been received increasing attention, as it is a potential way to achieve autonomous clock synchronization for envisioned space-based satellite networks with minimal ground segment capability. Existing satellite clock synchronization solutions either rely on prior information or modelling the relative motion by an approximated polynomial. In this paper, we propose a deep learning approach based on long short-term memory (LSTM) to decouple the clock parameters from pseudo-range measurements. The process of clock parameter estimation solely relies on the observed pseudo-range measurements, and the prior information of position and velocity are not required and the nonlinear relative motion process is modelled by training on historical data. The simulation results show that the proposed method outperforms the benchmark solutions in terms of accuracy.

We present a method to detect spoofing attack in Global Navigation Satellite System signals for single antenna receivers based on autocorrelation function distortion analysis in the Time–Frequency (TF) domain. In particular, Discrete Wavelet Transform (DWT) is considered as a TF tool to investigate the correlation taps outputs of the received signal. The statistical properties of the DWT coefficients of the autocorrelation function are processed in a fuzzy classifier as a feature vector to discriminate the presence of a spoofing attack. The detection performance of the method based on TF analysis of the autocorrelation function is verified using the real well-known Texas Spoofing Test Battery (TEXBAT) dataset. The findings demonstrate that the suggested technique for Pfa = 10−2 yields an average detection rate of more than 95% for the TEXBAT different cases, which shows improved detection sensitivity and robustness compared to other conventional and state-of-art methods.

The existing water vapor present in the lower regions of the atmosphere plays a pivotal role in both weather forecasting and the propagation of signals in satellite-based observations. This parameter introduces a delay in GNSS observations, known as tropospheric wet delay. Accurately predicting the spatial distribution of this parameter can significantly enhance our ability to forecast rainfall and floods. It can also improve satellite-based positioning techniques. One mathematical technique that proves invaluable in modeling various temporal aspects of a signal is the Dynamic Mode Decomposition (DMD) method. To construct the necessary snapshot matrix in the DMD method, we have opted to employ B-spline coefficient time series, computed by assimilating GNSS-derived Zenith et Delay (ZWD) values into the GPT3w model as a reference, with the Ensemble Kalman Filter (EnKF) method serving as the core of the assimilation process. In the DMD procedure, we have utilized a dataset spanning approximately 30 consecutive days, with a temporal resolution of roughly 5 min, to predict B-spline coefficients representing the spatial distribution of ZWD values for a 24-h period ahead. This dataset comprises ZWD values collected from 241 GNSS stations located in Germany and nearby regions throughout the year 2018. Comparative analysis has been performed, including 10 excluded GNSS stations from the assimilation and DMD procedure and 10 existing radiosonde stations within the study region. The results of the analysis step demonstrate the superiority of the proposed method over the ERA5, GFS, and GPT3w models, showcasing the Root Mean Squared Error (RMSE) of approximately 0.8 cm. This performance marks a substantial improvement, being approximately 51%, 57%, and 74% lower than each respective model. In the prediction phase, the proposed method outperforms the ERA5 and GFS models up to the 6-h and 24-h prediction windows in comparison with the GPT3w model.

This paper provides a description of the GLONASS-K yaw turn maneuvers that regularly occur at orbit noon and orbit midnight when the Sun’s elevation angle relative to the satellite orbital plane is between − 2.0 and + 2.0 degrees. Formulas for maneuver modeling are presented, which can be easily integrated into any Global Navigation Satellite System (GNSS) software. Triple-frequency carrier phase observations from the global International GNSS Service tracking network are analyzed to evaluate the performance of the model. Yaw angle estimates for the first GLONASS-K1 and first GLONASS-K2 spacecraft indicate that the actual yaw attitude follows the theoretical steering model with an accuracy of about 2 degrees. In addition to the regular yaw maneuvers, examples of other systematic deviations from the ideal GLONASS-K yaw attitude are presented.

Carrier-to-noise ratio ( \(C/{N}_{0}\) ) represents the ratio of signal power and noise power density, and it is of great significance in many applications of Global Navigation Satellite System (GNSS), such as satellite signal quality monitoring, spoofing detection, position accuracy estimation, etc. Accurate \(C/{N}_{0}\) estimation results will benefit a lot for short data situations like snapshot receivers, fast spoofing detection, adjusting tracking loop parameters based on fast \(C/{N}_{0}\) estimation and so on. However, most classical \(C/{N}_{0}\) estimation methods rely on the tracking stage of a GNSS receiver, which requires at least seconds of data to get an accurate estimation and further limits the application of \(C/{N}_{0}\) for such situations. To address the limitations of \(C/{N}_{0}\) estimation for short GNSS data, we introduce a \(C/{N}_{0}\) estimation method based on the Acquisition Correlation Ratio (ACR) that estimates \(C/{N}_{0}\) within only a few milliseconds signals. We derive the theoretical performance of ACR and three classical \(C/{N}_{0}\) estimation methods. It can be proved that the proposed ACR method has lower theoretical RMSE than the other three methods. Monte Carlo simulations are consistent with the theoretical analysis, which indicates that the accuracy of ACR method can approach the theoretical bound. Experiment results of signal simulator test and real-world test both indicate that the proposed method can enhance the estimation accuracy of \(C/{N}_{0}\) under short data conditions, achieving an estimation RMSE improvement of 0.8 dB-Hz on average with 20 ms data.

K2 is a new generation of GLONASS satellites that provides code division multiple access (CDMA) signals in the L1, L2 and L3 frequency bands in addition to legacy L1 and L2 signals based on frequency division multiple access (FDMA) modulation. The first GLONASS-K2 satellite was launched in August 2023 and started signal transmission in early September 2023. Based on measurements with a 30-m high-gain antenna, spectral characteristics of the various signal components are described and relative power levels are identified. A 3 dB (L1) to 4 dB (L2) higher total power is determined for the CDMA signal compared to the legacy FDMA signal and an equal power of the open service and secured CDMA signal components is found. The ranging code of the L2 channel for service information, which has not been publicly disclosed so far, is identified as a Gold code sequence consistent with the data channel of the L1 open service CDMA signal. The high-gain antenna measurements are complemented by tracking data from terrestrial receivers that enable a first assessment of user performance. An up to 50% improvement in terms of noise and multipath performance is demonstrated for the new L1 and L2 CDMA signals in comparison with their legacy counterpart, but no obvious differences between the different binary phase-shift keying and binary offset carrier modulations of the data and pilot components of these signals could be identified for the test stations. Triple-frequency carrier phase observations from L1, L2, and L3 CDMA signals exhibit good consistency at the noise and multipath level, except for small variations that can be attributed to slightly different antenna phase patterns on the individual frequencies. Overall, the new CDMA signals are expected to notably improve and facilitate precise point positioning applications once fully deployed across the GLONASS constellation.