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• A new evaluation method considering periodic errors for GNSS atomic clocks on board is proposed. • The correlation relationship between the sun elevation and orbit radial error, fitting precision, frequency stability, amplitude is revealed. • The evaluation results of GPS satellite clocks in orbit that more approach to the real performance are obtained. The performance of the atomic clock in orbit is of terrific significance for the Global Navigation Satellite System (GNSS). With the rapid development of satellite navigation and atomic clock technology, the periodic error of satellite clocks caused by the environment is more prominent. This paper focuses on the analysis and quantification of the systematic periodic error in the clock offset and proposes a more accurate evaluation method for GPS satellite clocks. The fact that the J2 relativistic effect and orbit radial error are the main sources of the systematic periodic term has been revealed. Then, the Fast Fourier Transform (FFT) is employed using the sliding window to investigate the periodic influence caused by satellite orbit and the J2 relativistic effect on clock offset through six GPS satellites with different orbital planes, these satellites also cover all four types of GPS satellite blocks. The results show that there is an obvious relationship between the sun elevation and orbit radial error, clock offset fitting precision, frequency stability and amplitude. The different geometric configurations of the satellite and the varying environment make this relationship different. Based on the clock offset provided by European Space Agency (ESA), the period of clock offset is extracted and quantized, with the period of 24 h, 12 h, 8 h, 6 h, 4 h, and 3 h. According to the daily extraction results of the time-varying periodic terms, the two most noticeable terms correction on satellite clock offset has been proven to be effective in eliminating periodic errors. Compared to those without periodic correction, the fitting precision and frequency stability can improve by 48.5% and 42.6%, respectively. In addition, all GPS satellite clocks in orbit are evaluated by this periodic correction method, and the results are more approach to the actual performance of the satellite clock. Furthermore, this method can also be adapted to evaluate satellite clocks of other GNSS systems. Therefore, when we evaluate the high-precision atomic clock flying on board GNSS satellites and compare them with the manufacturers' specifications, the periodic error cannot be neglected. [ABSTRACT FROM AUTHOR]

Global navigation satellite system (GNSS) positioning technology is widely used in landslide monitoring due to its unique real-time and high-precision advantages. However, in complex landslide environments with severe occlusion, multipath error becomes one of the main error sources affecting GNSS real-time kinematic high-precision positioning, as it cannot be eliminated by differential correction. Traditional sidereal filtering methods cannot retain deformation information, which affects the accuracy of landslide early warning. To mitigate multipath error and preserve landslide deformation information, an improved sidereal filtering method based on mutation points and landslide evolution stage recognition is proposed. The method considers the landslide evolution stage, establishes a dataset for sidereal filtering, matches the multi-day correlation data with the sliding section-related data, and constructs a multipath model using averaging. Experimental results show that, compared with the traditional sidereal filtering and conventional segmentation methods, the proposed method reduces the coordinate deviation (QE) in the 3D direction by 25.02% and 22.13% and reduces the fitting deviation (QR) by 4.01% and 36.21% during the stabilization stage. During the critical sliding stage, QE decreases by 48.54% and 23.8%, and QR decreases by 60.12% and 42.54%, respectively. The proposed method has the best smoothness and power spectral density indicators in both stages. It has also been successfully applied to the Heifangtai landslide in Gansu Province, providing more stable and reliable data than traditional methods, avoiding delayed and false alarms, and issuing a red warning 3 h before the landslide failure, demonstrating its practical value. [ABSTRACT FROM AUTHOR]

• 1. A quality control method for estimating multi-GNSS real-time satellite clock offset is proposed. • 2. The satellite clock offset accuracy of GPS, Galileo, BDS-3 and Galileo is improved. • 3.The precise point positioning accuracy can be improved by using the clock offset. Real-time satellite clock offset plays a prominent role in the Global Navigation Satellite System (GNSS) community. However, the GNSS raw observations are impacted by outliers, resulting in the quality of observations becomes poorer, which will dramatically affect the performance of estimated multi-GNSS satellite clock offset in real-time. In this contribution, an improved Inter Quartile Range (IQR) method is proposed to improve the quality of multi-GNSS satellite clock offset estimation in real-time, in which the improvements include two aspects. Firstly, the empirical threshold C 1 is determined to adapt multi-GNSS satellite clock offset estimation, if one residual is not between (Q 1 - C 1 ∗ I Q R , Q 3 + C 1 ∗ I Q R) , the observation is deleted. More importantly, to guarantee the clock offset of each satellite can be estimated at each epoch, if one satellite corresponding to all observation of stations is deleted, the IQR is conducted again at the current epoch for these observations. Three schemes are designed: 50 stations are used to perform multi-GNSS satellite clock offset estimation in real-time, which are without quality control (S1), with the proposed quality control method in this contribution(S2), and with quality control method using 8.5 medians of residuals (S3). Compared to S1, the satellite clock offset accuracy of GPS, Galileo, BDS-3, and GLONASS for S2 can be significantly improved from 0.082 to 0.055 ns, 0.106 to 0.072 ns, 0.178 to 0.083 ns, and 0.146 to 0.100 ns, respectively. The improvement is 32.93%, 32.07%, 53.37%, and 31.51%, respectively. The clock offset performance of S2 is better than that of S3 in terms of stability and reliability for GPS, BDS-3, and GLONASS. Another 52 stations are applied to perform multi-GNSS kinematic real-time precise point positioning (RT-PPP). For the convergence time and positioning accuracy, the RT-PPP employing the satellite clock offset generated from S2 shows the best performance. The experiment shows that the proposed quality control method can obtain real-time, stable, high-precision, and reliable multi-GNSS real-time satellite clock offset. [ABSTRACT FROM AUTHOR]

[Display omitted] • The long-term performance of GLONASS satellite clocks were revealed for the first time. • The periodic terms existed in the clock are detected. • The comparison between GLONASS and other GNSS satellite clock is conducted. The cesium atomic clock installed on the GLObal NAvigation Satellite System (GLONASS) is a key piece of equipment. However, its performance is easily affected by the external environment and its physical characteristics. Therefore, it is essential to evaluate the long-term performance of the clock. In this study, using eight years of continuous GLONASS precise satellite clock offset products, the long-term performance of GLONASS satellite clocks is revealed for the first time. The results showed that the mean number of phase and frequency jumps for one satellite clock in one year were 0.29 and 0.19, respectively. The fitting precision, which is the standard deviation of the fitting residuals, was 0.88 nanoseconds (ns). Except for the R06 satellite clock, the first or second period was 11.24 h in the clock offset. In terms of clock stability, the short-term clock offset prediction accuracy was 0.52 ns, the frequency stability at 1000 and 10000 s was 4.03 × 10-13 and 1.01 × 10-13, respectively. Both the short-term clock offset prediction accuracy and frequency stability were inferior to those of the rubidium atomic clock of the Global Positioning System (GPS) Block IIF satellites, the second-generation BeiDou Navigation Satellite System (BDS-2), Quasi-Zenith Satellite System (QZSS), and Galileo Passive Hydrogen Maser (PHM). The mean switching number for each GLONASS satellite clock was 0.27 per year. Furthermore, the R15 satellite clock, maybe owing to its hardware noise, delivered the poorest performance among those of all the GLONASS satellite clocks. [ABSTRACT FROM AUTHOR]

In order to provide better service for the Asia-Pacific region, the BeiDou navigation satellite system (BDS) is designed as a constellation containing medium earth orbit (MEO), geostationary earth orbit (GEO), and inclined geosynchronous orbit (IGSO). However, the multi-orbit configuration brings great challenges for orbit determination. When orbit maneuvering, the orbital elements of the maneuvered satellites from broadcast ephemeris are unusable for several hours, which makes it difficult to estimate the initial orbit in the process of precise orbit determination. In addition, the maneuvered force information is unknown, which brings systematic orbit integral errors. In order to avoid these errors, observation data are removed from the iterative adjustment. For the above reasons, the precise orbit products of maneuvered satellites are missing from IGS (international GNSS (Global Navigation Satellite System) service) and iGMAS (international GNSS monitoring and assessment system). This study proposes a method to determine the precise orbits of maneuvered satellites for BeiDou GEO and IGSO. The initial orbits of maneuvered satellites could be backward forecasted according to the precise orbit products. The systematic errors caused by unmodeled maneuvered force are absorbed by estimated pseudo-stochastic pulses. The proposed method for determining the precise orbits of maneuvered satellites is validated by analyzing data of stations from the Multi-GNSS Experiment (MGEX). The results show that the precise orbits of maneuvered satellites can be estimated correctly when orbit maneuvering, which could supplement the precise products from the analysis centers of IGS and iGMAS. It can significantly improve the integrality and continuity of the precise products and subsequently provide better precise products for users. [ABSTRACT FROM AUTHOR]

Expansive soils pose a significant challenge in geotechnical engineering, especially in coastal areas. While research has mainly focused on their elastic properties, this study explores the overlooked aspect of inelastic subsidence during prolonged droughts, utilizing decade‐long GPS datasets from the University of Houston Coastal Center. Our findings reveal substantial subsidence, approximately one to two dm, during the summer droughts of 2018, 2020, 2022, and 2023, due to compaction within the upper 4 m of expansive soils. Inelastic subsidence constitutes roughly 10% of the total subsidence, resulting in step‐like permanent land elevation loss over time. Notably, drought‐induced subsidence is prominent in open‐field areas with expansive soils but is minor in built‐up areas or in non‐expansive soil regions. The occurrence of inelastic subsidence challenges traditional assessments of relative sea‐level rise and coastal flooding, emphasizing the need to consider it in coastal infrastructure planning for enhanced resilience against climate uncertainties. Plain Language Summary: Expansive soils, often found in coastal regions, are known for causing issues like land shifts and unstable buildings. Our research adds a new dimension: prolonged droughts can lead to significant, irreversible sinking of expansive soils, permanently lowering the elevation of open land areas. Using a decade of GPS data, we found that during droughts, these soils can sink considerably and will not fully recover. Interestingly, in developed regions where pavement covers the soils, thereby minimizing moisture loss, this sinking is observed to be minimal. In the Galveston coastal area, drought‐induced sinking can reach one to two dm, with irreversible subsidence making up about 10% of the total subsidence. This becomes a growing concern as droughts become more frequent due to climate change, especially in coastal areas. Additionally, our results suggest that current methods for estimating sea‐level rise may be missing a key factor: we have underestimated the speed at which uninhabited coastal lands are sinking because we did not account for this irreversible sinking due to droughts. Key Points: Prolonged droughts cause up 2 dm of subsidence in shallow expansive soils (<4 m deep) in Galveston, TX, 10% of which is inelasticProlonged droughts lead to notable subsidence in open fields with expansive soils, but less in built‐up areas or non‐expansive soil areasRecurring droughts lead to permanent land elevation losses in open‐field coast, possibly skewing sea‐level rise and flood risk projections [ABSTRACT FROM AUTHOR]

For real-time (RT) precise point positioning (PPP), the state space representation (SSR) information is often delayed due to possible communication delays and specific broadcast intervals. In this case, the positioning results will diverge and re-converge due to the increase of SSR products extrapolation errors. In addition, RT orbit and clock offset accuracy, as well as their extrapolation errors, will vary in different systems and satellites. We propose a PPP with ambiguity resolution (PPP-AR) method that combines a time-differenced carrier phase (TDCP) model, in which the characteristics of the orbit and clock are considered. Under normal communication, the PPP-AR solution is obtained by fixing satellites with small SSR product errors. When the communication is abnormal, the TDCP model is utilized to extrapolate user coordinates by considering different extrapolation error characteristics of satellites. The experimental results show that GPS and Galileo SSR products have better accuracy than BDS, with signal-in-space user ranger errors (SISREs) of 2.7, 2.2, and 8.6 cm, respectively. Optimizing the PPP stochastic model based on SISREs can effectively reduce the convergence time. Under 5 min SSR delay, SISREs caused by clock and orbit extrapolation for GPS/Galileo/BDS are 3.5, 1.4, and 2.6 cm, respectively. After optimizing the TDCP stochastic model based on extrapolation errors, the horizontal and vertical positioning accuracies can be maintained at 0.7 cm and 5.0 cm. For multi-GNSS, the combination of the TDCP and PPP-AR can overcome the influence of short delay. After optimizing the stochastic model, the GPS/Galileo/BDS positioning accuracy can be maintained at about 2.4 cm under 3 min delay, showing an accuracy improvement rate of 59.3% compared with the traditional method using only PPP. Additionally, the rapid PPP convergence results can be obtained by inheriting previous filter state information when the communication recovers normally. [ABSTRACT FROM AUTHOR]

Obtaining reliable GNSS uncalibrated phase delay (UPD) or integer clock products is the key to achieving ambiguity-fixed solutions for real-time (RT) precise point positioning (PPP) users. However, due to the influence of RT orbit errors, the quality of UPD/integer clock products estimated with a globally distributed GNSS network is difficult to ensure, thereby affecting the ambiguity resolution (AR) performance of RT-PPP. In this contribution, by fully utilising the consistency of orbital errors in regional GNSS network coverage areas, a method is proposed for estimating regional integer clock products to compensate for RT orbit errors. Based on Centre National d'Études Spatiales (CNES) RT precise products, the regional GPS/BDS integer clock was estimated with a CORS network in the west of China. Results showed that the difference between the estimated regional and CNES global integer clock/bias products was generally less than 5 cm for GPS, whereas clock differences of greater than 10 cm were observed for BDS due to the large RT orbit error. Compared with PPP using global integer clock/bias products, the AR performance of PPP using the regional integer clock was obviously improved for four rover stations. For single GPS, the horizontal and vertical accuracies of ambiguity-fixed PPP solutions were improved by 56.2% and 45.3% on average, respectively, whereas improvements of 67.5% and 50.5% in the horizontal and vertical directions, respectively, were observed for the combined GPS/BDS situation. Based on a regional integer clock, the RMS error of a kinematic ambiguity-fixed PPP solution in the horizontal direction could reach 0.5 cm. In terms of initialisation time, the average time to first fix (TTFF) in combined GPS/BDS PPP was shortened from 18.2 min to 12.7 min. In view of the high AR performance realised with the use of regional integer clocks, this method can be applied to scenarios that require high positioning accuracy, such as deformation monitoring. [ABSTRACT FROM AUTHOR]

• This study proposes a GNSS network RTK algorithm called virtual atmosphere constraint (VAC) for high-precision landslide monitoring. • The effectiveness of the proposed algorithm was validated compared to traditional virtual reference station (VRS) technology. • The VAC method exhibited better accuracy, stability, and ambiguity fixing rates than the VRS method, and noise reduction further reduced the error. • After noise reduction, the RMS values of the VAC method at the stable and the other corrupted monitoring point were both reduced to a mm-level accuracy. GNSS technology is an effective all-weather, continuous and real-time method of detecting three-dimensional landslide displacement. However, current positioning methods such as the network real-time kinematic (RTK) technique based on virtual reference station (VRS) technology have some limitations, particularly a sensitivity to atmospheric modeling error. In this study, taking advantage of existing GNSS continuously operating reference stations (CORS), we propose a network RTK algorithm (virtual atmosphere constraint (VAC)) for high-precision landslide monitoring. Network modeling atmosphere delays were used as virtual observations for the terminal position solution, by which their accuracy information can be considered. Additionally, a noise reduction method that combines complementary ensemble empirical mode decomposition and median filtering was proposed to reduce GNSS signal residual errors in the original RTK coordinate time series. To validate the effectiveness of the algorithm, we processed one week of data from two monitoring receivers on the Heifangtai landslide and four surrounding CORS using the VAC and VRS methods. Results show that the original displacement time series processed with VRS was prone to jitter, whereas the VAC method exhibited better accuracy, stability, and ambiguity fixing rates. Horizontal and vertical RMS errors at a stable monitoring point were 1.7 cm and 3.9 cm for VRS-RTK and 0.9 cm and 2.3 cm for VAC-RTK; thus, VAC reduced the error by 40.1% and 20.5%, respectively. After noise reduction, the RMS values of the VAC method at the stable and the other collapsed monitoring point were both reduced to an mm-level accuracy. [ABSTRACT FROM AUTHOR]