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The Global Navigation Satellite System (GNSS) can be utilized for long-distance and high-precision time transmission. With the ongoing development of low Earth orbit (LEO) satellites and the rapidly changing geometric relationships between them, the convergence rate of ambiguity parameters in Precise Point Positioning (PPP) algorithms has increased, enabling fast and reliable time transfer. In this paper, GPS is used as an experimental case, the LEO satellite constellation is designed, and simulated LEO observation data are generated. Then, using the GPS observation data provided by IGS, a LEO-enhanced PPP model is established. The LEO-augmented PPP model is employed to facilitate faster and more reliable high-precision time transfer. The application of the LEO-augmented PPP model to time transfer is examined and discussed through experimental examples. These examples show multiple types of time transfer links, and the experimental outcomes are uniform. GPS + LEO is compared with exclusive GPS time transfer schemes. The clock offset of the time transfer link for the GPS + LEO scheme converges more swiftly, meaning that the time required for the clock offset to reach a stable level is the briefest. In this paper, standard deviation is employed to assess stability, and Allan deviation is utilized to assess frequency stability. The results show that the clock offset stability and frequency stability achieved by the GPS + LEO scheme are superior within the convergence time range. Controlled experiments with different numbers of satellites for LEO enhancement indicate that time transfer performance can be improved by increasing the number of satellites. As a result, augmenting GPS tracking data with LEO observations enhances the time transfer service compared to GPS alone. [ABSTRACT FROM AUTHOR]

The global navigation satellite system radio occultation (GNSS-RO) is an important means of space-based meteorological observation. It is necessary to test the Global Navigation Satellite System Occultation signal receiver on the ground before the deployment of space-based occultation detection systems. The current approach of testing the GNSS signal receiver on the ground is mainly the mountaintop-based testing approach, which has problems such as high cost and large simulation error. In order to overcome the limitations of the mountaintop-based test approach, this paper proposes an accurate, repeatable, and controllable GNSS atmospheric occultation simulation system and builds a load performance evaluation approach based on the ground-based GNSS atmospheric occultation simulation system on the basis of it. The GNSS atmospheric occultation simulation system consists of the visualization and interaction module, the GNSS-RO simulation signal generation module, the GNSS-RO simulator module, the GNSS-RO signal receiver module, and the GNSS-RO inversion and evaluation module, combined with the preset atmospheric model to generate GNSS-RO simulation signals with a high degree of simulation, and comparing the atmospheric parameters of the inversion performance of the GNSS-RO signal receiver with the parameters of the preset atmospheric model to obtain the error data. The overall performance of the GNSS-RO signal receiver can be evaluated based on the error information. The novel approach to evaluate the GNSS-RO signal receiver performance proposed in this paper is validated by using the FY-3E (FengYun-3E) receiver qualification parts that have been verified in orbit, and the results confirm that the approach can meet the requirements of the GNSS-RO receiver performance test. This study shows that the novel approach to evaluate the GNSS-RO signal receiver performance in terms of the ground-based atmospheric occultation simulation system can efficiently and accurately be used to carry out the receiver test and provides an effective solution for the ground-based test of GNSS-RO signal receivers. [ABSTRACT FROM AUTHOR]

To address the issue of integrity monitoring for a multi-source information fusion navigation system, a theoretical framework of two-level integrity monitoring is proposed. Firstly, at the system level, a system-integrity-monitoring method based on the Kalman filter weighted least-squares form is established to detect and isolate faulty navigation sources. Secondly, at the sensor level, considering the redundancy of the faulty navigation sources, this paper presents the design of a multi-mode comprehensive fault-detection method for non-redundant navigation sources. Additionally, an extended-dimension matrix optimized sensor-fault detection and verification method for redundant navigation sources is proposed. Finally, integrity risk allocation criteria are established based on the effectiveness of navigation sources to calculate the system protection level and trigger integrity alarms. The two-level integrity-monitoring method was tested on a multi-source information fusion navigation system integrated with an inertial navigation system (INS), global positioning system (GPS), BeiDou satellite navigation system (BDS), Doppler velocity log (DVL), barometric altimeter (BA), and terrain-aided navigation (TAN). Test results demonstrate that the proposed method can effectively isolate the faulty navigation source within 10 s. Furthermore, it can detect the faulty sensors within the faulty navigation sources, thereby enhancing the reliability and robustness of the multi-source information fusion navigation system. [ABSTRACT FROM AUTHOR]

The fast motion of low Earth orbit (LEO) satellites provides rapid geometric changes in a short time, which can accelerate the initialization of precise point positioning (PPP). The rapid convergence of ambiguity parameters is conducive to the rapid success of ambiguity fixing. This paper presents the performance of single- and four-system combined PPP Ambiguity Resolution (AR), enhanced with an ambiguity-float solution LEO. Two LEO constellations were designed: L was a typical polar orbit constellation, with a higher number of visible satellites at high latitudes than at low and middle latitudes; and M was designed to compensate for the lack of visible satellites at low and middle latitudes. The ground observation data of the LEO satellites at the MGEX stations were simulated. Because the global navigation satellite systems (GNSSs) were fully operational, the GNSS data were real observation data from the MGEX stations. Based on the daily observation datasets collected at 258 stations in the global MGEX observation network over three days (from 1 January to 3 January 2022), in addition to the LEO simulation data, we evaluated the positioning performance of LEO ambiguity-float solution-enhanced PPP ambiguity resolution and compared it with LEO-enhanced PPP. The L+M mixed constellation was able to reduce the time to first fix (TTFF) of the four-system combined PPP-AR to 5 min, and four LEO satellites were sufficient to achieve this. L+M mixed constellation was able to reduce the convergence time of the four-system combined PPP to 2 min. Unlike PPP-AR, PPP required more LEO satellites for augmentation to saturate. [ABSTRACT FROM AUTHOR]

The increased number of satellites and stations leads to the serious time consumption of the integrated precise orbit determination (POD), especially in the current global navigation satellite system (GNSS) with more than 120 satellites. To improve the computational efficiency of multi-GNSS-integrated POD, this paper proposed an improved parameter estimation method based on intel oneAPI high-performance computing, where the inactive parameters are eliminated in a batch mode. Compared with the classical estimation method based on the "one-by-one" elimination, the efficiencies were significantly improved with ratios of 2.53, 4.21, and 5.38 for 79, 126, and 171 stations' GPS/BDS/Galileo/GLONASS-integrated POD, respectively. The elapsed time of the improved method by using 126 stations was the same as that of 79 stations' POD by the classical estimation method. In terms of precision, the one-dimensional root mean square error (RMS) reductions were 0.1 cm (7%), 34.3 cm (11%), 1.9 cm (18%), 0.4 cm (8%), 0.2 cm (13%), and 0.4 cm (13%) for GPS, BDS GEO, BDS IGSO, BDS MEO, Galileo, and GLONASS satellites, respectively. [ABSTRACT FROM AUTHOR]

Alignment technology plays an important role in navigation, and is used extensively throughout military and civilian applications. However, the existing in-flight alignment methods cannot be applied to the low-cost based strap-down inertial navigation system/global positioning system integrated navigation system, used in short-endurance and high-speed rotation flight bodies, since they cannot quickly obtain alignment results to meet the accuracy requirements of a flight body with special movement characteristics of short-endurance and high-speed rotation. In this paper, in order to solve this challenging problem of alignment for flight body with short-endurance and high-speed rotation, a fast in-flight alignment method based on the Lie group is proposed. First, an in-flight alignment model based on vector observations was established by using the Lie group. Second, addressing the problem that the alignment accuracy is greatly affected by the low-cost inertial sensor bias, an improved unscented Kalman filter was constructed in the Lie group on the basis of fully considering the characteristics of the system equations to estimate and feedback the correlated errors. Finally, a trajectory simulation of high-speed flight body and field semi-physical test was carried out to evaluate the proposed method. Evaluation of the system performance in comparison with existing state-of-the-art methods indicated that the proposed in-flight alignment method has better alignment accuracy and faster alignment velocity for a low-cost strap-down inertial navigation system/global positioning system integrated navigation system. [ABSTRACT FROM AUTHOR]

The accurate spatial positioning of the target in a fixed camera image is a critical sensing technique. Conventional visual spatial positioning methods rely on tedious camera calibration and face great challenges in selecting the representative feature points to compute the position of the target, especially when existing occlusion or in remote scenes. In order to avoid these deficiencies, this paper proposes a deep learning approach for accurate visual spatial positioning of the targets with the assistance of Global Navigation Satellite System (GNSS). It contains two stages: the first stage trains a hybrid supervised and unsupervised auto-encoder regression network offline to gain capability of regressing geolocation (longitude and latitude) directly from the fusion of image and GNSS, and learns an error scale factor to evaluate the regression error. The second stage firstly predicts regressed accurate geolocation online from the observed image and GNSS measurement, and then filters the predictive geolocation and the measured GNSS to output the optimal geolocation. The experimental results showed that the proposed approach increased the average positioning accuracy by 56.83%, 37.25%, 41.62% in a simulated scenario and 31.25%, 7.43%, 38.28% in a real-world scenario, compared with GNSS, the Interacting Multiple Model−Unscented Kalman Filters (IMM-UKF) and the supervised deep learning approach, respectively. Other improvements were also achieved in positioning stability, robustness, generalization, and performance in GNSS denied environments. [ABSTRACT FROM AUTHOR]

Atmospheric weighted mean temperature (Tm) is a key parameter used by the Global Navigation Satellite System (GNSS) for calculating precipitable water vapor (PWV). Some empirical Tm models using meteorological or non-meteorological parameters have been proposed to calculate PWV, but their accuracy and reliability cannot be guaranteed in some regions. To validate and determine the optimal Tm model for PWV retrieval in China, this paper analyzes and evaluates some typical Tm models, namely, the Linear, Global Pressure and Temperature 3 (GPT3), the Tm model for China (CTm), the Global Weighted Mean Temperature-H (GTm-H) and the Global Tropospheric (GTrop) models. The Tm values of these models are first obtained at corresponding radiosonde (RS) stations in China over the period of 2011 to 2020. The corresponding Tm values of 87 RS stations in China are also calculated using the layered meteorological data and regarded as the reference. Comparison results show that the accuracy of these five Tm models in China has an obvious geographical distribution and decreases along with increasing altitude and latitude, respectively. The average root mean square (RMS) and Bias for the Linear, GPT3, CTm, GTm-H and GTrop models are 4.2/3.7/3.4/3.6/3.3 K and 0.7/−1.0/0.7/−0.1/0.3 K, respectively. Among these models, Linear and GPT3 models have lower accuracy in high-altitude regions, whereas CTm, GTm-H and GTrop models show better accuracy and stability throughout the whole China. These models generally have higher accuracy in regions with low latitude and lower accuracy in regions with middle and high latitudes. In addition, Linear and GPT3 models have poor accuracy in general, whereas GTm-H and CTm models are obviously less accurate and stable than GTrop model in regions with high latitude. These models show different accuracies across the four geographical regions of China, with GTrop model demonstrating the relatively better accuracy and stability. Therefore, the GTrop model is recommended to obtain Tm for calculating PWV in China. [ABSTRACT FROM AUTHOR]

Atmospheric water vapor is one of the important parameters for weather and climate studies. Generally, atmospheric water vapor can be monitored by some techniques, such as the Global Navigation Satellite System (GNSS), radiosonde (RS), remote sensing and numerical weather forecast (NWF). However, the comprehensive retrieval and application of precipitable water vapor (PWV) using multi techniques has been hardly performed before, which becomes the focus of this study. A comprehensive PWV retrieval and application platform (CPRAP) is first established by combing the ground-based (GNSS), space-based (Fengyun-3A, Sentinel-3A) and reanalysis-based (the fifth-generation reanalysis dataset of the European Centre for Medium-Range Weather Forecasting, ERA5) techniques. Additionally, its applications are then extended to drought and rainfall monitoring using the CPRAP-derived PWV. The statistical result shows that PWV derived from ground-based GNSS has high accuracy in China, with the root mean square (RMS), Bias and mean absolute error (MAE) of 2.15, 0.05 and 1.65 mm, respectively, when the RS-derived PWV is regarded as the reference. In addition, the accuracy of PWV derived from the space-based (FY-3A and Sentinel-3A) techniques technique is also validated and the RMS, Bias and MAE of a Medium Resolution Spectral Imager (MERSI) onboard Fengyun-3A (FY-3A) and an Ocean and Land Color Instrument (OLCI) onboard Sentinel-3A are 4.46/0.56/3.61 mm and 2.95/0.01/1.37 mm, respectively. Then, the performance of ERA5-derived PWV is evaluated based on GNSS-derived and RS-derived PWV. The result also shows good accuracy of ERA5-provided PWV with the averaged RMS, Bias and MAE of 1.86/0.11/1.48 mm and 0.90/−0.05/1.51 mm, respectively. Finally, the PWV data derived from the established CPRAP are further used for drought and rainfall monitoring. The applied results reveal that the calculated the standardized precipitation evapotranspiration index (SPEI) using the CPRAP-derived PWV can monitor the drought and the correlation coefficient ranges from 0.83 to 0.9 when compared with the SPEI. Furthermore, in this paper correlation analysis between PWV derived from the CPRAP and rainfall, and its potential for rainfall monitoring was also validated. Such results verify the significance of the established CPRAP for weather and climate studies. [ABSTRACT FROM AUTHOR]

The current tsunami early warning systems always issue alarms once large undersea earthquakes are detected, inevitably resulting in false warnings since there are no deterministic scaling relations between earthquake size and tsunami potential. In this paper, we assess tsunami potential by analyzing co-seismic ionospheric disturbances (CIDs). We examined CIDs of three megathrusts (the 2014 Mw 8.2 Iquique, the 2015 Mw 8.3 Illapel, and the recent 2021 Mw 8.2 Alaska events) as detected by Global Navigation Satellite System (GNSS) observations. We found that CIDs near the epicenter generated by the 2021 Mw 8.2 Alaska event were significantly weaker than those of the two Chilean events, despite having similar earthquake magnitudes. The propagation direction of CIDs from the Mw 8.2 Alaska earthquake further revealed ruptures toward the deeper seismogenic zone, implying less seafloor uplift and hazardous flooding. Our work sheds light on incorporating GNSS-based CIDs for more trustworthy tsunami warning systems. [ABSTRACT FROM AUTHOR]

Interference multipath is an important factor to affect the anti-jamming performance for the global navigation satellite system (GNSS) antenna array receiver. However, interference multipath must be considered in practical application. In this paper, the antenna array model for interference multipath is analyzed, and an equivalent model for interference multipath is proposed. According to the equivalent interference multipath model, the influence of interference multipath on anti-jamming performance is analyzed from the space only processing (SOP) and space-time adaptive processing (STAP). Interference multipath can cause loss of the degree of freedom (DoF) of SOP. Through analysis of the equivalent model and STAP mechanism, it further reveals how the STAP can solve the interference multipath. The simulation experiments prove that the equivalent model is effective, and the analysis conclusion is correct. This paper also points out that the interference bandwidth is wider and more taps in STAP are required, under the same experiment conditions. [ABSTRACT FROM AUTHOR]

Accurate integrity risk evaluation is of significance in ensuring that aviation navigation applications satisfy the predefined integrity requirement. The integrity risk evaluation method over a specified exposure interval has been proposed in previous works for the development of advanced receiver autonomous integrity monitoring (ARAIM) (ARAIM technical subgroup reference airborne algorithm description document v4.1, 2022). However, this method typically relies on an underlying optimistic assumption that the satellite geometry remains constant throughout the exposure interval. The variation in satellite geometry due to potential satellite outages undermines the widely-used geometry constant assumption. Thus, we investigate the influence of satellite geometry variations throughout the exposure interval on the integrity performance by introducing a geometry-sensitive risk-evaluation model. The findings demonstrate that, under the nominal situation, the region where the ARAIM fails to meet predefined integrity requirement could expand by a maximum of 2.93% when accounting for satellite geometry variations. Furthermore, in the situation of a single satellite outage, this hazardous region has significantly expanded from 13.12% of the global coverage to 66.82%. Based on these findings, we recommend that the ARAIM should consider satellite outages as a critical factor in real-time integrity risk evaluation. [ABSTRACT FROM AUTHOR]

Recently, the NOAA has included GNSS (Global Navigation Satellite System) Radio Occultation (RO) data as one of the crucial long-term observables for weather and climate applications. To include more GNSS RO data in its numerical weather prediction systems, the NOAA Commercial Weather Data Pilot program (CWDP) started to explore the commercial RO data available on the market. After two rounds of pilot studies, the CWDP decided to award the first Indefinite Delivery Indefinite Quantity (IDIQ) contract to GeoOptics and Spire Incs. in 2020. This study examines the quality of Spire RO data products for weather and climate applications. Spire RO data collected from commercial CubeSats are carefully compared with data from Formosa Satellite Mission 7–Constellation Observing System for Meteorology, Ionosphere, and Climate-2 (COSMIC-2), the fifth-generation European Centre for Medium-Range Weather Forecasts (ECMWF) atmospheric reanalysis (ERA5), and high-quality radiosonde data. The results demonstrate that, despite their generally lower Signal-Noise-Ratio (SNR), Spire RO data show a pattern of lowest penetration height similar to that of COSMIC-2. The Spire and COSMIC-2 penetration heights are between 0.6 and 0.8 km altitude over tropical oceans. Although using different GNSS RO receivers, the precision of Spire STRATOS receivers is of the same quality as those of the COSMIC-2 TriG (Global Positioning System—GPS, GALILEO, and GLObal NAvigation Satellite System—GLONASS) RO Receiver System (TGRS) receivers. Furthermore, the Spire and COSMIC-2 retrieval accuracies are quite comparable. We validate the Spire temperature and water vapor profiles by comparing them with collocated radiosonde observation (RAOB) data. Generally, over the height region between 8 km and 16.5 km, the Spire temperature profiles match those from RS41 RAOB very well, with temperature biases of <0.02 K. Over the height range from 17.8 to 26.4 km, the temperature differences are ~−0.034 K, with RS41 RAOB being warmer. We also estimate the error covariance matrix for Spire, COSMIC-2, and KOMPSAT-5. The results show that the COSMIC-2 estimated error covariance values are slightly more significant than those from Spire over the oceans at the mid-latitudes (45°N–30°N and 30°S–45°S), which may be owing to COSMIC-2 SNR being relatively lower at those latitudinal zones. [ABSTRACT FROM AUTHOR]

Scintillation due to ionospheric plasma irregularities remains a challenging task for the space science community as it can severely threaten the dynamic systems relying on space-based navigation services. In the present paper, we probe the ionospheric current and plasma irregularity characteristics from a latitudinal arrangement of magnetometers and Global Navigation Satellite System (GNSS) stations from the equator to the far low latitude location over the Indian longitudes, during the severe space weather events of 6–10 September 2017 that are associated with the strongest and consecutive solar flares in the 24th solar cycle. The night-time influence of partial ring current signatures in ASYH and the daytime influence of the disturbances in the ionospheric E region electric currents (Diono) are highlighted during the event. The total electron content (TEC) from the latitudinal GNSS observables indicate a perturbed equatorial ionization anomaly (EIA) condition on 7 September, due to a sequence of M-class solar flares and associated prompt penetration electric fields (PPEFs), whereas the suppressed EIA on 8 September with an inverted equatorial electrojet (EEJ) suggests the driving disturbance dynamo electric current (Ddyn) corresponding to disturbance dynamo electric fields (DDEFs) penetration in the E region and additional contributions from the plausible storm-time compositional changes (O/N2) in the F-region. The concurrent analysis of the Diono and EEJ strengths help in identifying the pre-reversal effect (PRE) condition to seed the development of equatorial plasma bubbles (EPBs) during the local evening sector on the storm day. The severity of ionospheric irregularities at different latitudes is revealed from the occurrence rate of the rate of change of TEC index (ROTI) variations. Further, the investigations of the hourly maximum absolute error (MAE) and root mean square error (RMSE) of ROTI from the reference quiet days' levels and the timestamps of ROTI peak magnitudes substantiate the severity, latitudinal time lag in the peak of irregularity, and poleward expansion of EPBs and associated scintillations. The key findings from this study strengthen the understanding of evolution and the drifting characteristics of plasma irregularities over the Indian low latitudes. [ABSTRACT FROM AUTHOR]

Global Navigation Satellite System Reflectometry (GNSS-R) is a rapidly developing Earth observation technology that makes use of signals of opportunity from Global Navigation Satellite Systems that have been reflected off the Earth's surface. The Cyclone Global Navigation Satellite System (CyGNSS) is a constellation of eight small satellites launched by NASA in 2016, carrying dedicated GNSS-R payloads to measure ocean surface wind speed at low latitudes (±35° North/South). The ESA ECOLOGY project evaluated CyGNSS v3.0 products, which were recently released following various calibration updates. This paper examines the performance of the new calibration by evaluating CyGNSS v3.0 Level-1 Normalised Bistatic Radar Cross Section (NBRCS) and Leading Edge Slope (LES) data from individual CyGNSS units and different GPS transmitters under constant ocean wind conditions. Results indicate that L1 NBRCS from individual CyGNSS units are well inter-calibrated and remarkably stable over time, a significant improvement over previous versions of the products. However, prominent geographical biases reaching over 3 dB are found in NBRCS, linked to factors including the choice of GPS transmitter and the bistatic geometry. L1 LES shows similar anomalies as well as a secondary geographical pattern of biases. These findings provide a basis for further improvement of CyGNSS Level-2 wind products and have wider applicability to improving the calibration of GNSS-R sensors for the remote sensing of non-ocean Earth surfaces. [ABSTRACT FROM AUTHOR]

The integration of global navigation satellite system (GNSS) single-frequency (SF) real-time kinematics (RTKs) and inertial navigation system (INS) has the advantages of low-cost and low-power consumption compared to the multiple-frequency GNSS RTK/INS integration system. However, due to the vulnerability of GNSS signal reception, the application of the GNSS SF-RTK/INS integration is limited in complex environments. To improve the positioning accuracy of SF-RTK/INS integration in GNSS-blocked environments, we present a low-cost tight integration system based on BDS/GPS SF-RTK, a low-cost inertial measurement unit (IMU), and a monocular camera. In such a system, a multi-state constraint Kalman filter (MSCKF) is adopted to integrate the single-frequency pseudo-range, phase-carrier, inertial measurements, and visual data tightly. A wheel robot dataset collected under satellite signal-blocked conditions is used to evaluate its performance in terms of position, attitude, and run time, respectively. Results illustrated that the presented model can provide higher position accuracy compared to those provided by the RTK/INS tight integration system and visual-inertial tight integration system. Moreover, the average running time presents the potential of the presented method in real-time applications. [ABSTRACT FROM AUTHOR]

Considering the problem of GNSS service interruption caused by the insufficient number of available satellites in complex environments, Low Earth Orbit (LEO) satellites can supplement GNSS effectively. To eliminate the unknown satellite clock error and the atmospheric delay error with spatial correlation in LEO observations, a Differential-Low Earth Orbit opportunistically enhancing GNSS (D-LoeGNSS) navigation framework is proposed. Firstly, because of the uncertainty of the LEO orbit, we derive the effect of the LEO orbit error on the differential measurement model. Secondly, aiming at the noise amplification and correlation in double-difference (DD), we propose a Householder-Based D-LoeGNSS (HB-DLG) algorithm, which suppresses noise by introducing an orthogonal matrix. Thirdly, in D-LoeGNSS, the typical measurement of LEO is Doppler, which is heterogeneous with the GNSS pseudorange, rendering the Dilution of Precision (DOP) evaluation method unsuitable. Given the unbiasedness of differential measurements, the Cramer Rao Lower Bound (CRLB) is derived as a metric to characterize the positioning accuracy and satellite spatial distribution. Finally, a field experiment using Orbcomm (ORB) and GPS is conducted. The experimental results show that the performance of the HB-DLG algorithm is superior to DD. Especially when the number of satellites is insufficient or the measurement redundancy is poor; the D-LoeGNSS framework has advantages of rapid convergence and high accuracy compared with a single constellation. [ABSTRACT FROM AUTHOR]

Global navigation satellite system (GNSS) signals are affected by refraction when traveling through the troposphere, which result in tropospheric delay. Generally, the tropospheric delay is estimated as an unknown parameter in GNSS data processing. With the increasing demand for GNSS real-time applications, high-precision tropospheric delay augmentation information is vital to speed up the convergence of PPP. In this research, we estimate the zenith tropospheric delay (ZTD) from 2018 to 2019 by static precise point positioning (PPP) using the fixed position mode; GNSS observations were obtained from the National Geomatics Center of China (NGCC). Firstly, ZTD outliers were detected, and data gaps were interpolated using the K-nearest neighbor algorithm (KNN). Secondly, The ZTD differences between the KNN and periodic model were employed as input datasets to train the long short-term memory (LSTM) neural network. Finally, LSTM forecasted ZTD differences and the ZTD periodic signals were combined to recover the final forecasted ZTD results. In addition, the forecasted ZTD results were applied in static PPP as a prior constraint to reduce PPP convergence time. Numerical results show that the average root-mean-square error (RMSE) of predicting ZTD is about 1 cm. The convergence time of the PPP which was corrected by the LSTM-ZTD predictions is reduced by 13.9, 22.6, and 30.7% in the summer, autumn, and winter, respectively, over GPT2-ZTD corrected PPP and unconstrained conventional PPP for different seasons. [ABSTRACT FROM AUTHOR]

On 15 January 2022, a violent eruption and tsunami of the Hunga Tonga-Hunga Ha'apai (HTHH) volcano in Tonga, South Pacific, caused widespread international concern. In order to detect the anomalous environmental response caused by the HTHH volcanic eruption based on GNSS ionospheric data, GNSS tropospheric data and GNSS coordinate time series, a new method combining the zenith non-hydrostatic delay difference method and the extreme-point symmetric mode decomposition (ESMD) method, was proposed to detect tropospheric anomalies. The moving interquartile range method and the ESMD method were introduced to detect ionospheric anomalous and coordinate time series anomalies, respectively. The results showed that 9–10 h before the eruption of the Tonga volcano and 11–12 h after the eruption of the Tonga volcano, obvious total electron content (TEC) anomalies occurred in the volcanic eruption center and its northeast and southeast, with the maximum abnormal value of 15 TECU. Significant tropospheric anomalies were observed on the day of the HTHH volcano eruption as well as 1–3 days and 16–17 days after the eruption, and the abnormal intensity was more than 10 times that of normal. The coordinate time series in direction E showed very significant anomalies at approximately 2:45 p.m. on 14 January, at approximately 4:30 a.m.–5:40 a.m. on 15 January, and at approximately 3:45 a.m. on 16 January, with anomalies reaching a maximum of 7–8 times daily. The abnormality in the direction north (N) is not obvious. Very prominent anomalies can be observed in the direction up (U) at approximately 4:30 a.m.–5:40 a.m., with the intensity of the anomalies exceeding the normal by more than 10 times. In this study, GNSS was successfully used to detect the anomalous environmental response during this HTHH volcano eruption. [ABSTRACT FROM AUTHOR]

Potential evapotranspiration (PET) can reflect the characteristics of drought change in different time scales and is the key parameter for calculating the standardized precipitation evapotranspiration index (SPEI). The Thornthwaite (TH) and Penman–Monteith (PM) models are generally used to calculate PET, but the precision of PET derived from the TH model is poor, and a large number of meteorological parameters are required to evaluate the PM model. To obtain high-precision PET with fewer meteorological parameters, a high-precision PET (HPET) model is proposed to calculate PET by introducing precipitable water vapor (PWV) from Global Navigation Satellite System (GNSS) observation. The PET difference (DPET) between TH- and PM-derived PET was calculated first. Then, the relationship between the DPET and GNSS-derived PWV/temperature was analysed, and a piecewise linear regression model was calculated to fit the DPET. Finally, the HPET model was established by adding the fitted DPET to the initial PET derived from the TH model. The Loess Plateau (LP) was selected as the experiment area, and the statistical results show the satisfactory performance of the proposed HPET model. The averaged root mean square (RMS) of the HPET model over the whole LP area is 8.00 mm, whereas the values for the TH and revised TH (RTH) models are 34.25 and 12.55 mm, respectively, when the PM-derived PET is regarded as the reference. Compared with the TH and RTH models, the average improvement rates of the HPET model over the whole LP area are 77.5 and 40.5%, respectively. In addition, the HPET-derived SPEI is better than that of the TH and RTH models at different month scales, with average improvement rates of 49.8 and 23.1%, respectively, over the whole LP area. Such results show the superiority of the proposed HPET model to the existing PET models. [ABSTRACT FROM AUTHOR]