Search

Abstract Among all the ambiguity resolution techniques, the Full Ambiguity Resolution (FAR), Partial Ambiguity Resolution (PAR) and Best Integer Equivariant (BIE) estimator are widely used. Although the researches have been done on the different classes of ambiguity resolution, we still hope to find the relationships among these specific algorithms. In this work, we unify the PAR and FAR algorithms under a whole framework of BIE by applying multiple integer candidates. A concise estimation formula of the variance of Gaussian BIE estimator based on the variance of float solution and the probability distribution of the candidates is first derived. Then, we propose an algorithm named Multiple Integer Candidates Ambiguity Resolution (MICAR) to discover as many ambiguities in the BIE as possible that can be estimated more precisely by PAR (FAR) algorithm instead of BIE. In the experiments, we utilize the simulated data of GPS (Global Positioning System) + BDS (BeiDou Navigation Satellite System) + Galileo (Galileo navigation satellite system) to contrast the effects of MICAR and single candidate estimator, i.e., FAR. By taking the threshold of 5 cm at 95% confidence level as an example, MICAR accelerates the convergence process by about 3.0 min. When the positioning sequence converges, MICAR reduces the root mean square of the positioning error by 9.8% in horizontal directions and 3.5% in vertical direction, which is attributed to more fixed NL.

The riverbed and riparian zone are the hotspots of nitrogen removal in rivers. Denitrification plays an important role in the process of nitrogen removal. In this study, sediments from the straight channel riverbed and point bars were examined using indoor culture and acetylene inhibition techniques. The primary focus was to investigate the differences in denitrification rates between these sediments. The secondary focus was on the effects of temperature and carbon-nitrogen (C/N) ratios on the denitrification process. The results showed that denitrification rates were higher in point bar sediments compared to those in the straight channel bed. Denitrification rates were also higher in the near water area of the point bar than in the near bank area. Denitrification rates at 30 °C were significantly higher than at 10 °C for each sediment group as well as in samples having carbon and nitrogen amendments. Notably, when the C/N ratio was 2.5, the denitrification rate for samples with carbon and nitrogen additions was significantly higher than for samples without them. On average, denitrification rates increased by 2.56 times, 2.73 times and 2.87 times for sediments from the straight channel, inner part of the point bar, and near bank of the point bar, respectively. At the same time, the number of denitrifying bacteria was found to be higher in the point bar than in the straight channel. These findings highlight the beneficial role of point bars in accelerating sediment denitrification rates and emphasize the potential for increasing nitrogen removal capacity in rivers by optimizing temperature and C/N ratios. Changing the diversity of riverbed geomorphology, temperature and C/N can effectively enhance the nitrogen removal capacity of river ecosystems.

Abstract With climate change, there will be higher requirements for monitoring storm surges (SSs) in nearshore areas. However, this capability is limited by the sparseness of tide gauge (TG) stations. Establishing and maintaining a permanent, high‐spatial coverage, in situ TG network is complex and expensive. Here, we propose a joint modeling method developed from the all‐site modeling data‐driven framework by importing temporary TGs into coastal regions with insufficient permanent TG stations. The assessments show that this method can significantly optimize the capability of extreme SS monitoring during typhoons and hurricanes. Moreover, the evaluation based on Coupled Model Intercomparison Project Phase 6 data indicates that it will monitor extreme SSs more effectively during 2025–2050 compared with only using existing permanent in situ TGs (reducing root mean square error and absolute mean bias by ∼50%). The joint modeling method provides an applicable and sustainable solution for optimizing the SS monitoring capability in coastal areas.

Abstract The presence of a static tilt between the inner core and mantle is an ongoing discussion encompassing the geodynamic state of the inner core. Here, we confirm an approximate 8.5 yr signal in polar motion is the inner core wobble (ICW), and find that the ICW is also contained in the length-of-day variations of the Earth’s rotation. Based on the determined amplitudes of the ICW and its good phase consistency in both polar motion and the length-of-day variations, we infer that there must be a static tilt angle θ between the inner core and the mantle of about 0.17 ± 0.03°, most likely towards ~90°W relative to the mantle, which is two orders of magnitude lower than the 10° assumed in certain geodynamic research. This tilt is consistent with the assumption that the average density in the northwestern hemisphere of the inner core should be greater than that in the other regions. Further, the observed ICW period (8.5 ± 0.2 yr) suggests a 0.52 ± 0.05 g/cm3 density jump at the inner core boundary.

Abstract The Green's function approach is well‐established and widely used for modeling the surface mass loading displacements. Global mean Green's functions (MGFs) are commonly applied without considering local variations of the crustal structure. Derived from the modified layered Earth structure, the local Green's functions (LGFs) are theoretically beneficial to generate more accurate deformation, since they consider interior information of the local crust. This paper analyzed the differences among MGFs from Gutenberg–Bullen A model and two sets of LGFs derived from modified PREM Earth models consolidating with two crust models TEA12 and CRUST1.0, hereafter called PREMTEA and PREMCRU, respectively. Utilizing MGFs and two sets of LGFs, we modeled the corresponding 3D atmospheric loading displacements for 984 ITRF2014 stations and compared them with the ITRF2014 residuals. The results show that LGFs from PREMTEA and PREMCRU perform well in further promoting scatter reduction for ∼72%, ∼56%, and ∼85% of stations for the Up, East and North components, respectively. The improvements for the North components are significant (up to 3.6%). In particular, stations in the east coastal areas of North America and the west edge of Greenland exhibit further promoting scatter reduction for the East components (up to ∼2.5%), while those located in west coastline of North America show better performance for the North components. Nevertheless, there are significant anomalies in northern Europe for PREMCRU, the mutation margin of which should be carefully considered when using a resolution higher than 1°. In the area around station MORP (358.31°W, 55.21°N, sited at coastline of Britain), we suggest using PREMTEA model.

AbstractIn-stream restoration structures, such as woody weirs, are intended to enhance hyporheic exchange, thus altering temperature dynamics in restored reaches. However, the relative effects of various in-stream structure types and streambed settings (i.e. the size, spacing, number and sediment hydraulic conductivity) remain poorly understood. Here, we conducted a field experiment with a channel-spanning weir in a stream to study its impact on hyporheic exchange and streambed and surface water temperatures. We subsequently applied numerical models to explore the effects of height, spacing and number of weirs and sediment permeability on hyporheic exchange and thermal distribution characteristics. Based on the field experiments and numerical models, the results showed that the addition of a weir enhanced hyporheic exchange and produced a characteristic temperature heterogeneity pattern in sediment that varied with height, spacing, number of weirs and sediment permeability. The spatial extent and rate of hyporheic exchange and temperature heterogeneity near the weir primarily increased with weir height and sediment permeability. With increasing spacing, the exchange flux and thermally heterogenous area increased, but the exchange intensity decreased, and the sediment temperature readily stabilized. With increasing number of weirs, the exchange flux first decreased and then increased, and the region exhibiting temperature heterogeneity increased. The interaction between the introduction of in-stream structures introduction and streambed settings must be understood to improve vertical connectivity in rivers, increase the thermal heterogeneity in the hyporheic zone and create localized but potentially valuable thermal refuge areas.

As one of the Analysis Centers (AC) of the International GNSS Service (IGS), Wuhan University (WHU) has been contributing to the IGS by providing ultra-rapid as well as rapid orbit and clock solutions for the established GPS and GLONASS since 2012. In the same year, the IGS initiated the Multi-GNSS Experiment (MGEX) to support the analysis of the emerging GNSS systems and prepare the IGS for Multi-GNSS, which includes GPS, GLONASS, the European Galileo system, the Chinese Beidou Navigation Satellite System (BDS), the Japanese Quasi-Zenith Satellite System (QZSS) and the Indian Regional Navigation Satellite System (IRNSS/NaVIC). The major products, i.e., orbits, Earth Orientation Parameters (EOPs), satellite clock as well as attitude have also been provided by WHU since 2012. More recently, WHU has engaged the third reprocessing of IGS for generating the highly accurate station coordinates as inputs for establishment of the International Terrestrial Reference Frame (ITRF) 2020 during 2019—2020. This article presents the recent major advancements of the IGS AC at Wuhan University, including precise products, real-time products, bias products, antenna phase center calibration, and the non-linear motion modeling for GNSS Reference Stations.

Abstract Background Real‐world evidence on immune‐related adverse events (irAEs) are relatively insufficient. Herein patterns and outcomes of irAEs after administration of anti‐programmed cell death 1 (PD‐1) and its legend 1 (PD‐L1) antibodies were investigated. Methods Patients treated with anti‐PD‐1/PD‐L1 drugs from January 2018 to September 2021 at Huadong Hospital, Fudan University were included. Common Terminology Criteria for Adverse Events (CTCAE) was used for irAEs evaluation. The primary endpoints were the clinical description of irAEs. Results Two hundred and forty‐one solid tumor patients were included, with lung cancer as the most common tumor type (56%). 187 (77.6%) patients presented any kind of irAEs. The median time to any irAE onset was 28 (95% CI 24–32) days. Skin toxicities are the most common irAEs (46.1%) and the irAEs (36.5%) occurred earliest after immune‐checkpoint inhibitors. The most frequently occurred all‐grade irAEs were rash (23.7%), myelosuppression (20.7%), and hepatic injury (19.5%). 23 (9.5%) patients died of severe irAEs, which consists of 10 patients with pneumonitis, four colitis, four myocarditis, and one each for gastritis, pulmonary embolism, myelosuppression, hypophysitis, and encephalitis. Patients with any irAE onset had significantly longer progression‐free survival (PFS) (p = 0.013) and overall survival (OS) (p = 0.007), respectively, than patients without irAEs. In addition, patients with skin toxicities (p = 0.012) or blood toxicities (p = 0.015) had achieved a longer PFS, than those without corresponding toxitities, respectively. Conclusion Most irAEs are mild and manageable, while some irAEs can present at later time or can be life‐threatening, especially pneumonitis as we observed. Patients with any irAE onset may achieve a better prognosis than those without irAEs, and presentation of skin or blood toxicities will indicate a better PFS.

High-speed railway suspension bridges (HSRSBs) have been constructed with the new advancements in technology. The deformation prediction for HSRSBs is essential to their safety and maintenance. The conventional prediction methods are developed for bridges without high-speed railway. Different factors, including temperature (TEMP), time delay compensation (TDC), train live load (TLL), are considered in these methods. However, the train side (TS) and train instantaneous position (TIP) have a significant impact on deformation for HSRSBs, and they are not used in the prediction. More importantly, the coupling issue among different factors is so significant that it cannot be neglected. In this study, we propose a deformation prediction model based on a backpropagation (BP) neural network. This model uses different factors as model input, including TEMP, TDC, TLL, TS, and TIP. The coupling issue is addressed by using the new model. The new model was evaluated using a dataset of 10-day field measurements. It achieves a mean absolute error (MAE) of 8.81 mm, a mean relative error (MRE) of 9.82%, and coefficient of determination (R2) of 0.94. The new model will provide high-precision prediction for deformation and will be used in the development of an early warning system.

The study of inter-system bias (ISB) is important for multi-system fusion and the performance of different signal compatibility. In this paper, the stability of ISB at the BDS3/BDS2 receiver end is calculated and analyzed for different time spans (DOY 060∼090 in 2021) from a total of 31 MGEX and iGMAS stations. We adopted two estimation strategies, random walk and constant approach, using the precision products of orbit and clock bias provided by WUM, the influence of which on ISB was also analyzed. Our results showed that the ISB value varied little within a day, and the mean of daily ISB standard deviation was only 0.037 m when the observation condition was good. The signal reception was continuous, indicating a high ISB stability for one day. If extending the time series to one month, however, the ISB standard deviation calculated by constant approach, in which a constant ISB is estimated on a daily basis was about 0.1 m, and the results of adjacent days were not continuous, with no apparent pattern. Concerning the random walk approach, the obtained ISB time series also had a jump, and the conclusion was the same as that of the constant strategy. Besides, receiver types showed a strong regularity in ISB numerical situation, and the distribution of ISB values corresponding to the same receiver type was relatively close. Therefore, we conclude that the ISB parameters remain stable in the short term (one day) and less stable in the long-term period. It is recommended that the ISB term should be set as a constant estimate every day in BDS3/BDS2 solutions, regardless of receiver type consistency.

Slant range geometry plays a crucial role in interpreting synthetic aperture radar (SAR) observations, especially in converting line-of-sight (LOS) surface deformations to actual vertical subsidence. This paper proposes a new conversion model to retrieve vertical settlements of the embankment slopes using the geometrical parameters of the dam and the SAR sensor. The simulation results highlight the impact of slope foreshortening and heading direction of the satellite on deformation retrieval. Various SAR data with different resolutions and bands are used to analyze the model’s performance, revealing a high conformity of the model with practical conversion parameters exceeding 80% for TerraSAR-X and Cosmo-SkyMed data.

Abstract Analyzing the features of extreme events and estimating their probabilities robustly require high spatial coverage, high temporal resolution, and sufficiently long storm surge (SS) records. However, in situ observations cannot always meet these demands due to spatiotemporal sparseness. Here, we proposed a novel regional all‐site modeling framework based on a machine learning method, the extreme gradient boosting tree. This framework can reconstruct long SS records simply and quickly and can estimate storm surges simultaneously at both gauged and ungauged locations. Compared to in situ observations, the distribution patterns of SS variations during extreme events can be recognized easily from the reconstructed hourly SS data set. Since its available record is longer than 60 years (1959–2020), the estimation uncertainties of extreme event probabilities are significantly decreased. Noticeably high extreme SS return levels were found along the coast of the northern Gulf of Mexico, which should be given great attention.

Abstract Background Innate lymphoid cells (ILCs), as an important group of innate immunity, could respond rapidly to Mycobacterium tuberculosis (Mtb) infection. In this research, we studied the phenotypic changes of circulatory ILCs in active tuberculosis (TB) disease. Methods We recruited 40 patients with active Mtb infection (TB group) and 41 healthy subjects (NC group), and collected their clinical information and peripheral blood. Circulating ILCs, ILC subsets, dendritic cells (DCs), macrophages, and the production of cytokines in ILCs were tested by flow cytometry (FCM). Enzyme-linked immunosorbent assay (ELISA) was used to detect plasma IL-23. Results Compared with healthy control, total ILCs (0.73% vs. 0.42%, P = 0.0019), ILC1 (0.55% vs. 0.31%, P = 0.0024) and CD117+ ILC2 (0.02% vs. 0.01%, P = 0.0267) were upregulated in TB group. The total IL-17+ lymphocytes were elevated (3.83% vs. 1.76%, P = 0.0006) while the IL-22+ lymphocytes remained unchanged. Within ILC subsets, ILC3, CD117+ ILC2 and ILC1 in TB group all expressed increased IL-17 (15.15% vs. 4.55%, 19.01% vs. 4.57%, 8.79% vs. 3.87%, P

Based on a satellite constellation composed of two GRACE-type satellite formations with different inclinations (near polar orbit + low inclination) and the theory of repeat orbit cycle, we discuss the methods for selecting medium-low inclinations for global and local gravity fields. The effects of this constellation configuration on gravity field inversion are comparatively analyzed using a whole-course dynamics simulation. The results show that compared with the single GRACE-type satellite formation, the use of satellite constellations with different inclination configurations improves the gravity solution precision by 34%. The inclusion of multi-directional observations can improve the spatio-temporal resolution of the satellite missions, and yield gravity field solutions with higher isotropic sensitivity. Furthermore, it is necessary to select the optimal low inclination according to the study area, which will have a significant influence on the gravity field solution.

Summary: Due to limited detection sensitivity and contrast limitation, imaging substrates with 129Xe MRI in living cells is still a challenge. Here, we present an effective protocol to detect and image substrates in human lung cancer cells A549 with hyperpolarized 129Xe MRI. This protocol was optimized for a cryptophane-based probe sensitive to biothiols and can be expanded to other Xe-based probes to detect potential biomarkers in other mammalian cells.For complete details on the use and execution of this protocol, please refer to Zeng et al. (2021). : Publisher’s note: Undertaking any experimental protocol requires adherence to local institutional guidelines for laboratory safety and ethics.

At present, high-precision GNSS positioning technology is an important means to monitor the health of bridges and other structures. However, the GNSS signal of reference stations and monitoring stations used for bridge monitoring can easily be blocked by bridge towers, vehicles, or other objects, resulting in low positioning accuracy and insufficient availability of GNSS, which affects the effectiveness of bridge structural health monitoring. Therefore, according to the characteristics of bridge structure, this paper proposes to take the bridge tower monitoring station as a moving-base station to build the baselines with other monitoring stations and use the moving-base RTK-GNSS method to realize the relative positioning, so as to improve the availability of GNSS in the application of bridge structure health monitoring. In this paper, the moving-base RTK-GNSS model is derived and verified via GNSS monitoring data of the Ganzhou dedicated high-speed railway bridge. The results show that the ambiguity in the fixing rate can be improved using the moving-base RTK-GNSS method with the tower monitoring station as the reference station. The deformation and vibration characteristics of each monitoring point can be reflected, and the displacement and vibration amplitude estimation accuracy can achieve results better than 4 mm. Therefore, the moving-base RTK-GNSS method can be used as an alternative scheme when the observation environment of the base station is poor or the banded engineering monitoring is applied, so as to improve the monitoring capability of GNSS.

ObjectiveTo evaluate the longitudinal association of nut consumption with cognitive function in Chinese elderly.MethodsWe analyzed the data from Zhejiang Ageing and Health Cohort Study including 9,028 participants. Nut consumption was evaluated in baseline questionnaire beginning at 2014. Cognitive function was assessed repeatedly through the Mini-Mental State Examination (MMSE) at baseline and three waves of follow-up (2015, 2016, and 2019–2020). Cognitive impairment was defined using education-specific cut-off points. Log-binomial regression models with the generalized estimating equations, controlled for an extensive range of potential confounders, were utilized to evaluate the association and estimate relative risk (RR).ResultsAfter 6 years of follow-up, 3,266 (36.18%) participants were indicated as cognitive impairment by MMSE at least once. Compared with non-consumers or less-than-weekly consumers, participants consuming ≥70 g/week of nuts had 17% lower risks of cognitive impairment (RR = 0.83, 95% CI 0.75–0.91), whereas no association was found in those consuming

Abstract Precise point positioning (PPP) is famous for its capability of high-precision positioning with just one station as long as the receiver can receive global navigation satellite system (GNSS) signals. With the rapid development of BDS and Galileo, the number of available satellites for positioning has increased significantly. In addition, GPS III, GLONASS-K, BDS, and Galileo satellites can transmit triple-frequency signals. The potentials of multi-constellation GNSS PPP requires further analysis on a global scale. Therefore, we selected 96 multi-GNSS experiment (MGEX) stations with a global distribution and used 1 week’s data to assess the PPP performance. The results show that the PPP based on multi-frequency raw observations with spatial and temporal constraints has better performance than PPP using dual-frequency ionospheric-free observations. The main contribution of multi-constellation GNSS PPP is to shorten the convergence time. The convergence time for GPS PPP is approximately 40 min, which can be shortened to less than 20 min in multi-GNSS PPP. After convergence, the positioning accuracy of multi-GNSS PPP is improved by 0.5 to 1.0 cm compared with GPS or GLONASS PPP. The positioning accuracy of multi-GNSS could be further improved in the future with the BDS and Galileo precise products of orbits, clock and phase center offset/variation.

Previous studies have estimated the sea level rise (SLR) at various locations on the west coast of the USA and Vancouver Island in Canada. Here, we construct an entire SLR profile from Vancouver Island in the Pacific Northwest to San Diego in Southern California. First, we process global navigation satellite system (GNSS) measurements at 405 stations blanketing the whole coast to generate a profile of vertical land motion (VLM) known to bias century-long tide gauge (TG) measurements recording relative SLR (RSLR). We are then able to estimate the absolute SLR (ASLR) by correcting the SLR with the VLM. Our study emphasizes the relationship between the various tectonic movements (i.e., the Cascadia subduction zone, the San Andreas strike-slip fault system) along the Pacific coast which renders it difficult to accurately estimate the SLR. That is why we precisely model the stochastic noise of both GNSS and tide gauge time series using a combination of various models and information criterions (ICs). We also use the latest altimetry products and sea surface height (SSH) to compare it with ASLR at the same location as the TGs. This study supports previous analysis that the power law + white noise and generalized Gauss–Markov + white noise models are the best stochastic noise models for the GNSS time series. The new coastal profile confirms the large variability of VLM estimates in the Pacific Northwest around the Cascadia subduction zone in agreement with previous studies, and a similar result when the San Andreas fault comes onshore in Central California (San Francisco Bay). Negative RSLR values are mostly located in the Pacific Northwest (Vancouver Island and Olympic Peninsula). We also observe a much bigger variation (about 90–150%) of the ASLR in the Pacific Northwest which is predominantly due to glacial isostatic adjustment (GIA). Moreover, the comparison between the ASLR and the SSH estimates shows similarities in the center of the studied area (South Washington, Oregon planes, and some parts of Southern California) where the tectonic activity does not significantly influence the TG measurements. Finally, the twentieth-century satellite geocentric ocean height rates show a global mean of 1.5 to 1.9 mm/yr. Our estimates based on ASLR and SSH are within this interval.

Global Positioning System (GPS) has been confirmed to be a feasible tool to measure displacement of civil engineering structures. In this paper, we report on an analysis of annual deformations of a pumped-storage power station dam using historical GPS observations. Data spanning more than nine years are resolved using the GAMIT (GPS at MIT) software, and a GPS time-series method is employed to extract linear trends and annual cycle signals. It is evident that the monument located on the main dam has a linear trend, with rates of 1.0 mm/yr and 1.8 mm/yr in east and up directions, respectively. Annual cycles with amplitudes larger than 0.5 mm are shown in coordinate components at all monitoring stations. However, the annual amplitude can be 30–84% lower when a monitoring station whose monument materials and height are similar to other monitoring stations is chosen as the reference station. This suggests that differential thermal expansion of monuments could be 30% to 80% and even higher in baseline time series. A spurious offset style annual signal with 5 mm amplitude that is highly correlated with annual temperature variance is observed in the east–west direction of the monitoring station located at the east side of the reservoir. This suggests that upper ground layer movement correlated with temperature could be responsible for these annual cycles. Meanwhile, no periodic correlations are observed between the water level data and the baseline time series.

Abstract The Global Navigation Satellite System (GNSS) has proved to be a powerful tool for applications in meteorology. In this study, we propose a novel slant tropospheric delay (STD) model to obtain the vertical distribution of atmospheric refractivity based on a single ground‐based GNSS receiver. The new model is used to convert the STD into a function of the vertical gradient of temperature, and it is divided into two layers (above and below the tropopause) for integration. The optical vertical gradient of temperature can be estimated according to the STD obtained from the GNSS observations from a higher satellite elevation angle. The distribution of atmospheric refractivity can then be derived from the vertical gradient of temperature and the surface atmospheric refractivity. Moreover, to further improve the accuracy of the STD model‐derived atmospheric refractivity, we correct it using a “theoretical retrieval” method based on the STDs obtained at a lower elevation angle. The optical ranges of theoretical retrieval are obtained above and below 5 km. Finally, a search is performed for the value of atmospheric refractivity that best fits the model equations, and this value is taken as the final inversion result. Data collected from eight GNSS stations and nearby radiosonde stations in 2016 were used to verify the new method. Using the radiosonde‐derived values as a reference, the accuracy of the STD model‐derived atmospheric refractivity was improved by 13.4% compared with the traditional technique. In addition, again using the radiosonde‐derived values as a reference, the accuracy of the atmospheric refractivity derived with the optically corrected method was improved by 20.4% compared with the uncorrected STD model.

MicroRNAs (miRNAs) are small endogenous non‐coding RNAs that can negatively regulate the expression of their complementary mRNA targets, and have been implicated in various pathophysiological processes. In this study, we examined the effect of miR‐222‐3p on intervertebral disc degeneration (IDD). We found that expression of miR‐222‐3p was significantly higher in IDD tissues than in normal intervertebral disc tissue, and report that overexpression of miR‐222‐3p remarkably increased apoptosis and reduced proliferation of nucleus pulposus (NP) cells. In addition, miR‐222‐3p promoted secretion of matrix metalloproteinase‐3, and decreased collagen type II and aggrecan production. Cyclin‐dependent kinase inhibitor 1B (CDKN1B) was identified as a direct target of negative regulation by miR‐222‐3p in NP cells, and expression of miR‐222‐3p was found to be negatively correlated with that of CDKN1B in IDD tissue. Finally, we observed that transfection with miR‐222‐3p dramatically reduced CDKN1B expression in NP cells. In conclusion, miR‐222‐3p may be involved in IDD development, possibly through targeting CDKN1B.

Abstract Adaptive and accurate trend estimation of the sea level record is critically important for characterizing its nonlinear variations and its study as a consequence of anthropogenic climate change. Sea level change is a nonstationary or nonlinear process. The present modeling methods, such as least squares fitting, are unable to accommodate nonlinear changes, including the choice of a priori information to help constrain the modeling. All these problems affect the accuracy and adaptability of nonlinear trend estimation. Here, we propose a method called EMD‐SSA, that effectively combines adaptive empirical mode decomposition (EMD) and singular spectrum analysis (SSA). First, the sea level change time series is decomposed by EMD to estimate the intrinsic mode functions. Second, the periodic or quasiperiodic signals in the intrinsic mode functions can be determined using Lomb‐Scargle spectral analysis. Third, the numbers of the identified periodicities/quasiperiodicities are used as embedding dimensions of SSA to identify possible nonlinear trends. Then, the optimal nonlinear trend with the largest absolute Mann‐Kendall rank is selected as the final trend for the sea level change. Based on a comprehensive experiment using simulated sea level change time series, we concluded that the EMD‐SSA method can adaptively provide better estimate of the nonlinear trend in a realistic sea level change time series with consistency or high accuracy. We suggest that EMD‐SSA can be used not only to robustly extract nonlinear trends in sea level data, but also for trends in other geodetic or climatic records, including gravity, GNSS observed displacements, and altimetry observations.

Abstract Construction of noise model is an important task in the analysis of Global Positioning System (GPS) reference station coordinate time series. Ignoring the relationship between the noise on different components within a GPS station network may affect the accuracy of station's velocity and its uncertainty. In view of this problem, we propose to use the singular value decomposition (SVD) method to establish a new three‐dimensional (3‐D) noise model for GPS station networks. Our simulation tests show that the accuracy of the noise amplitude obtained based on the proposed 3‐D noise model is 30–50% higher than that directly obtained from Create and Analyze Time Series (CATS) software, thereby improving the accuracy of the velocity uncertainty by approximately two times. Taking the coordinate time series of 82 GPS stations from the Crustal Motion Observation Network of China (CMONOC) as an example, we confirm that significant correlation exists among noise amplitude estimates in the different components of the CMONOC stations. In general, the variation of white noise (WN) amplitude is 2–6% smaller than that of flicker noise (FN) amplitude, and the FN amplitude in the vertical component is 1% larger than that in the horizontal component. Compared with the velocity uncertainty obtained from CATS software, the variations of the velocity uncertainty obtained from the new 3‐D noise model in the horizontal components (7% for North, 8% for East) are slightly less than that in the Up component (9%). However, the velocity estimation is hardly affected by the new 3‐D noise model.

Intracerebral hemorrhage (ICH) is a common and severe neurological disorder that can effectively induce oxidative stress responses. NADPH oxidase 4 (NOX4) is a member of the NOX family of oxidases. It is expressed in the brain normally and involved in cell signal transduction and the removal of harmful substances. In some pathological conditions, it mediates inflammation and the aging of cells. However, few studies have focused on whether NOX4 is involved in brain injury caused by ICH. Therefore, this study aimed to clarify the role of NOX4 in the pathological process that occurs after ICH and the potential mechanism underlying its role. A rat model of ICH was established by the injection of collagenase type IV, and the expression of NOX4 was then determined. Further, siRNA-mediated protein expression knockdown technology was used for NOX4 knockdown, and western immunoblotting, immunohistochemistry, immunofluorescence, enzyme-linked immunosorbent assay (ELISA), and other molecular biological techniques were performed to assess the effects of NOX4 knockdown. Neurobiological scoring, brain water content determination, and other brain injury detection methods were also performed to assess the role of NOX4 following ICH. We found that the expression of NOX4 increased in the brains of rats after ICH, and that it was mainly expressed in neurons, astrocytes, vascular endothelial cells and microglia. Following NOX4 knockdown, the level of oxidative stress in the brain decreased considerably, the neurobehavioral scores improved, the levels of neuronal apoptosis reduced markedly, and the impairment of blood-brain barrier function was significantly ameliorated in rats with ICH. In conclusion, this study suggests that NOX4 expression is upregulated after ICH, which may cause an imbalance in the oxidative stress of relevant cells in the brain, leading to subsequent apoptosis of neurons and damage to the blood-brain barrier due to secondary brain injury following ICH.

Common Mode Error (CME) presents a kind of spatially correlated error that is widespread in regional Global Navigation Satellite System (GNSS) networks and should be eliminated during postprocessing of a GNSS position time series. Several spatiotemporal filtering methods have been developed to mitigate the effects of CME. However, such methodologies become inappropriate when missing and noisy data exists. In this research, we introduce a novel spatial filtering algorithm called Weighted Expectation Maximization Principal Component Analysis (WEMPCA) for detecting and removing CME from noisy GNSS position time series with missing values, among which formal errors of daily GNSS solutions are utilized to weight the input data. Compared with traditional PCA and the special case of EMPCA, simulation experiments demonstrate that the new WEMPCA algorithm always has outstanding performance over others. The WEMPCA algorithm was then successfully used to extract the CME from real noisy and missing GNSS position time series in Xinjiang province. Our results show that only the first principal component exhibits significant spatial response, with average values of 70.11%, 66.53%, and 52.45% for North, East, and Up (NEU) components, respectively, indicating that it represents the CME of this region. After removing CME, the canonical correlation coefficients and root mean square error of GNSS residual time series, as well as the amplitudes of power-law noises (PLN), are obviously decreased in all three directions. However, the white noise (WN) amplitudes are found to diminish exclusively in the North and East component, not in the Up components. Moreover, the average velocity differences before and after filtering CME are 0.19 mm/year, 0.03 mm/year, and −0.56 mm/year for the NEU components, respectively, indicating that CME has an influence on the GNSS station velocity estimation. The velocity uncertainty is also reduced by 43.51%, 38.64%, and 40.39% on average for the NEU components, respectively, implying that the velocity estimates are more reliable and accurate after removing CME. Therefore, we conclude that the new WEMPCA approach provides an efficient solution to detect and mitigate CME from the noisy and missing GNSS position time series.

The noise in position time series of 568 GPS (Global Position System) stations across North America with an observation span of ten years has been investigated using solutions from two processing centers, namely, the Pacific Northwest Geodetic Array (PANGA) and New Mexico Tech (NMT). It is well known that in the frequency domain, the noise exhibits a power-law behavior with a spectral index of around −1. By fitting various noise models to the observations and selecting the most likely one, we demonstrate that the spectral index in some regions flattens to zero at long periods while in other regions it is closer to −2. This has a significant impact on the estimated linear rate since flattening of the power spectral density roughly halves the uncertainty of the estimated tectonic rate while random walk doubles it. Our noise model selection is based on the highest log-likelihood value, and the Akaike and Bayesian Information Criteria to reduce the probability of over selecting noise models with many parameters. Finally, the noise in position time series also depends on the stability of the monument on which the GPS antenna is installed. We corroborate previous results that deep-drilled brace monuments produce smaller uncertainties than concrete piers. However, if at each site the optimal noise model is used, the differences become smaller due to the fact that many concrete piers are located in tectonic/seismic quiet areas. Thus, for the predicted performance of a new GPS network, not only the type of monument but also the noise properties of the region need to be taken into account.

In this paper, we construct a new 1′ × 1′ global seafloor topography model, BAT_VGG2021, using the satellite altimetric vertical gravity gradient anomaly model (VGG), SIO curv_30.1.nc, and ship soundings. Approximately 74.66 million single-beam depths and more than 180 GB of multibeam grids were downloaded and adopted from the National Centers for Environmental Information (NCEI), Japan Agency for Marine-Earth Science and Technology (JAMSTEC), and Geosciences Australia (GA). The SIO curv_30.1.nc model was used to predict seafloor topography at 15~160 km wavelengths, and ship soundings were used to calibrate topography to VGG ratios. The accuracy of the new BAT_VGG2021 model was assessed by comparing it with ship soundings and existing models. The results indicate that the standard deviation of differences between the predicted model and ship soundings is about 40~80 m, and ~93% of the differences are within 100 m, similar to that of the SIO topo_20.1.nc model. The new BAT_VGG2021 model shows better accuracy than the DTU18BAT, ETOPO1, and GEBCO_08 models, and has been improved significantly from our last model, BAT_VGG2014.

“Pass-by-pass” or “track-to-track” ambiguity resolution removes Global Navigation Satellite System (GNSS) satellite hardware delays between adjacent undifferenced (UD) ambiguities, which is often applied in precise orbit determination (POD) for Low Earth Orbit (LEO) satellites to improve the accuracy of orbits. In this study, we carried out an exploratory study to use the “pass-by-pass” ambiguity resolution by differencing the undifferenced ambiguity candidates for two adjacent passes in sidereal days for a single Global Positioning System (GPS) receiver static Precise Point Positioning (PPP). Using the GPS observations from 132 globally distributed reference stations of International GPS Service (IGS), we find that 99.08% wide-lane (WL) and 97.83% narrow-lane (NL) double-difference ambiguities formed by the “pass-by-pass” method for all stations can be fixed to their nearest integers within absolute fractional residuals of 0.2 cycles. These proportions are higher than the corresponding values of network solution with multiple receivers with 97.39% and 91.20%, respectively. About 97% to 98% of ambiguities can be fixed finally on average. The comparison of the estimated station coordinates with the IGS weekly solutions reveals that the Root Mean Square (RMS) in East and North directions are 2-4 mm and is about 6 mm in the Up direction. For hourly data, it is found that the mean positioning accuracy improvement can achieve to about 10% after ambiguity resolution. From a dam deformation monitoring application, it shows that the fixing rate of WL and NL ambiguity can be closed to 100% and higher than 90%, respectively. The time series generated by PPP are also in agreement with the short baseline solutions.

GNSS time-series prediction plays an important role in the monitoring of crustal plate movement, and dam or bridge deformation, and the maintenance of global or regional coordinate frames. Deep learning is a state-of-the-art approach for extracting high-level abstract features from big data without any prior knowledge. Moreover, long short-term memory (LSTM) networks are a form of recurrent neural networks that have significant potential for processing time series. In this study, a novel prediction framework was proposed by combining a multi-scale sliding window (MSSW) with LSTM. Specifically, MSSW was applied for data preprocessing to effectively extract the feature relationship at different scales and simultaneously mine the deep characteristics of the dataset. Then, multiple LSTM neural networks were used to predict and obtain the final result by weighting. To verify the performance of MSSW-LSTM, 1000 daily solutions of the XJSS station in the Up component were selected for prediction experiments. Compared with the traditional LSTM method, our results of three groups of controlled experiments showed that the RMSE value was reduced by 2.1%, 23.7%, and 20.1%, and MAE was decreased by 1.6%, 21.1%, and 22.2%, respectively. Our results showed that the MSSW-LSTM algorithm can achieve higher prediction accuracy and smaller error, and can be applied to GNSS time-series prediction.

Abstract The Global Positioning System (GPS) records monsoonal precipitable water vapor (PWV) and vertical crustal displacement (VCD) due to hydrological loading, and can thus be applied jointly to diagnose meteorological and hydrological droughts. We have analyzed the PWV and VCD observations during 2007.0–2015.0 at 26 continuous GPS stations located in Yunnan province, China. We also obtained equivalent water height (EWH) derived from the Gravity Recovery And Climate Experiment (GRACE) and precipitation at these stations with the same period. Then, we quantified the annual variations of PWV, precipitation, EWH and VCD and provided empirical relationships between them. We found that GPS-derived PWV and VCD (positive means downward movement) are in phase with precipitation and GRACE-derived EWH, respectively. The annual signals of VCD and PWV show linearly correlated amplitudes and a two-month phase lag. Furthermore, the results indicate that PWV and VCD anomalies can also be used to explore drought, such as the heavy drought during winter/spring 2010. Our analysis results verify the capability of GPS to monitor monsoon variations and drought in Yunnan and show that a more comprehensive understanding of the characteristics of regional monsoon and drought can be achieved by integrating GPS-derived PWV and VCD with precipitation and GRACE-derived EWH.

As one of the main error sources in high-precision Global Positioning System (GPS) data processing, higher-order ionospheric (HOI) delays cause significant effects on coordinate time series that cannot be ignored in analyses of long time series. Typically two geomagnetic models, DIPOLE model and International Geomagnetic Reference Field (IGRF) model, are used for calculating HOI corrections. This paper investigates the effects of HOI correction caused by the DIPOLE model on coordinate time series. GPS data from 104 globally distributed International GNSS Service (IGS) stations spanning from January, 1999 to December, 2003 were reprocessed following up-to-date processing strategies utilizing GAMIT and GLOBK software. Two coordinate time series solutions before and after applying HOI corrections using the DIPOLE model were derived for studying the effects in terms of seasonal variations and noise amplitudes. The results show that after applying the HOI corrections calculated with DIPOLE, the noise amplitudes of the coordinate time series increased, especially in the north and east directions, and the increased amplitudes of the flicker noise were larger than those of the white noise. Furthermore, spurious periodic signals that were probably introduced by the HOI corrections from the DIPOLE model were also found. Moreover, an apparent increase was confirmed for the power spectra of most of the stations, especially in the north direction, and the amplitudes of both the annual and semi-annual signals also increased in the north and east directions. It can be inferred that the quality of the external data sources such as the geomagnetic model might be the key factors that lead to the above results. The results also suggest that we should be very careful when the DIPOLE model is used for HOI corrections.

The Kuroshio Extension (KE) plays an important role in climate and environmental change in the North Pacific. In this paper, more than 20 years of merged absolute dynamic topography and merged sea level anomaly products from satellite altimetry are used to analyze the stability of the KE system. By analyzing the annually averaged sea surface topography, the variations of inter-annual path and annually averaged eddy kinetic energy at the KE region, the KE's two dynamic states are given as: the relatively stable state during 1993–1995, 2002–2005, and 2010–2012, and the unstable dynamic state among 1996–2001 and 2006–2009. During the stable state, the KE spindle had a shorter path length and smaller time-varying amplitude, as well as a trend to move northward. While during the unstable state, the KE spindle had a longer path length and an integral southward transport trend, and was observed to oscillate significantly over time. The analysis on the KE's upstream and downstream region gives the same variations, indicating that they are significantly affected by the El Nino events. The power spectrum of the mean latitudinal position variation of the KE's upstream and downstream shows significant quasi-decadal oscillation characteristics and strong annual signals. Furthermore, the correlation of the strength variation between the southern RG and the KE's upstream is calculated to be 0.50 after low-pass filtering, and that of the mean latitudinal position variation between the southern RG and the KE's upstream/downstream are 0.75/0.69 after low-pass filtering, respectively. The strong correlations demonstrated that the southern RG and the KE are closely linked.

The mean sea surface (MSS) model is an important reference for the study of charting datum and sea level change. A global MSS model named WHU2013, with 2′ × 2′ spatial resolution between 80°S and 84°N, is established in this paper by combining nearly 20 years of multi-satellite altimetric data that include Topex/Poseidon (T/P), Jason-1, Jason-2, ERS-2, ENVISAT and GFO Exact Repeat Mission (ERM) data, ERS-1/168, Jason-1/C geodetic mission data and Cryosat-2 low resolution mode (LRM) data. All the ERM data are adjusted by the collinear method to achieve the mean along-track sea surface height (SSH), and the combined dataset of T/P, Jason-1 and Jason-2 from 1993 to 2012 after collinear adjustment is used as the reference data. The sea level variations in the non-ERM data (geodetic mission data and LRM data) are mainly investigated, and a combined method is proposed to correct the sea level variations between 66°S and 66°N by along-track sea level variation time series and beyond 66°S or 66°N by seasonal sea level variations. In the crossover adjustment between multi-altimetric data, a stepwise method is used to solve the problem of inconsistency in the reference data between the high and low latitude regions. The proposed model is compared with the CNES-CLS2011 and DTU13 MSS models, and the standard derivation (STD) of the differences between the models is about 5 cm between 80°S and 84°N, less than 3 cm between 66°S and 66°N, and less than 4 cm in the China Sea and its adjacent sea. Furthermore, the three models exhibit a good agreement in the SSH differences and the along-track gradient of SSH following comparisons with satellite altimetry data.

We propose a multiple global navigation satellite system (multi-GNSS) differential phase kinematic post-processing method, expand the current Track ability, and finely tune processing parameters to achieve the best results for research purposes. The double-difference (DD) phase formulas of GLONASS are especially formulated, and the method of arc ambiguity resolution (AR) in post-processing is developed. To verify the feasibility of this AR method, a group of static baselines with ranges from 8 m to 100 km and two kinematic tests were used. The results imply that 100% of ambiguities in short baselines and over 90% in long baselines can be fixed with the proposed ambiguity resolution method. Better than a 10-mm positioning precision was achieved for all the horizonal components of those selected baselines and the vertical components of the short baselines, and the vertical precision for long baselines is around 20 to 40 mm. In the posterior residual analysis, the means of the residual root-mean-squares (RMSs) of different systems are better than 10 mm for short baselines and at the range of 10–20 mm for baselines longer than 80 km. Mostly, the residuals satisfy the standard normal distribution. It proves that the new method could be applied in bridge displacement and vibration monitoring and for UAV photogrammetry.

The BeiDou navigation satellite system (BDS) currently has 41 satellites in orbits and will reach its full constellation following the launch of the last BDS satellite in June 2020 to provide navigation, positioning, and timing (PNT) services for global users. In this contribution, we investigate the characteristics of inter-system bias (ISB) between BDS-2 and BDS-3 and verify whether an additional ISB parameter should be introduced for the BDS-2 and BDS-3 precise point positioning (PPP). The results reveal that because of different clock references applied for BDS-2 and BDS-3 in the International GNSS Service (IGS) precise satellites clock products and the inconsistent code hardware delays of BDS-2 and BDS-3 for some receiver types, an ISB parameter needs to be introduced for BDS-2 and BDS-3 PPP. Further, the results show that the ISB can be regarded as a constant within a day, the value of which is closely related to the receiver type. The ISB values of the stations with the same receiver type are similar to each other, but a great difference may be presented for different receiver types, up to several meters. In addition, the impact of ISB on PPP has also been studied, which demonstrates that the performance of kinematic PPP could be improved when ISB is introduced.

Removal of the common mode error (CME) is very important for the investigation of global navigation satellite systems’ (GNSS) error and the estimation of an accurate GNSS velocity field for geodynamic applications. The commonly used spatiotemporal filtering methods normally process the evenly spaced time series without missing data. In this article, we present the variational Bayesian principal component analysis (VBPCA) to estimate and extract CME from the incomplete GNSS position time series. The VBPCA method can naturally handle missing data in the Bayesian framework and utilizes the variational expectation-maximization iterative algorithm to search each principal subspace. Moreover, it could automatically select the optimal number of principal components for data reconstruction and avoid the overfitting problem. To evaluate the performance of the VBPCA algorithm for extracting CME, 44 continuous GNSS stations located in Southern California were selected. Compared to previous approaches, VBPCA could achieve better performance with lower CME relative errors when more missing data exists. Since the first principal component (PC) extracted by VBPCA is remarkably larger than the other components, and its corresponding spatial response presents nearly uniform distribution, we only use the first PC and its eigenvector to reconstruct the CME for each station. After filtering out CME, the interstation correlation coefficients are significantly reduced from 0.43, 0.46, and 0.38 to 0.11, 0.10, and 0.08, for the north, east, and up (NEU) components, respectively. The root mean square (RMS) values of the residual time series and the colored noise amplitudes for the NEU components are also greatly suppressed, with average reductions of 27.11%, 28.15%, and 23.28% for the former, and 49.90%, 54.56%, and 49.75% for the latter. Moreover, the velocity estimates are more reliable and precise after removing CME, with average uncertainty reductions of 51.95%, 57.31%, and 49.92% for the NEU components, respectively. All these results indicate that the VBPCA method is an alternative and efficient way to extract CME from regional GNSS position time series in the presence of missing data. Further work is still required to consider the effect of formal errors on the CME extraction during the VBPCA implementation.

Site-dependent effects are now the key factors that restrict the high accuracy applications of Global Navigation Satellite System (GNSS) technology, such as deformation monitoring. To reduce the effects of non-line-of-sight (NLOS) signal and multipath, methods and models applied to both of the function model and stochastic model of least-squares (LS) have been proposed. However, the existing methods and models may not be convenient to use and not be appropriate to all GNSS satellites. In this study, the SNR features of GPS and GLONASS are analyzed first, and a refined SNR based stochastic model is proposed, in which the links between carrier phase precision and SNR observation have been reasonably established. Compared with the existing models, the refined model in this paper could be used in real-time and the carrier phase precision could be reasonably shown with the SNR data. More importantly, it is applicable to all GNSS satellite systems. Based on this model, the site observation environment can be assessed in advance to show the obstruction area. With a bridge deformation monitoring platform, the performance of this model was tested in the aspect of integer ambiguity resolution and data processing. The results show that, compared with the existing stochastic models, this model could have the highest integer ambiguity resolution success rate and the lowest noise level in the data processing time series with obvious obstruction beside the site.

With the emergence of BeiDou and Galileo as well as the modernization of GPS and GLONASS, more available satellites and signals enhance the capability of Global Navigation Satellite Systems (GNSS) to monitor the ionosphere. However, currently the International GNSS Service (IGS) Ionosphere Associate Analysis Centers (IAACs) just use GPS and GLONASS dual-frequency observations in ionosphere estimation. To better determine the global ionosphere, we used multi-frequency, multi-constellation GNSS observations and a priori International Reference Ionosphere (IRI) to model the ionosphere. The newly estimated ionosphere was represented by a spherical harmonic expansion function with degree and order of 15 in a solar-geomagnetic frame. By collecting more than 300 stations with a global distribution, we processed and analysed two years of data. The estimated ionospheric results were compared with those of IAACs, and the averaged Root Mean Squares (RMS) of Total Electron Content (TEC) differences for different solutions did not exceed 3 TEC Unit (TECU). Through validation by satellite altimetry, it was suggested that the newly established ionosphere had a higher precision than the IGS products. Moreover, compared with IGS ionospheric products, the newly established ionosphere showed a more accurate response to the ionosphere disturbances during the geomagnetic storms.

Multi-frequency and multi-GNSS integration is currently becoming an important trend in the development of satellite navigation and positioning technology. In this paper, GPS/Galileo/BeiDou (BDS) precise point positioning (PPP) with ambiguity resolution (AR) are discussed in detail. The mathematical model of triple-system PPP AR and the principle of fractional cycle bias (FCB) estimation are firstly described. With the data of 160 stations in Multi-GNSS Experiment (MGEX) from day of year (DOY) 321-350, 2018, the FCBs of the three systems are estimated and the experimental results show that the range of most GPS wide-lane (WL) FCB is within 0.1 cycles during one month, while that of Galileo WL FCB is 0.05 cycles. For BDS FCB, the classification estimation method is used to estimate the BDS FCB and divide it into GEO and non-GEO (IGSO and MEO) FCB. The variation range of BDS GEO WL FCB can reach 0.5 cycles, while BDS non-GEO WL FCB does not exceed 0.1 cycles within a month. However, the accuracies of GPS, Galileo, and BDS non-GEO narrow-lane (NL) FCB are basically the same. In addition, the number of visible satellites and Position Dilution of Precision (PDOP) values of different combined systems are analyzed and evaluated in this paper. It shows that the triple-system combination can significantly increase the number of observable satellites, optimize the spatial distribution structure of satellites, and is significantly superior to the dual-system and single-system. Finally, the positioning characteristics of single-, dual-, and triple-systems are analyzed. The results of the single station positioning experiment show that the accuracy and convergence speed of the fixed solutions for each system are better than those of the corresponding float solutions. The average root mean squares (RMSs) of the float and the fixed solution in the east and north direction for GPS/Galileo/BDS combined system are the smallest, being 0.92 cm, 0.52 cm and 0.50 cm, 0.46 cm respectively, while the accuracy of the GPS in the up direction is the highest, which is 1.44 cm and 1.27 cm, respectively. Therefore, the combined system can accelerate the convergence speed and greatly enhance the stability of the positioning results.

It is difficult to enable traditional precise point positioning (PPP) with ambiguity resolution (AR) due to fractional cycle biases (FCBs), which limit the accuracy and reliability of positioning results. The BeiDou Navigation Satellite System (BDS) has been providing continuous positioning, navigation, and timing (PNT) services in the global region since the end of 2018. The BDS constellation includes geostationary earth orbit (GEO), inclined geostationary orbit (IGSO), and medium earth orbit (MEO) satellites. However, its hybrid constellation structure and the satellite-side multipath effect have hindered the BDS PPP AR for two main reasons: (1) some receivers have half-cycle biases between GEO and non-GEO satellites, which result in the inconsistency of hardware delays for each satellite type; (2) the correction model for elevation-dependent satellite-side multipath effect is only applicable to IGSO and MEO, while in the case of GEO the effect cannot be effectively weakened or eliminated. To rectify these problems, a suitable strategy is proposed for estimating BDS FCBs, whereby the GEO FCBs and non-GEO FCBs are estimated independently. Results show that the FCBs estimated by the new strategy for GEO and non-GEO are more stable compared to the traditional strategy. The GEO wide-lane (WL) FCBs fluctuate less than 0.3 cycle in one month, except for C05, while the variation of non-GEO WL FCBs is about 0.1 cycle. In addition, compared to the traditional strategy, the fractions of GEO WL ambiguities after the removal of FCBs estimated by the new strategy can be improved noticeably from 53.5% to 78.5%, and from 71.8% to 92.3% for

Utilizing global positioning system (GPS) to determine the precise kinematic orbits for the twin satellites of the Gravity Recovery and Climate Experiment (GRACE) plays a very important role in the earth’s gravitational and other scientific fields. However, the orbit quality is highly depended on the geometry of observed GPS satellites. In this study, we propose a kinematic orbit determination method for improving the GRACE orbit quality especially when the geometry of observed GPS satellites is weak, where an appropriate random walk clock constraint between adjacent epochs is recommended according to the stability of on-board GPS receiver clocks. GRACE data over one month were adopted in the experimental validation. Results show that the proposed method could improve the root mean square (RMS) by 20−40% in radial component and 5−20% in along and cross components. For those epochs with position dilution of precision (PDOP) larger than 4, the orbits were improved by 50−70% in radial component and 17−50% in along and cross components. Meanwhile, the Allan deviation of clock estimates in the proposed method was much closer to the reported Allan deviation of GRACE on-board oscillator. All the results confirmed the improvement of the proposed method.

In order to catch up the short-term clock variation of GNSS satellites, clock corrections must be estimated and updated at a high-rate for Precise Point Positioning (PPP). This estimation is already very time-consuming for the GPS constellation only as a great number of ambiguities need to be simultaneously estimated. However, on the one hand better estimates are expected by including more stations, and on the other hand satellites from different GNSS systems must be processed integratively for a reliable multi-GNSS positioning service. To alleviate the heavy computational burden, epoch-differenced observations are always employed where ambiguities are eliminated. As the epoch-differenced method can only derive temporal clock changes which have to be aligned to the absolute clocks but always in a rather complicated way, in this paper, an efficient method for high-rate clock estimation is proposed using the concept of “carrier-range” realized by means of PPP with integer ambiguity resolution. Processing procedures for both post- and real-time processing are developed, respectively. The experimental validation shows that the computation time could be reduced to about one sixth of that of the existing methods for post-processing and less than 1 s for processing a single epoch of a network with about 200 stations in real-time mode after all ambiguities are fixed. This confirms that the proposed processing strategy will enable the high-rate clock estimation for future multi-GNSS networks in post-processing and possibly also in real-time mode.

A high-precision image-aided inertial navigation system (INS) is proposed as an alternative to the carrier-phase-based differential Global Navigation Satellite Systems (CDGNSSs) when satellite-based navigation systems are unavailable. In this paper, the image/INS integrated algorithm is modeled by a tightly-coupled iterative extended Kalman filter (IEKF). Tightly-coupled integration ensures that the integrated system is reliable, even if few known feature points (i.e., less than three) are observed in the images. A new global observability analysis of this tightly-coupled integration is presented to guarantee that the system is observable under the necessary conditions. The analysis conclusions were verified by simulations and field tests. The field tests also indicate that high-precision position (centimeter-level) and attitude (half-degree-level)-integrated solutions can be achieved in a global reference.

The site displacement due to ocean tidal loading is regarded as one of the largest uncertainties in precise geodetic positioning measurements, among which the effect of minor ocean tides (MOT), except for the 11 main tidal constituents, are sometimes neglected in routine precise global positioning system (GPS) data processing. We find that MOT can cause large vertical loading displacements with peak-to-peak variations reaching more than 8 mm at coastal/island stations. The impact of MOT on the 24-hour GPS solution is slightly larger than the magnitude of MOT loading itself, with peak-to-peak displacement variation at about 10 mm for the horizontal and 30 mm for the vertical components. We also find that the vertical velocity of all the selected stations in the Southwest Pacific was reduced by more than 10% after considering the MOT effect, while stations with weighted root mean square reduced data account for 62%, 59%, and 36% for the up, east, and north components respectively, in particular for most coastal/island stations. Furthermore, MOT correction could significantly reduce the annual signal of the global stacked east component, the near fortnightly and the long-term periodic signals in the up component. The power of some anomalous harmonics of 1.04 cycle per year is also decreased to some extent. These results further proved the benefits of MOT correction in precise GPS data processing.

In multi-GNSS cases, two types of Double Difference (DD) ambiguity could be formed including an intra-system ambiguity and an inter-system ambiguity, which are identified as the DD ambiguity between satellites from the same and from different GNSS systems, respectively. We studied the relative positioning methods using intra-system DD observations and using Un-Difference (UD) observations, and developed a frequency-free approach for fixing inter-system ambiguity based on UD observations for multi-GNSS positioning, where the inter-system phase bias is calculated with the help of a fixed Single-Difference (SD) ambiguity. The consistency between the receiver-end uncalibrated phase delays (RUPD) and the SD ambiguity were investigated and the positioning performance of this new approach was assessed. The results show that RUPD could be modeled as a constant if the receiver were tracking satellites continuously. Furthermore, compared to the method using DD observations with only an intra-system DD ambiguity fixed, the new ambiguity fixing approach has a better performance, especially in hard environments with a large cut-off angle or serve signal obstructions.

Analysis of Global Positioning System (GPS) position time series and its common mode components (CMC) is very important for the investigation of GPS technique error, the evaluation of environmental loading effects, and the estimation of a realistic and unbiased GPS velocity field for geodynamic applications. In this paper, we homogeneously processed the daily observations of 231 Crustal Movement Observation Network of China (CMONOC) Continuous GPS stations to obtain their position time series. Then, we filtered out the CMC and evaluated its effects on the periodic signals and noise for the CMONOC time series. Results show that, with CMC filtering, peaks in the stacked power spectra can be reduced at draconitic harmonics up to the 14th, supporting the point that the draconitic signal is spatially correlated. With the colored noise suppressed by CMC filtering, the velocity uncertainty estimates for both of the two subnetworks, CMONOC-I (≈16.5 years) and CMONOC-II (≈4.6 years), are reduced significantly. However, the CMONOC-II stations obtain greater reduction ratios in velocity uncertainty estimates with average values of 33%, 38%, and 54% for the north, east, and up components. These results indicate that CMC filtering can suppress the colored noise amplitudes and improve the precision of velocity estimates. Therefore, a unified, realistic, and three-dimensional CMONOC GPS velocity field estimated with the consideration of colored noise is given. Furthermore, contributions of environmental loading to the vertical CMC are also investigated and discussed. We find that the vertical CMC are reduced at 224 of the 231 CMONOC stations and 170 of them are with a root mean square (RMS) reduction ratio of CMC larger than 10%, confirming that environmental loading is one of the sources of CMC for the CMONOC height time series.

The site displacement due to diurnal and semidiurnal atmospheric tides (S1/S2) is often neglected in the routine precise GPS data processing. We recall the S1/S2 modeling method and show the magnitude of the S1/S2 tides under the Center of Mass (CM) frame. The results show that the annual amplitudes caused by both S1 and S2 tides exceed 1 mm for stations near the equator. The impact of S1/S2 on the 24-h Global Positioning System (GPS) solution is typically at the sub-mm level, and the scatter of the S1/S2 caused displacement difference increases with the decreasing latitude for northern hemisphere stations, among which the maximum Standard Deviation (STD) reaches up to 1.5 mm, 1 mm and 0.7 mm for the Up, East and North components, respectively, at low-latitude stations. We also find that 65% of the stations’ vertical velocity change caused by S1/S2 is larger than 1%, among which the maximum velocity variation rate reaches more than 40% for some coastal/island stations, while stations with the weighted root mean square reduced account for 65%, 39%, and 38% for the up, east, and north components respectively, in particular for most coastal/island stations. Furthermore, the S1/S2 correction could partly reduce the annual and the semi-annual signals of the global stacked vertical component together with the semi-annual amplitude of the east component. The power of some anomalous harmonics of 1.04 cycle per year also decreased a lot. These results further prove the benefits of S1/S2 correction in the precise GPS data processing.

Mass redistribution of the atmosphere, oceans, and terrestrial water storage generates crustal displacements which can be predicted by environmental loading models and observed by the Global Positioning System (GPS). In this paper, daily height time series of 235 GPS stations derived from a homogeneously reprocessed Crustal Movement Observation Network of China (CMONOC) and corresponding loading displacements predicted by the Deutsche GeoForschungsZentrum (GFZ) are compared to assess the effects of loading corrections on the nonlinear variations of GPS time series. Results show that the average root mean square (RMS) of vertical displacements due to atmospheric, nontidal oceanic, hydrological, and their combined effects are 3.2, 0.6, 2.7, and 4.0 mm, respectively. Vertical annual signals of loading and GPS are consistent in amplitude but different in phase systematically. The average correlation coefficient between loading and GPS height time series is 0.6. RMS of the GPS height time series are reduced by 20% on average. Moreover, an investigation of 208 CMONOC stations with observing time spans of ~4.6 years shows that environmental loading corrections lead to an overestimation of the GPS velocity uncertainty by about 1.4 times on average. Nevertheless, by using a common mode component filter through principal component analysis, the dilution of velocity precision due to environmental loading corrections can be compensated.