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The presence of non-negligible atmospheric delays and multipath errors makes it difficult for the long-range baselines to provide high-accuracy real-time kinematic (RTK) deformation monitoring services, as is the case for short baseline. Despite considerable efforts to model the effects of tropospheric errors, multipath errors remain a challenging issue in high-accuracy GNSS positioning applications. We describe a strategy for mitigating the multipath errors in long-range baselines, enabling precise RTK positioning results. First, the double-differenced ionospheric-free residuals are converted to un-differenced (UD) residuals for each satellite of the associated stations. The troposphere and multipath are the main error sources in these UD residuals. Taking advantage of the different features of UD tropospheric and multipath errors when displayed as a function of the scale factors provided by the wet mapping functions, the residual zenith tropospheric delays of each station are therefore constructed and used to resolve the practical tropospheric errors of each slant signal. The multipath errors are extracted by subtracting the computed tropospheric errors from the converted UD ionospheric-free residuals. After correcting the tropospheric and multipath errors, high-accuracy RTK positioning results can be obtained from long-range baselines. Compared with traditional methods, the proposed approach gives a 43.2% improvement in the average 3D root mean square error. Moreover, improvements of 22.2%, 52.4%, and 47.3% are achieved in the east, north, and up components for a 127 km baseline, giving a final epoch-wise positioning accuracy of 6.2 mm, 4.3 mm, and 11.8 mm, respectively. Experimental results show that the proposed strategy is an efficient and promising method in high-accuracy deformation monitoring applications for long-range baselines. [ABSTRACT FROM AUTHOR]

Evidence on the association between hypertriglyceridemic-waist phenotype (HTGW) and chronic kidney disease (CKD) is limited and inconsistent. We aimed to explore such association among 7406 Chinese aged ≥ 45 years in a cohort setting, followed by a meta-analysis. Participants were categorized into four phenotypes: NTNW (normal triglycerides and normal waist circumference), NTGW (isolated enlarged waist circumference), HTNW (isolated high triglycerides), and HTGW (high triglycerides and enlarged waist circumference). We used multivariate logistic regression to determine the association between different phenotypes and risk of CKD in the cohort study. For meta-analysis, we searched relevant studies from Embase, Medline, PubMed, and Web of Science from dataset inception up to May 1, 2021. A random-effect model was used to estimate the pooled effect and I2 statistic was applied to evaluate heterogeneity. In the cohort study, compared to the NTNW phenotype, HTGW (OR 1.82, 95% CI 1.32 to 2.51, p < 0.01) and NTGW (OR 1.48, 95% CI 1.13 to 1.94, p = 0.004) were significantly associated with CKD risk after 4 years follow-up, but not for the HTNW phenotype. The meta-analysis also showed a positive association between HTGW phenotype and CKD risk (pooled OR 1.53, 95% CI 1.31 to 1.79, I2 = 62.4%). Assessment of triglyceridemic-waist phenotypes might help to identify individuals with high-risk of developing CKD. [ABSTRACT FROM AUTHOR]

The main challenge of ambiguity resolution in precise point positioning (PPP) is that it requires 30 min or more to succeed in the first fixing of ambiguities. With the full operation of the BeiDou (BDS) satellite system in East Asia, it is worthwhile to investigate the performance of GPS + BDS PPP ambiguity resolution, especially the improvements of the initial fixing time and ambiguity-fixing rate compared to GPS-only solutions. We estimated the wide- and narrow-lane fractional-cycle biases (FCBs) for BDS with a regional network, and PPP ambiguity resolution was carried out at each station to assess the contribution of BDS. The across-satellite single-difference (ASSD) GPS + BDS combined ambiguity-fixed PPP model was used, in which the ASSD is applied within each system. We used a two-day data set from 48 stations. For kinematic PPP, the percentage of fixing within 10 min for GPS only (Model A) is 17.6 %, when adding IGSO and MEO of BDS (Model B), the percentage improves significantly to 42.8 %, whereas it is only 23.2 % if GEO is added (Model C) due to the low precision of GEO orbits. For static PPP, the fixing percentage is 32.9, 53.3 and 28.0 % for Model A, B and C, respectively. In order to overcome the limitation of the poor precision of GEO satellites, we also used a small network of 10 stations to analyze the contribution of GEO satellites to kinematic PPP. We took advantage of the fact that for stations of a small network the GEO satellites appear at almost the same direction, such that the GEO orbit error can be absorbed by its FCB estimates. The results show that the percentage of fixing improves from 39.5 to 57.7 % by adding GEO satellites. [ABSTRACT FROM AUTHOR]

Because of the unknown systematic errors and special satellite constellations in the Beidou system (BDS), it is difficult to quickly and reliably determine the ambiguity over long-range baselines in continuously operating reference station (CORS) network. This study seeks to improve the effectiveness and reliability of BDS ambiguity resolution (AR) by combining the geometry-free and ionosphere-free (GFIF) combination and multipath mitigation algorithm. The GFIF combination composed with three-frequency signals is free of distance-dependent errors and can be used to determine the narrow lane ambiguity. The presence of multipath errors means that not all ambiguities can be correctly achieved by rounding the averaged GFIF ambiguity series. A multipath model of the single-differenced (SD) GFIF combination from the previous period is established for each individual satellite. This model is subtracted from the SD GFIF combination for the current day to remove the effects of multipath errors. Using three triangle networks with lengths of approximately 120, 80 and 50 km, we demonstrate that the proposed method improves the AR performance. The ambiguity averaged first fixing time is typically less than 1801 s for inclined geosynchronous orbit (IGSO) and medium earth orbit (MEO) satellites and less than 2007 s for the $$\sim $$ 42 $$^{\circ }$$ elevation geostationary earth orbit (GEO) C02 satellite. However, it is more time consuming for the low-elevation GEO satellites C04 ( $$\sim $$ 18 $$^{\circ }$$ ) and C05 ( $$\sim $$ 28 $$^{\circ }$$ ). Kalman filtering is used to estimate the troposphere delays and two unfixed ambiguities by employing the ionosphere-free observations of all ambiguity-fixed/unfixed satellites. The experimental results show that only tens of seconds are required for AR in around 90 km baselines. [ABSTRACT FROM AUTHOR]

The difficulty to detect and repair cycle slip of carrier phase measurements is a key limit for continuously high accuracy of GNSS positioning and navigation services. We propose an automated cycle slip detection and repair method for data preprocessing of a CORS network. The method jointly uses double-differenced (DD) geometry-free (GF) combination and ionospheric-free observation corrected for the computed geometrical distance (IF-OMC) to estimate the cycle slips in dual-frequency observations. The DD GF combination, which is only affected by the ionospheric residual, can be used to detect cycle slips with high reliability except for special pairs such as (77, 60) on GPS L1/L2 frequencies. The detection principle of the IF-OMC observable is such that there is a large discontinuity related to the previous epoch when cycle slips occur at the present epoch. The disadvantages of these two combinations can be overcome employing the proposed detection method. The cycle slip pair (77, 60) has no effect on the GF combination, while a change of 14.65 m is derived from GPS L1/L2 observations using the IF-OMC algorithm. Using pre-determined station coordinates as precise values, we found that the accuracy of the DD IF-OMC combination was 18 mm for a 200-km CORS baseline. Therefore, cycle slips in dual-frequency observations can be correctly and uniquely determined using DD GF and IF-OMC equations. The proposed method was verified by adding simulated cycle slips in observations collected from the CORS network under a quiet ionosphere and shown to be effective. Moreover, the method was assessed with observations made during intense ionospheric activity, which generated extensive cycle slips. The results show that the algorithm can detect and repair all cycle slips apart from two exceptions relating to long data gaps. [ABSTRACT FROM AUTHOR]

As is true of GPS, multipath disturbance is a limiting factor for further improvements in BDS high precision positioning applications. We investigate the characteristics of multipath errors and multipath mitigation for BDS geostationary earth orbit, inclined geosynchronous orbit and medium earth orbit satellites according to their orbital repeat periods. We argue that multipath errors can be mitigated using models extracted from a previous period since there is a strong agreement correlation in the multipath errors between subsequent periods. A multipath mitigation method, which is based on observation domain filtering and considers the repeat period of every satellite independently, was applied. The application of the proposed method shows that BDS positioning precision was improved by about 56, 48, and 48 % to 1.90, 1.28, and 4.37 mm in the north, east, and up components. After resolving BDS carrier phase multipath error, the positioning precision of the combined GPS&BDS with multipath correction reached to 0.95, 0.92, and 2.31 mm in the north, east, and up components that were more precise than either the GPS or BDS system alone. The more accurate and reliable precision obtained from the combined system after applying multipath mitigation method, would greatly contribute to high-performance precision deformation monitoring and seismological studies. [ABSTRACT FROM AUTHOR]

We construct Einstein metrics of non-positive scalar curvature on certain solid torus bundles over a Fano Kähler-Einstein manifold. We show, among other things, that the negative Einstein metrics are conformally compact, and the Ricci-flat metrics have slower-than-Euclidean volume growth and quadratic curvature decay. Also we construct positive Einstein metrics on certain 3-sphere bundles over a Fano Kähler-Einstein manifold. We classify the homeomorphism and diffeomorphism types of the total spaces when the base is the complex projective plane. [ABSTRACT FROM AUTHOR]

Recently, B. Chow and R.S. Hamilton [3] introduced the cross curvature flow on 3-manifolds. In this paper, we analyze two interesting examples for this new flow. One is on a square torus bundle over a circle, and the other is on a S 2 bundle over a circle. We show that the global flow exists in both cases. However, on the former the flow diverges at time infinity, and on the latter the flow converges at time infinity. [ABSTRACT FROM AUTHOR]

Based on a global GNSS tracking network, the B1I/B3I ionospheric-free phase center offsets (PCOs) are estimated for BeiDou Inclined Geosynchronous Orbit (IGSO) and Medium Earth Orbit (MEO) satellites. Peak-to-peak variations of up to several decimeters or even meters that depend on the solar radiation pressure (SRP) model and the sun elevation angle above the orbital plane (β angle) are found in the daily x-offset estimates. Different SRP modeling has a negligible effect on the y-offset estimation, but the scatter of y-offset estimates depends on the β angle. The z-offset estimates do neither exhibit a dependence on the SRP model nor the β angle, but they have a larger scatter than x-offset and y-offset estimates. By comparing the performance of different SRP models in the estimation of BeiDou PCOs, the SRP models suitable for the estimation of BeiDou-2 and BeiDou-3 PCOs are determined to solve final PCOs. The BeiDou satellite PCO estimates are compared with the model values currently used within the International GNSS Service, the manufacturer values published by the Test and Assessment Research Center of China Satellite Navigation Office, and a set of BeiDou-3 MEO PCO estimates previously reported by the Chang'an University. Finally, it is demonstrated that the orbit quality of BeiDou IGSO/MEOs and the accuracy of station coordinates obtained from BeiDou-only precise point positioning benefit from the newly estimated BeiDou PCO model. [ABSTRACT FROM AUTHOR]

The yaw mode history of BDS-2 IGSO/MEOs since 2016 is inferred from reverse kinematic precise point positioning. Experimental results show that C06 (IGSO-1) and C14 (MEO-6) satellites have abandoned the orbit-normal (ON) attitude mode in favor of continuous yaw-steering (CYS) mode since March and September 2017, respectively. BDS C13 (IGSO-6), launched in March 2016, and C16 (IGSO-7) always adopt the CYS mode during eclipse seasons. The majority of BDS-2 IGSO/MEOs still experience attitude switches between nominal and ON mode. Most of the attitude switches from nominal to ON mode take place when the sun elevation angle above the orbital plane (β angle) decreases below 4° (β < 4 ∘) . A few switches also occur for β slightly above 4°. However, most of the attitude switches from ON to nominal mode are undertaken when β increases to above 4°, but a few switches with β just below 4° happen. The exact switch condition between the two attitude modes is presented in this study. For BDS-2 IGSO/MEOs using the CYS mode, the yaw-attitude model previously established by the Wuhan University (indicated by WHU model) can basically reproduce their yaw maneuvers. However, reverse midnight-turn maneuvers occasionally occur for C13 and C14 for β angles falling into the range (0 ∘ , 0. 14 ∘) . This discrepancy in the form of a reversal in the yaw direction during the noon-turn maneuvers is first observed for C13 and C14 when the β angle is in the range of (- 0. 14 ∘ , 0 ∘) . The mismodeling of the satellites attitudes during reverse yaw maneuvers significantly degrades the performance of BDS precise orbit determination (POD). The phase observation residuals extracted from BDS POD reach 40 cm, which thereby leads to the misidentification of a substantial number of observations around orbital midnight and noon points as outliers when the WHU model is applied in our experiments. The WHU model is modified to reproduce the reverse yaw maneuvers of satellites in the post-processing BDS POD. The derived phase residuals decrease to normal levels, and the clock solutions become smoother relative to solutions employing the WHU model. [ABSTRACT FROM AUTHOR]