An ERA5 tropospheric parameters-augmented approach for improving GNSS precise point positioning

Precise Point Positioning(PPP) technology has developed into a potent instrument for geodetic positioning, ionospheric modeling, tropospheric atmospheric parameter detection, and seismic monitoring.As atmospheric reanalysis data products’ accuracy and spatiotemporal resolution have improved recently, it has become important to apply these products to obtain high-accuracy tropospheric delay parameters, like zenith tropospheric delay(ZTD) and tropospheric horizontal gradient. These tropospheric delay parameters can be applied to PPP to reduce the convergence time and to increase the accuracy in the vertical direction of the position. The European Centre for Medium-Range Weather Forecasts Reanalysis 5(ERA5) atmospheric reanalysis data is the latest product with a high spatiotemporal resolution released by the European Center for Medium-Range Weather Forecasts(ECMWF). Only a few researches have evaluated the application of ERA5 data to Global Navigation Satellite System(GNSS)PPP. Therefore, this study compared and validated the ZTD products derived from ERA5 data using ZTD values provided by 290 global International GNSS Service(IGS) stations for 2016-2017. The results indicated a stable performance for ZTD, with annual average bias and RMS values of 0.23 cm and 1.09 cm,respectively. Further, GNSS observations for one week in each of the four seasons(spring: DOY 92-98;summer: DOY 199-205;autumn: DOY 275-281;and winter: DOY 22-28) from 34 multi-GNSS experiments(MGEX) stations distributed globally in 2016 were considered to evaluate the performance of ERA5-derived tropospheric delay products in GNSS PPP. The performance of ERA5-enhanced PPP was compared with that of the two standard GNSS PPP schemes(without estimated tropospheric horizontal gradient and with estimated tropospheric horizontal gradient). The results demonstrated that ERA5-enhanced GNSS PPP showed no significant improvement in the convergence times in both the Eastern(E) and Northern(N) directions, while the average convergence time over four weeks in the vertical(U)direction improved by 53.3% and 52.7%, respectively(in the case of pngm station). The average convergence times for each week in the U direction of the northern and southern hemisphere stations indicated a decrease of 16.3%, 12.6%, 9.6%, and 9.1%, and 16.9%, 9.6%, 8.9%, and 14.5%, respectively.Regarding positioning accuracy, ERA5-enhanced PPP showed an improvement of 13.3% and 16.2% over the two standard PPP schemes in the U direction, respectively. No significant improvement in the positioning performance was observed in both the E and N directions. Thus, this study demonstrated the potential application of the ERA5 tropospheric parameters-augmented approach to Beidou navigation and positioning.

Estimation of annual variation of water vapor in the Arctic Ocean between 80°–87°N using shipborne GPS data based on kinematic precise point positioning

The measurement of atmospheric water vapor （WV） content and variability is important for meteorological and climatological research. A technique for the remote sensing of atmospheric WV content using ground-based Global Positioning System （GPS） has become available, which can routinely achieve accuracies for integrated WV content of 1-2 kg/m2. Some experimental work has shown that the accuracy of WV measurements from a moving platform is comparable to that of （static） land-based receivers. Extending this technique into the marine environment on a moving platform would be greatly beneficial for many aspects of meteorological research, such as the calibration of satellite data, investigation of the air-sea interface, as well as forecasting and climatological studies. In this study, kinematic precise point positioning has been developed to investigate WV in the Arctic Ocean （80°-87°N） and annual variations are obtained for 2008 and 2012 that are identical to those related to the enhanced greenhouse effect.

Signal quality analysis and quality check of BDS3 Precise Point Positioning in the Arctic Ocean

This study analyzes the signal quality and the accuracy of BeiDou 3 rd generation Satellite Navigation System(BDS3) Precise Point Positioning(PPP) in the Arctic Ocean. Assessment of signal quality of BDS3 includes signal to noise ratio(SNR), multipath(MP), dilution of precision(DOP), and code-minus-carrier combination(CC). The results show that, 5 to 13 satellites are visible at any time in the Arctic Ocean area as of September 2018, which are sufficient for positioning. In the mid-latitude oceanic region and in the Arctic Ocean, the SNR is 25–52 dB Hz and the MP ranges from-2 m to 2 m. As the latitude increases, the DOP values show large variation, which may be related to the distribution of BDS satellites. The CC values of signals B1 I and BIC range from-5 m to 5 m in the mid-latitude sea area and the Arctic Ocean, which means the effect of pseudorange noise is small. Moreover, as to obtain the external precise reference value for GNSS positioning in the Arctic Ocean region is difficult, it is hard to evaluate the accuracy of positioning results. An improved isotropy-based protection level method based on Receiver Autonomous Integrity Monitoring is proposed in the paper, which adopts median filter to smooth the gross errors to assess the precision and reliability of PPP in the Arctic Ocean. At first, the improved algorithm is verified with the data from the International GNSS Service Station Tixi. Then the accuracy of BDS3 PPP in the Arctic Ocean is calculated based on the improved algorithm. Which shows that the kinematic accuracy of PPP can reach the decimeter level in both the horizontal and vertical directions, and it meets the precision requirements of maritime navigation.

Comparison of availability and reliability among different combined-GNSS/RNSS precise point positioning

With emergence of the BeiDou Navigation Satellite System(BDS), the Galileo Satellite Navigation System(Galileo), the Quasi-Zenith Satellite System(QZSS)and the restoration of the Global Navigation Satellite System(GLONASS), the single Global Positioning System(GPS) has been gradually expanded into multiple global and regional navigation satellite systems(multi-GNSS/RNSS). In view of differences in these 5 systems, a consolidated multi-GNSS/RNSS precise point positioning(PPP) observation model is deduced in this contribution. In addition, the performance evaluation of PPP for multi-GNSS/RNSS is conducted using a large number of the multi-GNSS experiment(MGEX) station datasets. Experimental results show that multi-GNSS/RNSS can guarantee plenty of visible satellites effectively. Compared with single-system GPS, PDOP, HDOP, and VDOP values of the multi-GNSS/RNSS are improved by 46.8%, 46.5% and 46.3%, respectively. As for convergence time, the static and kinematic PPP of multi-GNSS/RNSS are superior to that of the single-system GPS, whose reliability, availability, and stability drop sharply with the increasing elevation cutoff. At satellite elevation cutoff of 40 °, the single-system GPS fails to carry out continuous positioning because of the insufficient visible satellites, while the multi-GNSS/RNSS PPP can still get positioning solutions with relatively high accuracy, especially in the horizontal direction.

Impact of Tropospheric Delay Gradients on Total Tropospheric Delay and Precise Point Positioning

GPS signals are electromagnetic waves that are affected by the Earth’s atmosphere. The Earth’s atmosphere can be categorized, according to its effect on GPS signals, into the ionosphere (ionospheric delay) and neutral atmosphere (tropospheric delay). The first-order ionospheric delay can be eliminated by linear combination of GPS observables on different frequencies. However, tropospheric delay cannot be eliminated because it is frequency-independent. The total tropospheric delay can be divided into three components. The first is the dry component, the second part is the wet component, and the third part is the horizontal gradients which account for the azimuthal dependence of tropospheric delay. In this paper, the effect of modeling tropospheric gradients on the estimation of the total tropospheric delay and station position is investigated. Long session, one month during January 2015, of GPS data is collected from ten randomly selected globally distributed IGS stations. Two cases are studied: the first case, the coordinates of stations are kept fixed to their actual values and the tropospheric delay is estimated twice, with and without tropospheric gradients. In the second case, the station position is estimated along with the total tropospheric delay with and without tropospheric gradients. It is shown that the average bias of the estimated total tropospheric delay when neglecting tropospheric gradients ranges from ?1.72 mm to 2.14 mm while the average bias when estimating gradients are ?0.898 mm to 1.92 mm which means that the bias is reduced by about 30%. In addition, the average standard deviation of the bias is 4.26 mm compared with 4.52 mm which means that the standard deviation is improved by about 6%.

Application of precise point positioning technology in airborne gravity measurement

The precise point positioning （PPP） technology is applied to an airborne gravity survey. By analyzing the advantages and disadvantages of several velocity and acceleration measurement methods and in combination with an actual marine gravity survey, the position difference method is confirmed to be a useful survey method for velocity and acceleration. Finally, the practicability of using PPP in airborne marine gravity survey is verified by measured data.

Performance analysis of real-time and post-mission kinematic precise point positioning in marine environments

This article focuses on the performance analysis of both real-time and post-mission kinematic precise point positioning(PPP)in challenging marine environments.For this purpose,a real dynamic experiment lasting 6 h was carried out on a lake dam in?orum City of Turkey.While the kinematic test was continuing,the real-time PPP coordinates were obtained for each measurement epoch with a commercial real-time PPP(RT-PPP)service,namely the Trimble Center Point RTX.Then the post-mission PPP(PM-PPP)coordinates were calculated by using Multi-GNSS data and the Multi-GNSS Experiment(MGEX)precise products.The kinematic RT-PPP and PM-PPP results showed that the PPP coordinates were consistent with the relative solution at centimetre and decimetre level in horizontal and height components,respectively.This study implies that PPP technique is a powerful tool for highly accurate positioning in both real-time and post-mission modes,even for dynamic applications in harsh environments.

Modeling and Prediction of Inter-System Bias for GPS/BDS-2/BDS-3 Combined Precision Point Positioning

The combination of Precision Point Positioning(PPP)with Multi-Global Navigation Satellite System(MultiGNSS),called MGPPP,can improve the positioning precision and shorten the convergence time more effectively than the combination of PPP with only the BeiDou Navigation Satellite System(BDS).However,the Inter-System Bias(ISB)measurement of Multi-GNSS,including the time system offset,the coordinate system difference,and the inter-system hardware delay bias,must be considered for Multi-GNSS data fusion processing.The detected ISB can be well modeled and predicted by using a quadratic model(QM),an autoregressive integrated moving average model(ARIMA),as well as the sliding window strategy(SW).In this study,the experimental results indicate that there is no apparent difference in the ISB between BDS-2 and BDS-3 observations if B1I/B3I signals are used.However,an obvious difference in ISB can be found between BDS-2 and BDS-3 observations if B1I/B3I and B1C/B2a signals are used.Meanwhile,the precision of the Predicted ISB(PISB)on the next day of all stations is about 0.1−0.6 ns.Besides,to effectively utilize the PISB,a new strategy for predicting the PISB for MGPPP is proposed.In the proposed strategy,the PISB is used by adding two virtual observation equations,and an adaptive factor is adopted to balance the contribution of the Observed ISB(OISB)and the PISB to the final estimations of ISB.To validate the effectiveness of the proposed method,some experimental schemes are designed and tested under different satellite availability conditions.The results indicate that in open sky environment,the selective utilization of the PISB achieves almost the same positioning precision of MGPPP as the direct utilization of the PISB,but the convergence time of MGPPP is reduced by 7.1%at most in the north(N),east(E),and up(U)components.In the blocked sky environment,the selective utilization of the PISB contributes to more significant improvement of the positioning precision and convergence time than that in the open sky environment.Compared with the direct utilization of the PISB,the selective utilization of the PISB improves the positioning precision and convergence time by 6.7%and 12.7%at most in the N,E,and U components,respectively.

Genes for the high life： New genetic variants point to positive selection for high altitude hypoxia in Tibetans

People living on the high plateaus of the world have long fascinated biological anthropologists and geneticists because they live in ＂thin air＂ and epitomize an extreme of human biological adaptation.

POSITIVE SOLUTIONS TO AN m-POINT BOUNDARY VALUE PROBLEM

The existence of positive solutions for second order m-point boundary value problemx″-q(t)f(x,x′)x′=0, x(0)= m i=2 b ix(ξ i),x′(1)=αx′(0)are investigated,where ξ i,b i and α are constants satisfying 0=ξ 1<ξ 2<...<ξ m-1 <ξ m=1,b i≥0 for i=2,...,m with β∶= m i=2 b i∈[0,1), and α>1. Our approach is based on the fixed point theorem in cones.

EXISTENCE OF POSITIVE FIXED POINTS FOR SEMIDIFFERENTIABLE SEMICOMPACT 1-SET-CONTRACTIONS

This paper obtains some fixed point theorems of semidifferentiable semicompact 1-set-contraction maps, which extend some known results in [1, 2, 4, 5, 7].

Effect of loading point position on fracture mode of rock

Anti symmetric four point bending specimen with different loading point positions was used to study effect of loading point position on fracture mode of rock in order to explore a feasible method for achieving Mode Ⅱ fracture and determining Mode Ⅱ fracture toughness of rock, K ⅡC . Numerical and experimental results show that the distance between the inner and outer loading points, L 1+ L 2, has a great influence on stresses at notch tip and fracture mode. When L 1+ L 2>0.5 L or 0.1 L < L 1+ L 2<0.5 L , maximum principal stress σ 1 exceeds the tensile strength σ t. The ratio of τ max / σ 1 is relatively low or high and thus Mode Ⅰ or mixed mode fracture occurs. When L 1+ L 2< 0.1 L , σ 1 is smaller than σ t and the ratio of τ max / σ 1 is much higher, which facilitates the occurrence of Mode Ⅱ fracture.

The mathematical weighting of GNSS observations based on different types of receivers/antennas and environmental conditions

Stochastic models play an important role in achieving high accuracy in positioning,the ideal estimator in the least-squares(LS)can be obtained only by using the suitable stochastic model.This study investigates the role of variance component estimation(VCE)in the LS method for Precise Point Positioning(PPP).This estimation is performed by considering the ionospheric-free(IF)functional model for code and the phase observation of Global Positioning System(GPS).The strategy for estimating the accuracy of these observations was evaluated to check the effect of the stochastic model in four modes:a)antenna type,b)receiver type,c)the tropospheric effect,and d)the ionosphere effect.The results show that using empirical variance for code and phase observations in some cases caused erroneous estimation of unknown components in the PPP model.This is because a constant empirical variance may not be suitable for various receivers and antennas under different conditions.Coordinates were compared in two cases using the stochastic model of nominal weight and weight estimated by LS-VCE.The position error difference for the east-west,north-south,and height components was 1.5 cm,4 mm,and 1.8 cm,respectively.Therefore,weight estimation with LS-VCE can provide more appropriate results.Eventually,the convergence time based on four elevation-dependent models was evaluated using nominal weight and LS-VCE weight.According to the results,the LS-VCE has a higher convergence rate than the nominal weight.The weight estimation using LS-VCE improves the convergence time in four elevation-dependent models by 11,13,12,and 9 min,respectively.

Obtaining accurate measurements of the sea surface height from a GPS buoy

A dedicated GPS buoy is designed for calibration and validation(Cal/Val)of satellite altimeters since 2014.In order to evaluate the accuracy of the sea surface height(SSH)measured by the GPS buoy,twelve campaigns have been done within China sea area between 2014 and 2021.In six of these campaigns,two static Global Navigation Satellite System stations were installed at distances of<1 km and 19 km from the buoy to assess how the baseline length influenced the derived SSH from the buoy solutions.The GPS buoy data was processed using the GAMIT/GLOBK software+TRACK module and CSRS-PPP tool to achieve the SSH.The SSH was compared with conventionally tide gauge(TG)data to evaluate the accuracy of the buoy with the standard deviation of the height element.The results showed that the difference in the standard deviation of the SSH from the buoy and the TG was less than 16 mm.The SSHs processed with different ephemeris(Ultra-Rapid,Rapid,Final)were not significantly different.When the baseline length was 19 km,the SSH solution of the GPS buoy performed well,with standard bias of less than 26 mm between the heights measured by the buoy and TG,meaning that the buoy could be used for Cal/Val of altimeters.The bias between the Canadian Spatial Reference System-precise point positioning tool and the TRACK varied a lot,and some of them were over 130 mm.This deemed too high to be useful for Cal/Val of satellite altimeters.Moreover,the GPS buoy solutions processed by GAMIT/GLOBK software+TRACK module were used for in-orbit Cal/Val of HY-2B/C satellites in ten campaigns.The SSH and significant wave height of the altimeters showed good agreements with the GPS buoy solutions.

GNSS rapid precise point positioning enhanced by low Earth orbit satellites

The Low Earth Orbit(LEO)satellites can be used to efectively speed up Precise Point Positioning(PPP)convergence.In this study,180 LEO satellites with a global distribution are simulated to evaluate their contribution to the PPP convergence.LEO satellites can give more redundant observations and improve satellite geometric distributions,particularly for a single Global Navigation Satellite System(GNSS).The convergence speed of the PPP foat solution using the Global Positioning System(GPS,G)or BeiDou Navigation Satellite System(BDS,C)single system as well as the G/C/Galileo navigation satellite system(Galileo,E)/GLObal NAvigation Satellite System(GLONASS,R)combined system with LEO satellites added is improved by 90.0%,91.0%,and 90.7%,respectively,with respect to the system without LEO satellites added.We introduced LEO observations to assist GNSS in PPP-AR(Ambiguity Resolution)and PPP-RTK(Real Time Kinematic).The success fx rate of a single system is signifcantly improved,and the Time-To-First-Fix(TTFF)of G and G/C/E is reduced by 86.4%and 82.8%,respectively,for the PPP-AR solution.We analyzed the positioning performance of LEO satellite assisted G/C/E PPP-RTK in the reference networks of diferent scales,namely diferent atmospheric delay interpolation accuracies.The success fx rate of the G/C/E combined system is improved from 86.8 to 94.9%,and the TTFF is reduced by 36.8%,with the addition of LEO satellites in the 57 km reference network.In the 110 km reference network,the success fx rate of the G/C/E combined system is improved from 64.0 to 88.6%,and the TTFF is reduced by 32.1%.GNSS PPP-RTK with adding the LEO satellites in the reference networks of diferent scales shows obvious improvement because the atmospheric correlation decreases with increasing distance from the reference networks.

The Characteristics of Glued Tensile Shear Strength Constituted of Wood Cut by CO_(2) Laser

The performance of engineered wood products is highly associated with proper bonding and an efficient cutting method.This paper investigates the influence of CO_(2) laser cutting on the wetting properties,the modified che-mical component of the laser-cut surface,and the strength and adhesive penetration near the bondline.Beech-wood is cut by the laser with varying processing parameters,cutting speeds,gas pressures,and focal point positions.The laser-cut samples were divided into two groups,sanded and non-sanded samples.Polyvinyl acetate adhesive(PVAc)was used to bond the groups of laser-cut samples.After assembly with cold pressing,the tensile shear test was carried out.Numerical modelling was carried out to determine the partial elongation and shear strain of the glue line.Based on this,the shear modulus and linear elasticity of the glue line were estimated.Scan-ning electron microscopy was used to assess the adhesive penetration into the porosity structure of the laser-cut samples,and the depth of the heat-affected zone.The laser-cut surface was analysed by Fourier transform infrared spectroscopy.The wetting properties of the laser-cut surface were investigated by using a contact angle goni-ometer.The numerical model of the strain-stress curve confirmed the experimental model.The highest modulus of the linear elasticity of the glue in the numerical calculation belongs to the joint containing laser-cut samples at a gas pressure of 21(bar).The penetration depth of PVAc adhesive into the porosity structure of the laser-cut sam-ples was similar to that of sawn samples.The deepest heat-affected zone in the laser-cut samples was 150µm.A PVAc drop disappeared immediately on the laser-cut surface without sanding,but gradually on the sanded surface.In contrast,the drop on the sawn surface remained with an angle of 32°–48°.The degradation of hemi-cellulose and lignin was proven by the lower intensity of the C=O and C-O Bonds,compared to the sawn surface.

Status of UnDifferenced and Uncombined GNSS Data Processing Activities in China

With the continued development of multiple Global Navigation Satellite Systems(GNSS)and the emergence of various frequencies,UnDifferenced and UnCombined(UDUC)data processing has become an increasingly attractive option.In this contribution,we provide an overview of the current status of UDUC GNSS data processing activities in China.These activities encompass the formulation of Precise Point Positioning(PPP)models and PPP-Real-Time Kinematic(PPP-RTK)models for processing single-station and multi-station GNSS data,respectively.Regarding single-station data processing,we discuss the advancements in PPP models,particularly the extension from a single system to multiple systems,and from dual frequencies to single and multiple frequencies.Additionally,we introduce the modified PPP model,which accounts for the time variation of receiver code biases,a departure from the conventional PPP model that typically assumes these biases to be time-constant.In the realm of multi-station PPP-RTK data processing,we introduce the ionosphere-weighted PPP-RTK model,which enhances the model strength by considering the spatial correlation of ionospheric delays.We also review the phase-only PPP-RTK model,designed to mitigate the impact of unmodelled code-related errors.Furthermore,we explore GLONASS PPP-RTK,achieved through the application of the integer-estimable model.For large-scale network data processing,we introduce the all-in-view PPP-RTK model,which alleviates the strict common-view requirement at all receivers.Moreover,we present the decentralized PPP-RTK data processing strategy,designed to improve computational efficiency.Overall,this work highlights the various advancements in UDUC GNSS data processing,providing insights into the state-of-the-art techniques employed in China to achieve precise GNSS applications.

On the Asymptotic Stability of Discrete Crocodilians Model

The sex ratio of crocodiles is strongly biased towards females, often as high as 10 females to 1 male. In crocodilians, the temperature of egg incubation is the environmental factor determining sex. If the temperature is low, around 30˚C, the hatchlings are all females. Higher temperature, around 34˚C, hatch all males. This study was made to consider the asymptotic stability of a positive equilibrium point in a nonlinear discrete model of the basic nesting population model, which is described in three-region depending on the temperature of egg incubation. This model is based on key life-historical data and Murray’s research. To study above, we have applied the classical linearization method and P. Cull’s method and moreover, we employ non-standard discretization methods for later our Equations (6)-(8) and (15).

Integrity monitoring of fixed ambiguity Precise Point Positioning(PPP)solutions

Traditional positioning methods,such as conventional Real Time Kinematic(cRTK)rely upon local reference networks to enable users to achieve high-accuracy positioning.The need for such relatively dense networks has significant cost implications.Precise Point Positioning(PPP)on the other hand is a positioning method capable of centimeter-level positioning without the need for such local networks,hence providing significant cost benefits especially in remote areas.This paper presents the state-of-the-art PPP method using both GPS and GLONASS measurements to estimate the float position solution before attempting to resolve GPS integer ambiguities.Integrity monitoring is carried out using the Imperial College Carrier-phase Receiver Autonomous Integrity Monitoring method.A new method to detect and exclude GPS base-satellite failures is developed.A base-satellite is a satellite whose measurements are differenced from other satellite’s measurements when using between-satellite-differenced measurements to estimate position.The failure detection and exclusion methods are tested using static GNSS data recorded by International GNSS Service stations both in static and dynamic processing modes.The results show that failure detection can be achieved in all cases tested and failure exclusion can be achieved for static cases.In the kinematic processing cases,failure exclusion is more difficult because the higher noise in the measurement residuals increases the difficulty to distinguish between failures associated with the base-satellite and other satellites.

ON THE EXISTENCE OF POSITIVE SOLUTIONS TO SECOND ORDER PERIODIC BVPS

The existence of positive solutions to second-order periodic BVPs-u'+Mu =j(t, u),t(0) = u(2π),u'(0) = '(2π) and u'+ Mu = I(t, u), u(0) = u(2π), u'(0) = u'(2π)is proved by a simple appliCation of a Fixed point Theorem in cones due to Krasnoselskii.