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].
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 appliCati...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.展开更多
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.
This paper deals with the existence of triple positive solutions for the 1-dimensional equation of Laplace-type （φ（x′（t）））′＋q（t）f（t,x（t）,x′（t））=0,t∈（0,1）,subject to the following boundary condit...This paper deals with the existence of triple positive solutions for the 1-dimensional equation of Laplace-type （φ（x′（t）））′＋q（t）f（t,x（t）,x′（t））=0,t∈（0,1）,subject to the following boundary condition：a1φ（x（0））-a2φ（x＇（0））=0,a3φ（x（1））＋a4φ（x＇（1））=0,where φ is an odd increasing homogeneous homeomorphism. By using a new fixed point theorem, sufficient conditions are obtained that guarantee the existence of at least three positive solu- tions. The emphasis here is that the nonlinear term f is involved with the first order derivative explicitly.展开更多
We establish the existence of positive periodic solutions of the second-order singular coupled systems{x′′＋ p_1（t）x′＋ q_1（t）x = f_1（t, y（t）） ＋ c_1（t）,y′′＋ p_2（t）y′＋ q_2（t）y = f_2（t, x（t）） ...We establish the existence of positive periodic solutions of the second-order singular coupled systems{x′′＋ p_1（t）x′＋ q_1（t）x = f_1（t, y（t）） ＋ c_1（t）,y′′＋ p_2（t）y′＋ q_2（t）y = f_2（t, x（t）） ＋ c_2（t）,where pi, qi, ci ∈ C（R/T Z; R）, i = 1, 2; f_1, f_2 ∈ C（R/T Z ×（0, ∞）, R） and may be singular near the zero. The proof relies on Schauder＇s fixed point theorem and anti-maximum principle.Our main results generalize and improve those available in the literature.展开更多
Currently,the BeiDou⁃3(BDS⁃3)precise point positioning(PPP)service(PPP⁃B2b)mostly employs the ionosphere⁃free(IF)combination model for precise timing,which tends to amplify the noise in observation values.To address t...Currently,the BeiDou⁃3(BDS⁃3)precise point positioning(PPP)service(PPP⁃B2b)mostly employs the ionosphere⁃free(IF)combination model for precise timing,which tends to amplify the noise in observation values.To address this issue,this paper proposes a real⁃time BDS⁃3 precise unidirectional timing model based on uncombined(UC)observations using the BDS⁃3 PPP⁃B2b service.This model resolves the challenge of the amplified observation noise inherent in the IF combination model.The experiment involved selecting eight global navigation satellite system(GNSS)observation stations within China and collecting continuous observation data for 15 d.A comparative analy⁃sis with the traditional dual⁃frequency IF combination PPP timing model showed that the BDS⁃3 UC PPP timing based on the BDS⁃3 PPP⁃B2b service can achieve a timing preci⁃sion of 0.5 ns.In addition,it was found that due to global positioning system(GPS)satellite clock products in the BDS⁃3 PPP⁃B2b service not being unified to the standard time,the GPS IF PPP timing method based on the BDS⁃3 PPP⁃B2b service is not recommended for precise timing.In summary,the BDS⁃3 UC PPP timing model proposed in this paper is suitable for precise timing,providing observa⁃tion values with smaller noise,and its timing accuracy is comparable to that of the BDS⁃3 IF PPP,with slightly better frequency stability.展开更多
Precise coseismic displacements in earthquake/tsunamic early warning are necessary to characterize earthquakes in real time in order to enable decision-makers to issue alerts for public safety.Real-time global navigat...Precise coseismic displacements in earthquake/tsunamic early warning are necessary to characterize earthquakes in real time in order to enable decision-makers to issue alerts for public safety.Real-time global navigation satellite systems(GNSSs)have been a valuable tool in monitoring seismic motions,allowing permanent displacement computation to be unambiguously achieved.As a valuable tool presented to the seismic commu nity,the GSeisRT software developed by Wuhan University(China)can realize multi-GNSS precise point positioning with ambiguity resolution(PPP-AR)and achieve centimeterlevel to sub-centimeter-level precision in real time.While the stable maintenance of a global precise point positioning(PPP)service is challenging,this software is capable of estimating satellite clocks and phase biases in real time using a regional GNSS network.This capability makes GSeisRT especially suitable for proprietary GNSS networks and,more importantly,the highest possible positio ning precision and reliability can be obtained.According to real-time results from the Network of the Americas,the mean root mean square(RMS)errors of kinematic PPP-AR over a 24 h span are as low as 1.2,1.3,and 3.0 cm in the east,north,and up components,respectively.Within the few minutes that span a typical seismic event,a horizontal displacement precision of 4 mm can be achieved.The positioning precision of the GSeisRT regional PPP/PPP-AR is 30%-40%higher than that of the global PPP/PPP-AR.Since 2019,GSeisRT has successfully recorded the static,dynamic,and peak ground displacements for the 2020Oaxaca,Mexico moment magnitude(Mw)7.4 event;the 2020 Lone Pine,California Mw 5.8 event;and the 2021 Qinghai,China Mw 7.3 event in real time.The resulting immediate magnitude estimates have an error of around 0.1 only.The GSeisRT software is open to the scientific community and has been applied by the China Earthquake Ne tworks Center,the EarthScope Consortium of the United States,the National Seismological Center of Chile,Institute of Geological and Nuclear Sciences Limited(GNS Science Te PūAo)of New Zealand,and the Geospatial Information Agency of Indonesia.展开更多
Zenith Tropospheric Delay(ZTD)is an important factor that restricts the high-precision positioning of global navigation satellite system(GNSS),and it is of great significance in establishing a real-time and highprecis...Zenith Tropospheric Delay(ZTD)is an important factor that restricts the high-precision positioning of global navigation satellite system(GNSS),and it is of great significance in establishing a real-time and highprecision ZTD model.However,existing ZTD models only consider the impact of linear terms on ZTD estimation,whereas the nonlinear factors have rarely been investigated before and thus become the focus of this study.A real-time and high-precision ZTD model for large height difference area is proposed by considering the linear and nonlinear characteristics of ZTD spatiotemporal variations and is called the realtime linear and nonlinearity ZTD(RLNZ)model.This model uses the ZTD estimated from the Global Pressure and Temperature 3(GPT3)model as the initial value.The linear impacts of periodic term and height on the estimation of ZTD difference between GNSS and GPT3 model are first considered.In addition,nonlinear factors such as geographical location and time are further used to fit the remaining nonlinear ZTD residuals using the general regression neural network method.Finally,the RLNZ-derived ZTD is obtained at an arbitrary location.The western United States,with height difference ranging from-500 to 4000 m,is selected,and the hourly ZTD of 484 GNSS stations provided by the Nevada Geodetic Laboratory(NGL)and the data of 9 radiosonde(RS)stations in the year 2021 are used.Experiment results show that a better performance of ZTD estimation can be retrieved from the proposed RLNZ model when compared with the GPT3 model.Statistical results show the averaged root mean square(RMS),Bias,and mean absolute error(MAE)of ZTD from GPT3 and RLNZ models are 33.7/0.8/25.7 mm and 22.6/0.1/17.4 mm,respectively.The average improvement rate of the RLNZ model is 33% when compared to the GPT3 model.Finally,the application of the proposed RLNZ model in simulated real-time Precise Point Positioning(PPP)indicates that the accuracy of PPP in N,E and U components is improved by 8%,2%,and 6% when compared with that from the GPT3-based PPP.Meanwhile,the convergence time in N and U components is improved by 23% and 7%,respectively.Such results verify the superiority of the proposed RLNZ model in retrieving realtime ZTD maps for GNSS positioning and navigation applications.展开更多
An integrity monitoring framework is proposed to ensure the quality of the real-time Precise Point Positioning(PPP)correction data at the service end.The key contributions are designing quantitative metrics to charact...An integrity monitoring framework is proposed to ensure the quality of the real-time Precise Point Positioning(PPP)correction data at the service end.The key contributions are designing quantitative metrics to characterize the integrity status of the precise Orbit,Clock(OC)and Code Bias(OCB)corrections,and deriving the corresponding algorithms to detect and exclude anomalies,and to evaluate the real-time accuracy levels of the OCB.Compared to many prior works whose interests focused on analyzing and improving the averaged long-term accuracy,this work is established from integrity perspective.In particular,a two-layer fault detection and identification approach is developed to reduce the miss detection and false alert probabilities.The test statistics are constructed based on the raw observations from a network of worldwide sparsely distributed monitor stations.In addition,a realistic data-driven model is established to compute the Quality Indicators(QI)for healthy OCB products.The proposed scheme is validated respectively for multi-constellation OC and code bias,using historical correction data.The results suggest that the detection algorithms can effectively identify and alert the faults,so that the remaining correction errors approximate well to Gaussian distributions.Moreover,the computed QI are shown to be consistent with the truth error variations in real time.Most importantly,the position domain verification shows noticeable positioning accuracy and robustness improvements under both nominal and faulty conditions of the OCB correction data.展开更多
In order to solve the problem that the star point positioning accuracy of the star sensor in near space is decreased due to atmospheric background stray light and rapid maneuvering of platform, this paper proposes a s...In order to solve the problem that the star point positioning accuracy of the star sensor in near space is decreased due to atmospheric background stray light and rapid maneuvering of platform, this paper proposes a star point positioning algorithm based on the capsule network whose input and output are both vectors. First, a PCTL (Probability-Coordinate Transformation Layer) is designed to represent the mapping relationship between the probability output of the capsule network and the star point sub-pixel coordinates. Then, Coordconv Layer is introduced to implement explicit encoding of space information and the probability is used as the centroid weight to achieve the conversion between probability and star point sub-pixel coordinates, which improves the network’s ability to perceive star point positions. Finally, based on the dynamic imaging principle of star sensors and the characteristics of near-space environment, a star map dataset for algorithm training and testing is constructed. The simulation results show that the proposed algorithm reduces the MAE (Mean Absolute Error) and RMSE (Root Mean Square Error) of the star point positioning by 36.1% and 41.7% respectively compared with the traditional algorithm. The research results can provide important theory and technical support for the scheme design, index demonstration, test and evaluation of large dynamic star sensors in near space.展开更多
This study explores the use of the Global Navigation Satellite System(GNSS)precise point positioning(PPP)technology to determine the natural vibration periods of towering structures through simulations and field testi...This study explores the use of the Global Navigation Satellite System(GNSS)precise point positioning(PPP)technology to determine the natural vibration periods of towering structures through simulations and field testing.During the simulation phase,a GNSS receiver captured vi-bration waveforms generated by a single-axis motion simulator based on preset signal parameters,analyzing how different satellite system configurations affect the efficiency of extracting vibration parameters.Subsequently,field tests were conducted on a high-rise steel singletube tower.The results indicate that in the simulation environment,no matter the PPP positioning data under single GPS or multisystem combination,the vibration frequency of singleaxis motion simulator can be accurately extracted after frequency do-main analysis,with multisystem setups providing more precise amplitude parameters.In the field test,the natural vibration periods of the main vibration modes of high-rise steel single-tube tower measured by PPP technology closely match the results of the first two modes derived from finite element analysis.The first mode period calculated by the em-pirical formula is approximately 6%higher than those determined through finite element analysis and PPP.This study demonstrates the potential of PPP for structural vibration analysis,offering significant benefits for assessing dynamic responses and monitoring the health of towering structures.展开更多
The application of Low Earth Orbit(LEO)satellite navigation can enhance geometric structure,increase observations and contribute to navigation and positioning.To improve the performance of the navigation constellation...The application of Low Earth Orbit(LEO)satellite navigation can enhance geometric structure,increase observations and contribute to navigation and positioning.To improve the performance of the navigation constellation in China,this study proposes an optimized method of LEO-enhanced navigation constellation for BDS based on Bayesian optimization algorithm.In this paper,four different optimal LEO constellation configurations are designed,and their enhancements to BDS3 navigation performance are analyzed,including Geometric Dilution of Precision(GDOP),the numbers of visible satellites,and the rapid convergence of precision point positioning(PPP).Additionally,the enhancement advantages in China compared to other regions are further discussed.The results demonstrate that regional enhanced constellations with 70,72,80,and 81 satellites at an altitude of 1000 km can significantly improve the navigation performance of the navigation constellation.Globally,the addition of optimized LEO constellations has reduced the hybrid constellation GDOP by 19.0%,18.3%,19.9%,and 20.3%.Similar results can be obtained using the genetic algorithm(GA),but the computational efficiency of Bayesian optimization algorithm is 53.9%higher than that of the genetic algorithm.The number of visible satellites of enhanced constellations in China has increased by more than four on average,which is better than that in other regions.In the PPP experiment,the convergence time of the stations in China and other regions is shortened by 83.0%and 76.2%,respectively,and the navigation performance of hybrid constellations in China is better.展开更多
The mathematical method of ZTD(zenith tropospheric delay)spatial prediction is important for precise ZTD derivation and real-time precise point positioning(PPP)augmentation.This paper analyses the performance of the p...The mathematical method of ZTD(zenith tropospheric delay)spatial prediction is important for precise ZTD derivation and real-time precise point positioning(PPP)augmentation.This paper analyses the performance of the popular optimal function coefficient(OFC),sphere cap harmonic analysis(SCHA),kriging and inverse distance weighting(IDW)interpolation in ZTD spatial prediction and Beidou satellite navigation system(BDS)-PPP augmentation over China.For ZTD spatial prediction,the average time consumption of the OFC,kriging,and IDW methods is less than 0.1 s,which is significantly better than that of the SCHA method(63.157 s).The overall ZTD precision of the OFC is 3.44 cm,which outperforms those of the SCHA(9.65 cm),Kriging(10.6 cm),and IDW(11.8 cm)methods.We confirmed that the low performance of kriging and IDW is caused by their weakness in modelling ZTD variation in the vertical direction.To mitigate such deficiencies,an elevation normalization factor(ENF)is introduced into the kriging and IDW models(kriging-ENF and IDW-ENF).The overall ZTD spatial prediction accuracies of IDW-ENF and kriging-ENF are 2.80 cm and 2.01 cm,respectively,which are both superior to those of the OFC and the widely used empirical model GPT3(4.92 cm).For BDS-PPP enhancement,the ZTD provided by the kriging-ENF,IDW-ENF and OFC as prior constraints can effectively reduce the convergence time.Compared with unconstrained BDS-PPP,our proposed kriging-ENF outperforms IDW-ENF and OFC by reducing the horizontal and vertical convergence times by approximately 13.2%and 5.8%in Ningxia and 30.4%and 7.84%in Guangdong,respectively.These results indicate that kriging-ENF is a promising method for ZTD spatial prediction and BDS-PPP enhancement over China.展开更多
Beidou-3 navigation satellite system(BDS-3)initiated a real-time service for precise point positioning(PPP)using the B2b signal,mainly for users in China and surrounding areas.In this paper,the performance of PPP-B2b ...Beidou-3 navigation satellite system(BDS-3)initiated a real-time service for precise point positioning(PPP)using the B2b signal,mainly for users in China and surrounding areas.In this paper,the performance of PPP-B2b service is experimentally analyzed first.Then,the ionosphere-free model is established.In order to solve the problem of slow convergence for traditional PPP,an adaptive robust extend Kalman filter(AREKF)algorithm is developed.Unlike the error compensation models,it reflects the noise information in real time by adjusting the covariance matrix of the measurements and the weight matrix of the state vector.The experimental results are analyzed last.Evaluation results indicate that the corrections provided by PPP-B2b can significantly reduce the discontinuous error of the orbits and clock offsets caused by broadcast ephemeris updating.Positioning results confirm that AREKF outperforms EKF both in static and kinematic modes.Around 20%improvement in accuracy and 25%improvement in convergence speed are achieved,making it valuable for PPP processing.展开更多
Crustal deformation can provide constraints for studying earthquake rupture and shock wave transmission for the Mw9.0 eastern Japan great earthquake. Using the single- epoch precise point positioning （PPP） method an...Crustal deformation can provide constraints for studying earthquake rupture and shock wave transmission for the Mw9.0 eastern Japan great earthquake. Using the single- epoch precise point positioning （PPP） method and the appropriate positioning flow, we process GPS data from six IGS （International GNSS Service） sites （e.g., MIZU, TSK2, USUD, MTKA, AIRA and KSMV） located in Japan and obtain the positioning results with centimeter scale precision. The displacement time series of the six sites are analyzed using the least squares spectral analysis method to estimate deformations caused by the Mw9.0 mainshock and the Mw7.9 aftershock, and the cumulative displacements after 1 day. Mainshock displacements at station MIZU, the nearest site to the mainshock in the North （N）, East （E）, and Up （U） directions, are -1.202 m, 2.180 m and -0.104 m, respectively, and the cumulative deformations after 1 day are -1.117 m, 2.071 m and -0.072 m, respectively. The displacements at station KSMV, the nearest site to the Mw7.9 aftershock in the N, E and U directions, are -0.032 m, 0.742 m and -0.345 m, respectively. The other sites obviously experienced eastern movements and subsidence. The deformation vectors indicate that the horizontal displacements caused by the earthquake point to the epicenter and rupture. Elastic bounds evidently took place at all sites. The results indicate that the crustal movements and earthquake were part of a megathrust caused by the Pacific Plate sinking under the North American Plate to the northeast of Japan island arc.展开更多
Most GPS positioning errors can be eliminated or removed by the differential technique or the modeling method,but the multipath effect is a special kind of system or gross error,so it is difficult to be simulated or e...Most GPS positioning errors can be eliminated or removed by the differential technique or the modeling method,but the multipath effect is a special kind of system or gross error,so it is difficult to be simulated or eliminated.In order to improve the accuracy of GPS positioning,the single-epoch pseudorange multipath effects at GPS station were calculated,and firstly modeled based on the spherical cap harmonic（SCH）,which is the function of satellite longitude and latitude with the robust method.The accuracy of the kinematic point positioning technique was improved by correcting pseudorange observations with the multipath effect calculated by the SCH model,especially in the elevation direction.The spherical cap harmonic can be used to model the pseudorange multipath effect.展开更多
A modified algorithm of combined GPS/GLONASS precise point positioning （GG-PPP） was developed by decreasing the number of unknowns to be estimated so that accurate position solutions can be achieved in the case of l...A modified algorithm of combined GPS/GLONASS precise point positioning （GG-PPP） was developed by decreasing the number of unknowns to be estimated so that accurate position solutions can be achieved in the case of less number of visible satellites. The system time difference between GPS and GLONASS （STDGG） and zenith tropospheric delay （ZTD） values were firstly estimated in an open sky condition using the traditional GG-PPP algorithm. Then, they were used as a priori known values in the modified algorithm instead of estimating them as unknowns. The proposed algorithm was tested using observations collected at BJFS station in a simulated open-pit mine environment. The results show that the position filter converges much faster to a stable value in all three coordinate components using the modified algorithm than using the traditional algorithm. The modified algorithm achieves higher positioning accuracy as well. The accuracy improvement in the horizontal direction and vertical direction reaches 69% and 95% at a satellite elevation mask angle of 50°, respectively.展开更多
采用非差非组合精密单点定位(precise point positioning,PPP)反演北斗GEO卫星穿刺点位置的垂直方向电子总含量(vertical total electron content,VTEC),利用GEO卫星在时域上穿刺点位置近似固定的特性,反演、分析了深圳市2020年的电离...采用非差非组合精密单点定位(precise point positioning,PPP)反演北斗GEO卫星穿刺点位置的垂直方向电子总含量(vertical total electron content,VTEC),利用GEO卫星在时域上穿刺点位置近似固定的特性,反演、分析了深圳市2020年的电离层空间环境参数,并详细评估了该区域VTEC实测值与国际GNSS服务(International GNSS Service,IGS)组织提供的全球电离层模型(global ionosphere model,GIM)电离层产品间的差异。结果表明:在深圳市,北斗GEO卫星的VTEC实测值与GIM产品具有较好的一致性,全年差值的日均值和标准差分别为-0.87 TECU和3.24 TECU,各月份差值的日间时段均值略小于夜间时段,差值的标准差呈现明显的季节性特性,其中,6月、7月、8月份较低。整体上,GIM的VTEC日峰值比实测值的小,全年差值的均值和标准差分别为3.51 TECU和5.98 TECU。展开更多
With the completion of Chinese BeiDou Navigation Satellite System(BDS),the world has begun to enjoy the Positioning,Navigation,and Timing(PNT)services of four Global Navigation Satellite Systems(GNSS).In order to impr...With the completion of Chinese BeiDou Navigation Satellite System(BDS),the world has begun to enjoy the Positioning,Navigation,and Timing(PNT)services of four Global Navigation Satellite Systems(GNSS).In order to improve the GNSS performance and expand its applications,Low Earth Orbit(LEO)Enhanced Global Navigation Satellite System(LeGNSS)is being vigorously advocated.Combined with high-,medium-,and low-earth orbit satellites,it can improve GNSS performance in terms of orbit determination,Precise Point Positioning(PPP)convergence time,etc.This paper comprehensively reviews the current status of LeGNSS,focusing on analyzing its advantages and challenges for precise orbit and clock determination,PPP convergence,earth rotation parameter estimation,and global ionosphere modeling.Thanks to the fast geometric change brought by LEO satellites,LeGNSS is expected to fundamentally solve the problem of the long convergence time of PPP without any augmentation.The convergence time can be shortened within 1 minute if appropriate LEO constellations are deployed.However,there are still some issues to overcome,such as the optimization of LEO constellation as well as the real time LEO precise orbit and clock determination.展开更多
文摘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].
文摘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.
文摘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.
基金Supported by the NNSF of China(10371006) Tianyuan Youth Grant of China(10626033).
文摘This paper deals with the existence of triple positive solutions for the 1-dimensional equation of Laplace-type （φ（x′（t）））′＋q（t）f（t,x（t）,x′（t））=0,t∈（0,1）,subject to the following boundary condition：a1φ（x（0））-a2φ（x＇（0））=0,a3φ（x（1））＋a4φ（x＇（1））=0,where φ is an odd increasing homogeneous homeomorphism. By using a new fixed point theorem, sufficient conditions are obtained that guarantee the existence of at least three positive solu- tions. The emphasis here is that the nonlinear term f is involved with the first order derivative explicitly.
基金Supported by the Scientific Research Funds for the Ningxia Universities(Grant No.NGY2015141)
文摘We establish the existence of positive periodic solutions of the second-order singular coupled systems{x′′＋ p_1（t）x′＋ q_1（t）x = f_1（t, y（t）） ＋ c_1（t）,y′′＋ p_2（t）y′＋ q_2（t）y = f_2（t, x（t）） ＋ c_2（t）,where pi, qi, ci ∈ C（R/T Z; R）, i = 1, 2; f_1, f_2 ∈ C（R/T Z ×（0, ∞）, R） and may be singular near the zero. The proof relies on Schauder＇s fixed point theorem and anti-maximum principle.Our main results generalize and improve those available in the literature.
基金The Basic Science Center Project of the National Natural Science Foundation of China(No.42388102)the Jiangsu Province Natural Resources Science and Technology Project(No.JSZRKJ202404).
文摘Currently,the BeiDou⁃3(BDS⁃3)precise point positioning(PPP)service(PPP⁃B2b)mostly employs the ionosphere⁃free(IF)combination model for precise timing,which tends to amplify the noise in observation values.To address this issue,this paper proposes a real⁃time BDS⁃3 precise unidirectional timing model based on uncombined(UC)observations using the BDS⁃3 PPP⁃B2b service.This model resolves the challenge of the amplified observation noise inherent in the IF combination model.The experiment involved selecting eight global navigation satellite system(GNSS)observation stations within China and collecting continuous observation data for 15 d.A comparative analy⁃sis with the traditional dual⁃frequency IF combination PPP timing model showed that the BDS⁃3 UC PPP timing based on the BDS⁃3 PPP⁃B2b service can achieve a timing preci⁃sion of 0.5 ns.In addition,it was found that due to global positioning system(GPS)satellite clock products in the BDS⁃3 PPP⁃B2b service not being unified to the standard time,the GPS IF PPP timing method based on the BDS⁃3 PPP⁃B2b service is not recommended for precise timing.In summary,the BDS⁃3 UC PPP timing model proposed in this paper is suitable for precise timing,providing observa⁃tion values with smaller noise,and its timing accuracy is comparable to that of the BDS⁃3 IF PPP,with slightly better frequency stability.
基金funded by National Science Foundation of China(42025401)National Key Research and Development Program of China(2022YFB3903800)。
文摘Precise coseismic displacements in earthquake/tsunamic early warning are necessary to characterize earthquakes in real time in order to enable decision-makers to issue alerts for public safety.Real-time global navigation satellite systems(GNSSs)have been a valuable tool in monitoring seismic motions,allowing permanent displacement computation to be unambiguously achieved.As a valuable tool presented to the seismic commu nity,the GSeisRT software developed by Wuhan University(China)can realize multi-GNSS precise point positioning with ambiguity resolution(PPP-AR)and achieve centimeterlevel to sub-centimeter-level precision in real time.While the stable maintenance of a global precise point positioning(PPP)service is challenging,this software is capable of estimating satellite clocks and phase biases in real time using a regional GNSS network.This capability makes GSeisRT especially suitable for proprietary GNSS networks and,more importantly,the highest possible positio ning precision and reliability can be obtained.According to real-time results from the Network of the Americas,the mean root mean square(RMS)errors of kinematic PPP-AR over a 24 h span are as low as 1.2,1.3,and 3.0 cm in the east,north,and up components,respectively.Within the few minutes that span a typical seismic event,a horizontal displacement precision of 4 mm can be achieved.The positioning precision of the GSeisRT regional PPP/PPP-AR is 30%-40%higher than that of the global PPP/PPP-AR.Since 2019,GSeisRT has successfully recorded the static,dynamic,and peak ground displacements for the 2020Oaxaca,Mexico moment magnitude(Mw)7.4 event;the 2020 Lone Pine,California Mw 5.8 event;and the 2021 Qinghai,China Mw 7.3 event in real time.The resulting immediate magnitude estimates have an error of around 0.1 only.The GSeisRT software is open to the scientific community and has been applied by the China Earthquake Ne tworks Center,the EarthScope Consortium of the United States,the National Seismological Center of Chile,Institute of Geological and Nuclear Sciences Limited(GNS Science Te PūAo)of New Zealand,and the Geospatial Information Agency of Indonesia.
基金supported by the National Natural Science Foundation of China(42274039)Shaanxi Provincial Innovation Capacity Support Plan Project(2023KJXX-050)+2 种基金The Open Grants of the State Key Laboratory of Severe Weather(2023LASW-B18)Scientific and technological research projects for major issues in military medicine and aviation medicine(2022ZZXM012)Local special scientific research plan project of Shaanxi Provincial Department of Education(22JE012)。
文摘Zenith Tropospheric Delay(ZTD)is an important factor that restricts the high-precision positioning of global navigation satellite system(GNSS),and it is of great significance in establishing a real-time and highprecision ZTD model.However,existing ZTD models only consider the impact of linear terms on ZTD estimation,whereas the nonlinear factors have rarely been investigated before and thus become the focus of this study.A real-time and high-precision ZTD model for large height difference area is proposed by considering the linear and nonlinear characteristics of ZTD spatiotemporal variations and is called the realtime linear and nonlinearity ZTD(RLNZ)model.This model uses the ZTD estimated from the Global Pressure and Temperature 3(GPT3)model as the initial value.The linear impacts of periodic term and height on the estimation of ZTD difference between GNSS and GPT3 model are first considered.In addition,nonlinear factors such as geographical location and time are further used to fit the remaining nonlinear ZTD residuals using the general regression neural network method.Finally,the RLNZ-derived ZTD is obtained at an arbitrary location.The western United States,with height difference ranging from-500 to 4000 m,is selected,and the hourly ZTD of 484 GNSS stations provided by the Nevada Geodetic Laboratory(NGL)and the data of 9 radiosonde(RS)stations in the year 2021 are used.Experiment results show that a better performance of ZTD estimation can be retrieved from the proposed RLNZ model when compared with the GPT3 model.Statistical results show the averaged root mean square(RMS),Bias,and mean absolute error(MAE)of ZTD from GPT3 and RLNZ models are 33.7/0.8/25.7 mm and 22.6/0.1/17.4 mm,respectively.The average improvement rate of the RLNZ model is 33% when compared to the GPT3 model.Finally,the application of the proposed RLNZ model in simulated real-time Precise Point Positioning(PPP)indicates that the accuracy of PPP in N,E and U components is improved by 8%,2%,and 6% when compared with that from the GPT3-based PPP.Meanwhile,the convergence time in N and U components is improved by 23% and 7%,respectively.Such results verify the superiority of the proposed RLNZ model in retrieving realtime ZTD maps for GNSS positioning and navigation applications.
基金supported by supported by the National Key Research and Development Plan,China(No.2023YFB3906501)the National Natural Science Foundation of China(No.42227802)the Fundamental Research Funds for the Central Universities,China(No.501JCGG2024133001)。
文摘An integrity monitoring framework is proposed to ensure the quality of the real-time Precise Point Positioning(PPP)correction data at the service end.The key contributions are designing quantitative metrics to characterize the integrity status of the precise Orbit,Clock(OC)and Code Bias(OCB)corrections,and deriving the corresponding algorithms to detect and exclude anomalies,and to evaluate the real-time accuracy levels of the OCB.Compared to many prior works whose interests focused on analyzing and improving the averaged long-term accuracy,this work is established from integrity perspective.In particular,a two-layer fault detection and identification approach is developed to reduce the miss detection and false alert probabilities.The test statistics are constructed based on the raw observations from a network of worldwide sparsely distributed monitor stations.In addition,a realistic data-driven model is established to compute the Quality Indicators(QI)for healthy OCB products.The proposed scheme is validated respectively for multi-constellation OC and code bias,using historical correction data.The results suggest that the detection algorithms can effectively identify and alert the faults,so that the remaining correction errors approximate well to Gaussian distributions.Moreover,the computed QI are shown to be consistent with the truth error variations in real time.Most importantly,the position domain verification shows noticeable positioning accuracy and robustness improvements under both nominal and faulty conditions of the OCB correction data.
文摘In order to solve the problem that the star point positioning accuracy of the star sensor in near space is decreased due to atmospheric background stray light and rapid maneuvering of platform, this paper proposes a star point positioning algorithm based on the capsule network whose input and output are both vectors. First, a PCTL (Probability-Coordinate Transformation Layer) is designed to represent the mapping relationship between the probability output of the capsule network and the star point sub-pixel coordinates. Then, Coordconv Layer is introduced to implement explicit encoding of space information and the probability is used as the centroid weight to achieve the conversion between probability and star point sub-pixel coordinates, which improves the network’s ability to perceive star point positions. Finally, based on the dynamic imaging principle of star sensors and the characteristics of near-space environment, a star map dataset for algorithm training and testing is constructed. The simulation results show that the proposed algorithm reduces the MAE (Mean Absolute Error) and RMSE (Root Mean Square Error) of the star point positioning by 36.1% and 41.7% respectively compared with the traditional algorithm. The research results can provide important theory and technical support for the scheme design, index demonstration, test and evaluation of large dynamic star sensors in near space.
基金The National Natural Science Foundation of China(No.41974214).
文摘This study explores the use of the Global Navigation Satellite System(GNSS)precise point positioning(PPP)technology to determine the natural vibration periods of towering structures through simulations and field testing.During the simulation phase,a GNSS receiver captured vi-bration waveforms generated by a single-axis motion simulator based on preset signal parameters,analyzing how different satellite system configurations affect the efficiency of extracting vibration parameters.Subsequently,field tests were conducted on a high-rise steel singletube tower.The results indicate that in the simulation environment,no matter the PPP positioning data under single GPS or multisystem combination,the vibration frequency of singleaxis motion simulator can be accurately extracted after frequency do-main analysis,with multisystem setups providing more precise amplitude parameters.In the field test,the natural vibration periods of the main vibration modes of high-rise steel single-tube tower measured by PPP technology closely match the results of the first two modes derived from finite element analysis.The first mode period calculated by the em-pirical formula is approximately 6%higher than those determined through finite element analysis and PPP.This study demonstrates the potential of PPP for structural vibration analysis,offering significant benefits for assessing dynamic responses and monitoring the health of towering structures.
基金founded by the National Natural Science Foundation of China(42030109)the Startup Foundation for Doctors of Liaoning Province(2021-BS-275)+4 种基金the Scientific Study Project for Institutes of Higher LearningMinistry of EducationLiaoning Province(LJKMZ20220673)the Project supported by the State Key Laboratory of Geodesy and Earths'DynamicsInnovation Academy for Precision Measurement Science and Technology(SKLGED2023-3-2)。
文摘The application of Low Earth Orbit(LEO)satellite navigation can enhance geometric structure,increase observations and contribute to navigation and positioning.To improve the performance of the navigation constellation in China,this study proposes an optimized method of LEO-enhanced navigation constellation for BDS based on Bayesian optimization algorithm.In this paper,four different optimal LEO constellation configurations are designed,and their enhancements to BDS3 navigation performance are analyzed,including Geometric Dilution of Precision(GDOP),the numbers of visible satellites,and the rapid convergence of precision point positioning(PPP).Additionally,the enhancement advantages in China compared to other regions are further discussed.The results demonstrate that regional enhanced constellations with 70,72,80,and 81 satellites at an altitude of 1000 km can significantly improve the navigation performance of the navigation constellation.Globally,the addition of optimized LEO constellations has reduced the hybrid constellation GDOP by 19.0%,18.3%,19.9%,and 20.3%.Similar results can be obtained using the genetic algorithm(GA),but the computational efficiency of Bayesian optimization algorithm is 53.9%higher than that of the genetic algorithm.The number of visible satellites of enhanced constellations in China has increased by more than four on average,which is better than that in other regions.In the PPP experiment,the convergence time of the stations in China and other regions is shortened by 83.0%and 76.2%,respectively,and the navigation performance of hybrid constellations in China is better.
基金co-supported by the National Nature Science Foundation of China(No.12303071)the Shanghai Science and Technology Plan Project,China(No.23YF1455500)+1 种基金the China Postdoctoral Science Foundation(No.2023M743653)Ministry of Industry and Information Technology of China through the High Precision Timing Service Project(No.TC220A04A-80)。
文摘The mathematical method of ZTD(zenith tropospheric delay)spatial prediction is important for precise ZTD derivation and real-time precise point positioning(PPP)augmentation.This paper analyses the performance of the popular optimal function coefficient(OFC),sphere cap harmonic analysis(SCHA),kriging and inverse distance weighting(IDW)interpolation in ZTD spatial prediction and Beidou satellite navigation system(BDS)-PPP augmentation over China.For ZTD spatial prediction,the average time consumption of the OFC,kriging,and IDW methods is less than 0.1 s,which is significantly better than that of the SCHA method(63.157 s).The overall ZTD precision of the OFC is 3.44 cm,which outperforms those of the SCHA(9.65 cm),Kriging(10.6 cm),and IDW(11.8 cm)methods.We confirmed that the low performance of kriging and IDW is caused by their weakness in modelling ZTD variation in the vertical direction.To mitigate such deficiencies,an elevation normalization factor(ENF)is introduced into the kriging and IDW models(kriging-ENF and IDW-ENF).The overall ZTD spatial prediction accuracies of IDW-ENF and kriging-ENF are 2.80 cm and 2.01 cm,respectively,which are both superior to those of the OFC and the widely used empirical model GPT3(4.92 cm).For BDS-PPP enhancement,the ZTD provided by the kriging-ENF,IDW-ENF and OFC as prior constraints can effectively reduce the convergence time.Compared with unconstrained BDS-PPP,our proposed kriging-ENF outperforms IDW-ENF and OFC by reducing the horizontal and vertical convergence times by approximately 13.2%and 5.8%in Ningxia and 30.4%and 7.84%in Guangdong,respectively.These results indicate that kriging-ENF is a promising method for ZTD spatial prediction and BDS-PPP enhancement over China.
文摘Beidou-3 navigation satellite system(BDS-3)initiated a real-time service for precise point positioning(PPP)using the B2b signal,mainly for users in China and surrounding areas.In this paper,the performance of PPP-B2b service is experimentally analyzed first.Then,the ionosphere-free model is established.In order to solve the problem of slow convergence for traditional PPP,an adaptive robust extend Kalman filter(AREKF)algorithm is developed.Unlike the error compensation models,it reflects the noise information in real time by adjusting the covariance matrix of the measurements and the weight matrix of the state vector.The experimental results are analyzed last.Evaluation results indicate that the corrections provided by PPP-B2b can significantly reduce the discontinuous error of the orbits and clock offsets caused by broadcast ephemeris updating.Positioning results confirm that AREKF outperforms EKF both in static and kinematic modes.Around 20%improvement in accuracy and 25%improvement in convergence speed are achieved,making it valuable for PPP processing.
基金supported partially by the National Natural Science Foundation of China(No.40974004 and 40974016)the Key Laboratory of Surveying and Mapping Technology on Island and Reef of NASMG,China(No.2011A01)the Key Laboratory of Advanced Surveying Engineering of NASMG,China(No.TJES1101)
文摘Crustal deformation can provide constraints for studying earthquake rupture and shock wave transmission for the Mw9.0 eastern Japan great earthquake. Using the single- epoch precise point positioning （PPP） method and the appropriate positioning flow, we process GPS data from six IGS （International GNSS Service） sites （e.g., MIZU, TSK2, USUD, MTKA, AIRA and KSMV） located in Japan and obtain the positioning results with centimeter scale precision. The displacement time series of the six sites are analyzed using the least squares spectral analysis method to estimate deformations caused by the Mw9.0 mainshock and the Mw7.9 aftershock, and the cumulative displacements after 1 day. Mainshock displacements at station MIZU, the nearest site to the mainshock in the North （N）, East （E）, and Up （U） directions, are -1.202 m, 2.180 m and -0.104 m, respectively, and the cumulative deformations after 1 day are -1.117 m, 2.071 m and -0.072 m, respectively. The displacements at station KSMV, the nearest site to the Mw7.9 aftershock in the N, E and U directions, are -0.032 m, 0.742 m and -0.345 m, respectively. The other sites obviously experienced eastern movements and subsidence. The deformation vectors indicate that the horizontal displacements caused by the earthquake point to the epicenter and rupture. Elastic bounds evidently took place at all sites. The results indicate that the crustal movements and earthquake were part of a megathrust caused by the Pacific Plate sinking under the North American Plate to the northeast of Japan island arc.
基金Project (41374009) supported by the National Natural Science Foundation of ChinaProjects (TJES1101,TJES1203) supported by the Key Laboratory of Advanced Engineering Surveying of NASMG,China+1 种基金Project (ZR2013DM009) supported by the Shandong Natural Science Foundation of ChinaProject (201412001) supported by the Public Benefit Scientific Research Project of China
文摘Most GPS positioning errors can be eliminated or removed by the differential technique or the modeling method,but the multipath effect is a special kind of system or gross error,so it is difficult to be simulated or eliminated.In order to improve the accuracy of GPS positioning,the single-epoch pseudorange multipath effects at GPS station were calculated,and firstly modeled based on the spherical cap harmonic（SCH）,which is the function of satellite longitude and latitude with the robust method.The accuracy of the kinematic point positioning technique was improved by correcting pseudorange observations with the multipath effect calculated by the SCH model,especially in the elevation direction.The spherical cap harmonic can be used to model the pseudorange multipath effect.
基金Project(41004011)supported by the National Natural Science Foundation of ChinaProject(2014M550425)supported by the China Postdoctoral Science Foundation
文摘A modified algorithm of combined GPS/GLONASS precise point positioning （GG-PPP） was developed by decreasing the number of unknowns to be estimated so that accurate position solutions can be achieved in the case of less number of visible satellites. The system time difference between GPS and GLONASS （STDGG） and zenith tropospheric delay （ZTD） values were firstly estimated in an open sky condition using the traditional GG-PPP algorithm. Then, they were used as a priori known values in the modified algorithm instead of estimating them as unknowns. The proposed algorithm was tested using observations collected at BJFS station in a simulated open-pit mine environment. The results show that the position filter converges much faster to a stable value in all three coordinate components using the modified algorithm than using the traditional algorithm. The modified algorithm achieves higher positioning accuracy as well. The accuracy improvement in the horizontal direction and vertical direction reaches 69% and 95% at a satellite elevation mask angle of 50°, respectively.
文摘采用非差非组合精密单点定位(precise point positioning,PPP)反演北斗GEO卫星穿刺点位置的垂直方向电子总含量(vertical total electron content,VTEC),利用GEO卫星在时域上穿刺点位置近似固定的特性,反演、分析了深圳市2020年的电离层空间环境参数,并详细评估了该区域VTEC实测值与国际GNSS服务(International GNSS Service,IGS)组织提供的全球电离层模型(global ionosphere model,GIM)电离层产品间的差异。结果表明:在深圳市,北斗GEO卫星的VTEC实测值与GIM产品具有较好的一致性,全年差值的日均值和标准差分别为-0.87 TECU和3.24 TECU,各月份差值的日间时段均值略小于夜间时段,差值的标准差呈现明显的季节性特性,其中,6月、7月、8月份较低。整体上,GIM的VTEC日峰值比实测值的小,全年差值的均值和标准差分别为3.51 TECU和5.98 TECU。
基金the National Natural Science Funds of China[grant numbers 41874030,42074026]Natural Science Funds of Shanghai[grant number 21ZR1465600]+3 种基金the Program of Shanghai Academic Research Leader[grant number 20XD1423800]the Innovation Program of Shanghai Municipal Education Commission[grant number 2021-01-07-00-07-E00095]the“Shuguang Program”supported by Shanghai Education Development Foundation and Shanghai Municipal Education Commission[grant number 20SG18]the Scientific and Technological Innovation Plan from Shanghai Science and Technology Committee[grant numbers 20511103302,20511103402 and 20511103702].
文摘With the completion of Chinese BeiDou Navigation Satellite System(BDS),the world has begun to enjoy the Positioning,Navigation,and Timing(PNT)services of four Global Navigation Satellite Systems(GNSS).In order to improve the GNSS performance and expand its applications,Low Earth Orbit(LEO)Enhanced Global Navigation Satellite System(LeGNSS)is being vigorously advocated.Combined with high-,medium-,and low-earth orbit satellites,it can improve GNSS performance in terms of orbit determination,Precise Point Positioning(PPP)convergence time,etc.This paper comprehensively reviews the current status of LeGNSS,focusing on analyzing its advantages and challenges for precise orbit and clock determination,PPP convergence,earth rotation parameter estimation,and global ionosphere modeling.Thanks to the fast geometric change brought by LEO satellites,LeGNSS is expected to fundamentally solve the problem of the long convergence time of PPP without any augmentation.The convergence time can be shortened within 1 minute if appropriate LEO constellations are deployed.However,there are still some issues to overcome,such as the optimization of LEO constellation as well as the real time LEO precise orbit and clock determination.
