The Global Positioning System (GPS) uses accurate atomic clocks in satellites and on the ground to provide world-wide position and time determination. These clocks have gravitational and motional frequency shifts whic...The Global Positioning System (GPS) uses accurate atomic clocks in satellites and on the ground to provide world-wide position and time determination. These clocks have gravitational and motional frequency shifts which are so large that, without properly accounting for relativistic effects, the system would not work. As a practical matter, therefore, many individuals who use the GPS need to understand how relativistic effects accounted for in the system. This paper discusses relativistic effects arising from both special relativity and general relativity, and how these effects are incorporated in GPS operations. Two introductory sections on kinematics in special and general relativity, respectively, are followed by a section which describes how relativistic effects should be accounted for. The concept of synchroization in the Earth-Centered Inertial frame is discussed in detail. Numerical and experimental examples are given, showing the sizes of the various effects. The treatment of special and general relativity is sufficiently complete that a person should be able to follow the development without much reference to external material, except that a few standard results have been quoted from textbooks without derivation.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
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...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.展开更多
Abnormal effects in GPS broadcast ephemerides can have a significant effect on real-time navigation and positioning solutions that use the orbit and clock error data provided by GPS broadcast ephemerides.This paper de...Abnormal effects in GPS broadcast ephemerides can have a significant effect on real-time navigation and positioning solutions that use the orbit and clock error data provided by GPS broadcast ephemerides.This paper describes three types of non-integerhour navigation data in GPS broadcast ephemeris data.Compared with GPST integer hour data,we find that there are two types of data blocks for non-integer-hour navigation containing gross errors with different levels of precision,which is reflected in the user range accuracy(URA)of the broadcast ephemeris.These gross errors can cause large deviations when using the GPS broadcast ephemeris for orbit calculation and lead to a decrease in the kinematic positioning accuracy.An improved weighting method which is based on the consistency relationship between the URA value and the orbital precision is proposed to improve the positioning accuracy by controlling the effect of gross errors in the broadcast ephemerides.The correction algorithm proposed in this paper was applied to real-time kinematic positioning with shipborne GPS data over the South China Sea.The results showed that the proposed positioning algorithm can effectively reduce the effects of gross errors in the broadcast ephemeris,and significantly improve the accuracy of the navigation and positioning.展开更多
By constructing two suitable generalized Lyapunov functions,we derived a generalized ellipsoidal estimate of the globally attractive set and positively invariant set of the unified chaotic system with the parameters ...By constructing two suitable generalized Lyapunov functions,we derived a generalized ellipsoidal estimate of the globally attractive set and positively invariant set of the unified chaotic system with the parameters α=1/29 and 1/29<α<2/29,respectively,which extends some related results of Li,et al. [Li DM,Lu JA,Wu XQ,Chen GR,Estimating the global basin of attraction and positively invariant set for the Lorenz system and a unified chaotic system,Journal of Mathematical Analysis and Applications,2006,323(2): 844-853]. The theoretical results obtained in this paper will find wide application in chaos control and synchronization.展开更多
In this paper, it is attempted to examine and compare different orientation, one recreational and another more precise, in the performance of two （global positioning system） receivers of forested areas. In doing thi...In this paper, it is attempted to examine and compare different orientation, one recreational and another more precise, in the performance of two （global positioning system） receivers of forested areas. In doing this, a field test on horizontal and vertical positional errors of GPS positioning at different points in the forested area of Taxiarchis-Vrastama University forest was conducted. The two GPS receivers were used to determine the positional accuracy of a selected number of points under tree canopies. Specifically, the precision and accuracy of Garmin＇s GPS positioning at different points were calculated and compared with the corresponding positioning and accuracy of another GPS system, namely the TOPCON GPS. By the calculation of various measures of accuracy and precision suitable for GPS receivers and the use of statistical methods, accuracy between the different receivers differed significantly is shown. Also, regression analysis revealed that the basal area and the number of available satellites are the most important factors for predicting position error.展开更多
为了分析当前GPS(Global Positioning System)、Galileo(Galileo Navigation Satellite System)和BDS-3(Beidou Navigation Satellite System with Global Coverage)广播星历的精度,详细分析研究了各种偏差改正及消除方法,并尽可能地消...为了分析当前GPS(Global Positioning System)、Galileo(Galileo Navigation Satellite System)和BDS-3(Beidou Navigation Satellite System with Global Coverage)广播星历的精度,详细分析研究了各种偏差改正及消除方法,并尽可能地消除了系统误差和粗差对评估结果的影响。选取2021-11-01/12-31共61天MGEX(multi-GNSS experiment)发布的多系统混合广播星历与武汉大学分析中心发布的事后精密星历数据进行实验,对GPS、Galileo和BDS-3近期广播星历精度进行对比分析,实验结果表明:3个系统广播星历整体精度由高到低依次是Galileo、BDS-3和GPS,其空间信号测距误差的RMS(root mean square)分别优于0.17、0.25和0.37 m,整体轨道精度的RMS分别优于0.17、0.12和0.25 m,BDS-3广播星历的轨道精度最高,钟差误差的RMS分别优于0.15、0.23和0.27 m,Galileo广播星历的钟差精度最高。对于GPS卫星的广播星历,blockⅢA卫星钟差和轨道精度均优于其他GPS类型卫星。展开更多
基金This work was supported in pert by NIST Contract No. 40RANB9B8112.
文摘The Global Positioning System (GPS) uses accurate atomic clocks in satellites and on the ground to provide world-wide position and time determination. These clocks have gravitational and motional frequency shifts which are so large that, without properly accounting for relativistic effects, the system would not work. As a practical matter, therefore, many individuals who use the GPS need to understand how relativistic effects accounted for in the system. This paper discusses relativistic effects arising from both special relativity and general relativity, and how these effects are incorporated in GPS operations. Two introductory sections on kinematics in special and general relativity, respectively, are followed by a section which describes how relativistic effects should be accounted for. The concept of synchroization in the Earth-Centered Inertial frame is discussed in detail. Numerical and experimental examples are given, showing the sizes of the various effects. The treatment of special and general relativity is sufficiently complete that a person should be able to follow the development without much reference to external material, except that a few standard results have been quoted from textbooks without derivation.
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.
文摘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.
基金The authors would like to thank to Second Institute of Oceanography for the marine GPS data in the South China Sea.And this study is under the support by the National Key Research and Development Program of China(2016YFB0501701 and 2016YFB0501900).National Natural Science Foundation of China(Grant Nos.41574013 and 41874032)and the Funded by the State Key Laboratory of Geo-information Engineering(SKLGIE2016-M-1-1).
文摘Abnormal effects in GPS broadcast ephemerides can have a significant effect on real-time navigation and positioning solutions that use the orbit and clock error data provided by GPS broadcast ephemerides.This paper describes three types of non-integerhour navigation data in GPS broadcast ephemeris data.Compared with GPST integer hour data,we find that there are two types of data blocks for non-integer-hour navigation containing gross errors with different levels of precision,which is reflected in the user range accuracy(URA)of the broadcast ephemeris.These gross errors can cause large deviations when using the GPS broadcast ephemeris for orbit calculation and lead to a decrease in the kinematic positioning accuracy.An improved weighting method which is based on the consistency relationship between the URA value and the orbital precision is proposed to improve the positioning accuracy by controlling the effect of gross errors in the broadcast ephemerides.The correction algorithm proposed in this paper was applied to real-time kinematic positioning with shipborne GPS data over the South China Sea.The results showed that the proposed positioning algorithm can effectively reduce the effects of gross errors in the broadcast ephemeris,and significantly improve the accuracy of the navigation and positioning.
文摘By constructing two suitable generalized Lyapunov functions,we derived a generalized ellipsoidal estimate of the globally attractive set and positively invariant set of the unified chaotic system with the parameters α=1/29 and 1/29<α<2/29,respectively,which extends some related results of Li,et al. [Li DM,Lu JA,Wu XQ,Chen GR,Estimating the global basin of attraction and positively invariant set for the Lorenz system and a unified chaotic system,Journal of Mathematical Analysis and Applications,2006,323(2): 844-853]. The theoretical results obtained in this paper will find wide application in chaos control and synchronization.
文摘In this paper, it is attempted to examine and compare different orientation, one recreational and another more precise, in the performance of two （global positioning system） receivers of forested areas. In doing this, a field test on horizontal and vertical positional errors of GPS positioning at different points in the forested area of Taxiarchis-Vrastama University forest was conducted. The two GPS receivers were used to determine the positional accuracy of a selected number of points under tree canopies. Specifically, the precision and accuracy of Garmin＇s GPS positioning at different points were calculated and compared with the corresponding positioning and accuracy of another GPS system, namely the TOPCON GPS. By the calculation of various measures of accuracy and precision suitable for GPS receivers and the use of statistical methods, accuracy between the different receivers differed significantly is shown. Also, regression analysis revealed that the basal area and the number of available satellites are the most important factors for predicting position error.
文摘为了分析当前GPS(Global Positioning System)、Galileo(Galileo Navigation Satellite System)和BDS-3(Beidou Navigation Satellite System with Global Coverage)广播星历的精度,详细分析研究了各种偏差改正及消除方法,并尽可能地消除了系统误差和粗差对评估结果的影响。选取2021-11-01/12-31共61天MGEX(multi-GNSS experiment)发布的多系统混合广播星历与武汉大学分析中心发布的事后精密星历数据进行实验,对GPS、Galileo和BDS-3近期广播星历精度进行对比分析,实验结果表明:3个系统广播星历整体精度由高到低依次是Galileo、BDS-3和GPS,其空间信号测距误差的RMS(root mean square)分别优于0.17、0.25和0.37 m,整体轨道精度的RMS分别优于0.17、0.12和0.25 m,BDS-3广播星历的轨道精度最高,钟差误差的RMS分别优于0.15、0.23和0.27 m,Galileo广播星历的钟差精度最高。对于GPS卫星的广播星历,blockⅢA卫星钟差和轨道精度均优于其他GPS类型卫星。
