Orbit fitting is used in many GPS applications. For example, in Precise Point Positioning (PPP), GPS orbits (SP3 orbits) are normally retrieved either from IGS or from one of its Analysis Centers (ACs) with 15 minutes...Orbit fitting is used in many GPS applications. For example, in Precise Point Positioning (PPP), GPS orbits (SP3 orbits) are normally retrieved either from IGS or from one of its Analysis Centers (ACs) with 15 minutes’ sampling, which is much bigger than the normal observation sampling. Therefore, algorithms should be derived to fit GPS orbits to the observation time. Many methods based on interpolation were developed. Using these methods the orbits fit well at the sampling points. However, these methods ignore the physical motion model of GPS satellites. Therefore, the trajectories may not fit the true orbits at the periods in between 2 sampling epochs. To solve this problem, we develop a dynamic approach, in which a model based on Helmert transformation is developed in GPS orbit fitting. In this orbit fitting approach, GPS orbits at sampling points are treated as pseudo-observations. Thereafter, Helmert transformation is built up between the pseudo-observations and dynamically integrated orbits at each epoch. A set of Helmert parameters together with corrections of GPS initial orbits are then modeled as unknown parameters. Results show that the final fit orbits have the same precision as the IGS final orbits.展开更多
Previous studies have not evaluated the systematic errors implied in the third generation of BeiDou-3 Navigation Satellite System(BDS-3)broadcast ephemeris.In this paper we evaluate the systematic pattern described by...Previous studies have not evaluated the systematic errors implied in the third generation of BeiDou-3 Navigation Satellite System(BDS-3)broadcast ephemeris.In this paper we evaluate the systematic pattern described by the Helmert transformation parameters,including translations,rotations,and scale.BDS-3 broadcast and precise ephemerides from December 2019 to 2022 are collected,and the characteristics of the transformation parameters as well as their effects on the signal in space error are analysed.The annual variation in the z-translation is obtained,and the similar amplitudes of 5.5 cm and phases of approximate 300 days are obtained for different years.When the rotation parameters are considered in the orbit comparison,the Root Mean Square(RMS)errors of the along-and cross-track orbital differences decrease from 29.1 to 12.5 cm and from 30.6 to 9.2 cm,respectively,because the three rotation parameters compensate for the majority of the errors in the BDS-3 broadcast ephemeris.Moreover,the high correlations in the obtained rotation parameters among the three orbital planes suggest that the orientation of the BDS-3 broadcast ephemeris is influenced by common model errors,i.e.,uncertainty of Earth Rotation Parameters(ERPs).Further research is required because an offset of 1.5×10^(–9)for the scale parameter is observed.A degraded User Range Error(URE)for epochs of up to 84%is attained when the systematic pattern is considered,though the impact of the systematic pattern indicated by the z-translation and rotation parameters on the URE is less than 5.0 cm.With the refinement of the ERPs implemented in the new generation of broadcast ephemeris,we anticipate that the broadcast ephemeris performance of BDS-3 will be improved.展开更多
In this paper,we propose an approach to determine seven parameters of the Helmert transfor-mation by transforming the coordinates of a continuous GNSS network from the World Geodetic System 1984(WGS84)to the Internati...In this paper,we propose an approach to determine seven parameters of the Helmert transfor-mation by transforming the coordinates of a continuous GNSS network from the World Geodetic System 1984(WGS84)to the International Terrestrial Reference Frame.This includes(1)convert-ing the coordinates of common points from the global coordinate system to the local coordinate system,(2)identifying and eliminating outliers by the Dikin estimator,and(3)estimating seven parameters of the Helmert transformation by least squares(LS)estimation with the“clean”data(i.e.outliers removed).Herein,the local coordinate system provides a platform to separate points’horizontal and vertical components.Then,the Dikin estimator identifies and eliminates outliers in the horizontal or vertical component separately.It is significant because common points in a continuous GNSS network may contain outliers.The proposed approach is tested with the Géoazur GNSS network with the results showing that the Dikin estimator detects outliers at 6 out of 18 common points,among which three points are found with outliers in the vertical compo-nent only.Thus,instead of eliminating all coordinate components of these six common points,we only eliminate all coordinate components of three common points and only the vertical component of another three common points.Finally,the classical LS estimation is applied to“clean”data to estimate seven parameters of the Helmert transformation with a significant accuracy improvement.The Dikin estimator’s results are compared to those of other robust estimators of Huber and Theil-Sen,which shows that the Dikin estimator performs better.Furthermore,the weighted total least-squares estimation is implemented to assess the accuracy of the LS estimation with the same data.The inter-comparison of the seven estimated parameters and their standard deviations shows a small difference at a few per million levels(E-6).展开更多
The Global Navigation Satellite System(GNSS)positioning method has been significantly developed in geodetic surveying.However,the height obtained through GNSS observations is given in a geodetic height system that nee...The Global Navigation Satellite System(GNSS)positioning method has been significantly developed in geodetic surveying.However,the height obtained through GNSS observations is given in a geodetic height system that needs to be converted to orthometric height for engineering applications.Information on geoid height,which can be calculated using the global geopotential mode,is required to convert such GNSS observations into orthometric height.However,its accuracy is still insufficient for most engineering purposes.Therefore,a reliable geoid model is essential,especially in areas growing fast,e.g.,the central part of Java,Indonesia.In this study,we modeled the local geoid model in the central part of Java,Indonesia,using terrestrial-based gravity observations.The Stokes'formula with the second Helmert's condensation method under the Remove-Compute-Restore approach was implemented to model the geoid.The comparison between our best-performing geoid model and GNSS/leveling observations showed that the standard deviation of the geoid height differences was estimated to be 4.4 cm.This geoid result outperformed the commonly adopted global model of EGM2008 with the estimated standard deviation of geoid height differences of 10.7 cm.展开更多
文摘Orbit fitting is used in many GPS applications. For example, in Precise Point Positioning (PPP), GPS orbits (SP3 orbits) are normally retrieved either from IGS or from one of its Analysis Centers (ACs) with 15 minutes’ sampling, which is much bigger than the normal observation sampling. Therefore, algorithms should be derived to fit GPS orbits to the observation time. Many methods based on interpolation were developed. Using these methods the orbits fit well at the sampling points. However, these methods ignore the physical motion model of GPS satellites. Therefore, the trajectories may not fit the true orbits at the periods in between 2 sampling epochs. To solve this problem, we develop a dynamic approach, in which a model based on Helmert transformation is developed in GPS orbit fitting. In this orbit fitting approach, GPS orbits at sampling points are treated as pseudo-observations. Thereafter, Helmert transformation is built up between the pseudo-observations and dynamically integrated orbits at each epoch. A set of Helmert parameters together with corrections of GPS initial orbits are then modeled as unknown parameters. Results show that the final fit orbits have the same precision as the IGS final orbits.
基金This study is sponsored by the National Natural Science Foundation of China(42204019,42030109)the Key Research and Development Plan Project of Hubei Province(grant number 2020BIB006)+1 种基金Young Elite Scientists Sponsorship Program by CAST(YESS20200308)Beijing Nova Program(Z211100002121068).
文摘Previous studies have not evaluated the systematic errors implied in the third generation of BeiDou-3 Navigation Satellite System(BDS-3)broadcast ephemeris.In this paper we evaluate the systematic pattern described by the Helmert transformation parameters,including translations,rotations,and scale.BDS-3 broadcast and precise ephemerides from December 2019 to 2022 are collected,and the characteristics of the transformation parameters as well as their effects on the signal in space error are analysed.The annual variation in the z-translation is obtained,and the similar amplitudes of 5.5 cm and phases of approximate 300 days are obtained for different years.When the rotation parameters are considered in the orbit comparison,the Root Mean Square(RMS)errors of the along-and cross-track orbital differences decrease from 29.1 to 12.5 cm and from 30.6 to 9.2 cm,respectively,because the three rotation parameters compensate for the majority of the errors in the BDS-3 broadcast ephemeris.Moreover,the high correlations in the obtained rotation parameters among the three orbital planes suggest that the orientation of the BDS-3 broadcast ephemeris is influenced by common model errors,i.e.,uncertainty of Earth Rotation Parameters(ERPs).Further research is required because an offset of 1.5×10^(–9)for the scale parameter is observed.A degraded User Range Error(URE)for epochs of up to 84%is attained when the systematic pattern is considered,though the impact of the systematic pattern indicated by the z-translation and rotation parameters on the URE is less than 5.0 cm.With the refinement of the ERPs implemented in the new generation of broadcast ephemeris,we anticipate that the broadcast ephemeris performance of BDS-3 will be improved.
基金supported by the Ministry of Education and Training of Vietnam[B2020-XDA-05].
文摘In this paper,we propose an approach to determine seven parameters of the Helmert transfor-mation by transforming the coordinates of a continuous GNSS network from the World Geodetic System 1984(WGS84)to the International Terrestrial Reference Frame.This includes(1)convert-ing the coordinates of common points from the global coordinate system to the local coordinate system,(2)identifying and eliminating outliers by the Dikin estimator,and(3)estimating seven parameters of the Helmert transformation by least squares(LS)estimation with the“clean”data(i.e.outliers removed).Herein,the local coordinate system provides a platform to separate points’horizontal and vertical components.Then,the Dikin estimator identifies and eliminates outliers in the horizontal or vertical component separately.It is significant because common points in a continuous GNSS network may contain outliers.The proposed approach is tested with the Géoazur GNSS network with the results showing that the Dikin estimator detects outliers at 6 out of 18 common points,among which three points are found with outliers in the vertical compo-nent only.Thus,instead of eliminating all coordinate components of these six common points,we only eliminate all coordinate components of three common points and only the vertical component of another three common points.Finally,the classical LS estimation is applied to“clean”data to estimate seven parameters of the Helmert transformation with a significant accuracy improvement.The Dikin estimator’s results are compared to those of other robust estimators of Huber and Theil-Sen,which shows that the Dikin estimator performs better.Furthermore,the weighted total least-squares estimation is implemented to assess the accuracy of the LS estimation with the same data.The inter-comparison of the seven estimated parameters and their standard deviations shows a small difference at a few per million levels(E-6).
文摘The Global Navigation Satellite System(GNSS)positioning method has been significantly developed in geodetic surveying.However,the height obtained through GNSS observations is given in a geodetic height system that needs to be converted to orthometric height for engineering applications.Information on geoid height,which can be calculated using the global geopotential mode,is required to convert such GNSS observations into orthometric height.However,its accuracy is still insufficient for most engineering purposes.Therefore,a reliable geoid model is essential,especially in areas growing fast,e.g.,the central part of Java,Indonesia.In this study,we modeled the local geoid model in the central part of Java,Indonesia,using terrestrial-based gravity observations.The Stokes'formula with the second Helmert's condensation method under the Remove-Compute-Restore approach was implemented to model the geoid.The comparison between our best-performing geoid model and GNSS/leveling observations showed that the standard deviation of the geoid height differences was estimated to be 4.4 cm.This geoid result outperformed the commonly adopted global model of EGM2008 with the estimated standard deviation of geoid height differences of 10.7 cm.
