Study on systematic errors of BDS‑3 broadcast ephemeris and their effects with Helmert transformation

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.

Orbital Elements Ephemerides and Interfaces Design of LEO Satellites

Low earth orbit satellites,with unique advantages,are prosperous types of navigation augmentation satellites for the GNSS satellites constellations.The broadcast ephemeris element needs to be designed as an important index of the augmented LEOs.The GPS ephemerides of 16/18 elements cannot be directly applied to the LEOs because of the poor fitting accuracies in along-track positional component.Besides,the ill-conditioned problem of the normal-matrix exists in fitting algorithm due to the small eccentricity of the LEO orbits.Based on the nonsingular orbital elements,5 sets of ephemerides with element numbers from 16 to 19 were designed respectively by adding or modifying orbital elements magnifying the along-track and radial positional components.The fitting experiments based on the LEO of 300 to 1500 km altitudes show that the fitting UREs of the proposed 16/17/18/18*/19-element ephemerides are better than 10/6/4/5/2.5 cm,respectively.According to the dynamical range of the fitting elements,the interfaces were designed for the 5 sets of ephemerides.The effects of data truncation on fitting UREs are at millimeter level.The total bits are 329/343/376/379/396,respectively.29/15 bits are saved for the 16/17-element ephemerides compared with the GPS16 ephemeris,while 64/61/41 bits can be saved for the 18/18*/19-element ephemerides compared with the GPS18 elements ephemeris.

An optimal design of the broadcast ephemeris for LEO navigation augmentation systems

As the deployment of large Low Earth Orbiters(LEO)communication constellations,navigation from the LEO satellites becomes an emerging opportunity to enhance the existing satellite navigation systems.The LEO navigation augmentation(LEO-NA)systems require a centimeter to decimeter accuracy broadcast ephemeris to support high accuracy positioning applications.Thus,how to design the broadcast ephemeris becomes the key issue for the LEO-NA systems.In this paper,the temporal variation characteristics of the LEO orbit elements were analyzed via a spectrum analysis.A non-singular element set for orbit fitting was introduced to overcome the potential singularity problem of the LEO orbits.Based on the orbit characteristics,a few new parameters were introduced into the classical 16 parameter ephemeris set to improve the LEO orbit fitting accuracy.In order to identify the optimal parameter set,different parameter sets were tested and compared and the 21 parameters data set was recommended to make an optimal balance between the orbit accuracy and the bandwidth requirements.Considering the real-time broadcast ephemeris generation procedure,the performance of the LEO ephemeris based on the predicted orbit is also investigated.The performance of the proposed ephemeris set was evaluated with four in-orbit LEO satellites and the results indicate the proposed 21 parameter schemes improve the fitting accuracy by 87.4%subject to the 16 parameters scheme.The accuracy for the predicted LEO ephemeris is strongly dependent on the orbit altitude.For these LEO satellites operating higher than 500 km,10 cm signal-in-space ranging error(SISRE)is achievable for over 20 min prediction.

Improving BDS broadcast ephemeris accuracy using ground-satellite-link observations

The BeiDou Navigation Satellite System(BDS)employs a hybrid constellation including GEO(Geosynchronous Earth Orbit),IGSO(Inclined Geosynchronous Orbit),and MEO(Medium Earth Orbit)satellites,where the GEO and IGSO satellites are critical to providing continuous and reliable Positioning,Navigation,and Timing(PNT)services in the Asia–Pacifc region.To handle the inconsistency between the satellite orbits and clocks in the broadcast ephemeris,which are determined by the Orbit Determination and Time Synchronization(ODTS)and the Two-way Satellite Time Frequency Transfer(TWSTFT)technique,respectively,we present the strategies using ground-satellite-link observations to improve the accuracy of broadcast ephemeris.The clock diferences between the ODTS and TWSTFT techniques are used for correcting the radial orbit component to derive the refned orbits,which are used to generate the refned broadcast ephemeris.The test results show the precision of the refned orbits is improved by 50–60%in the 3-h to 12-h predicted arcs for the GEO satellites,and by 40–50%for the IGSO satellites.Moreover,the validation using satellite laser ranging observations shows the mean precision of the refned broadcast ephemeris is improved by 27%compared to the original one.Applying the proposed strategies in the BDS Operational Control Segment(OCS),the time evolution of BDS Single Point Positioning(SPP)in the period from Jan.2016 to April 2021 is evaluated.The SPP accuracy is improved from 1.94,2.06 and 3.29 m to 1.39,1.85,and 2.39 m in the north,east,and up components,respectively.Further update with the inclusion of BDS-3 satellites improve the corresponding SPP precision to 0.68,0.70 and 1.91 m.

SIS accuracy and service performance of the BDS-3 basic system

On December 27,2018,the basic system of the third-generation BeiDou navigation satellite system(BDS-3)completed the deployment of its constellation of 18 MEO networking satellites as well as the construction of the operation control system(OCS)and began to provide basic navigation services to users worldwide.Compared with BDS-2,BDS-3 aims to offer users better navigation signals and higher precision with a series of new technologies.For example,the spaceborne atomic clock of BDS-3 is upgraded for higher performance,the Ka-band inter-satellite link is adopted for inter-satellite ranging and communication,and new B1C and B2a signals are broadcast in addition to B1I and B3I signals(compatible with BDS-2).In addition,a 9-parameter model based on a spherical harmonic function is employed for ionospheric delay corrections.Using the observation data from 18 satellites of the basic system,this paper conducts a comprehensive evaluation of the pseudorange measurement characteristics,signal-in-space(SIS)accuracy of navigation messages and global service capability of BDS-3.The results indicate that the pseudorange measurement multipath effect and observation noise of BDS-3 satellites are better than those of BDS-2;additionally,with the support of inter-satellite links,the user range error(URE)of the BDS-3 satellite broadcast ephemeris is better than 10 cm,the precision of the broadcast clock parameter is better than 1.5 ns,and the SIS accuracy is better than 0.6 m overall.Different from the traditional Klobuchar model,the BeiDou global broadcast ionospheric delay correction model(BDGIM)can provide ionospheric delay corrections better than 70%for worldwide single-frequency users.The service capability evaluation of the basic system consists mainly of the accuracy improvement of the B1I and B3I signals according to BDS-2 as well as the global positioning accuracy of the new signals.These results prove that the BDS-3 basic system has achieved the design goal;that is,both the horizontal and the vertical global positioning accuracies are better than 10 m(95%).In the future,6 MEO satellites as well as 3 GEO satellites and 3 IGSO satellites for regional enhancement purposes will be deployed for full operation;consequently,BDS-3 will definitely provide a higher SIS accuracy and better service capability.