A new interpolation method based on satellite physical character in using IGS precise ephemeris

Due to the deficiency of sliding Lagrange polynomial interpolation, the author proposes a new interpolation method, which considers the physical character of satellite movement in coordinate transformation and reasonable selection of interpolation function. Precision of the two methods is compared by a numerical example. The result shows that the new method is superior to the sliding Lagrange polynomial interpolation in interpolation and extrapolation, especially in extrapolation that is over short time spans.

Low-thrust trajectory optimization in a full ephemeris model

The low-thrust trajectory optimization with complicated constraints must be considered in practical engineering. In most literature, this problem is simplified into a two-body model in which the spacecraft is subject to the gravitational force at the center of mass and the spacecraft＇s own electric propulsion only, and the gravity assist （GA） is modeled as an instantaneous velocity increment. This paper presents a method to solve the fuel-optimal problem of low-thrust trajectory with complicated constraints in a full ephemeris model, which is closer to practical engineering conditions. First, it introduces various perturbations, including a third body＇s gravity, the nonspherical perturbation and the solar radiation pressure in a dynamic equation. Second, it builds two types of equivalent inner constraints to describe the GA. At the same time, the present paper applies a series of techniques, such as a homotopic approach, to enhance the possibility of convergence of the global optimal solution.

A 16-parameter GEO Broadcast Ephemeris

Currently,the broadcast ephemerides used in GEOs are same as those of the MEOs and IGSOs in the BeiDou navigation constellation.However,a trade-off strategy,i.e.an orbital inclination of 5°rotation,is needed in the fitting algorithm to solve the ephemeris parameters as well as the user satellite position computation for GEOs.Based on the standard broadcast ephemerides,the representations of both the orbit and its perturbation were revised according to the second class of nonsingular orbital elements.In this research,a 16-parameter broadcast ephemeris is presented specifically for GEOs,and user satellite position computation formulas were derived correspondingly.Fit simulations show that the root of mean squares(RMS)of user range error(URE)with two hour and three hour data sets are better than 0.05 m and 0.1 m,respectively.

Heuristics Scheduling Algorithm on the Links Scheduling of Satellite-Ground Clock Synchronization and Ephemeris Uploading in COMPASS System

The execution process of satellite-ground clock synchronization and ephemeris uploading in the system is analyzed,as well as their characterized operation and their relationship.Based on the analysis of the scheduling goal and constraint character,a heuristics rule-based multi-stage link scheduling algorithm was put forward.The algorithm distinguishes the on-off-frontier satellites from the others and schedules them by turns.The paper presented the main flow as well as the detailed design of the rule.Finally based on the current COMPASS global system,some typical resources and constraints are selected to generate an instance.Then the comparison analysis between the heuristics scheduling algorithm and three other traditional scheduling strategies are carried out.The result shows the validity and reasonability of the multi-stage strategy.

Two Unified Algorithms for Fundamental Planetary Ephemeris

In the present paper, we established two unified algorithms. The first algorithm is for the transformations between J2000.0 Keplerian orbital elements and B1950.0 elements, while the second is for the transformations between the equatorial orbital elements and the ecliptic orbital elements. Mathematica Modules of the algorithms are given together with some numerical applications.

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.

Opportunities search of transfer between interplanetary halo orbits in ephemeris model

In this paper,a two-level search method for searching transfer opportunities between interplanetary halo orbits,exploiting the invariant manifolds of the restricted three-body problem,is proposed.In the method,the first-level search procedure is performed under the conditions of the initial time of escape manifold trajectory of the Sun-Earth halo orbit and the terminal time of capture manifold of the target planet fixed,by solving the optimal two-impulsive heliocentric trajectory to connect the two manifold trajectories.The contour map,helpful to the understanding of the global characteristics of the transfer opportunities,taking the initial time of escape manifold and the terminal time of capture manifold as variables,the optimal velocity increment of the first-level search as objective function,is used for the second-level search.Finally,taking the Earth-Mars and Earth-Venus halo to halo transfers for example,the transfer opportunities in 2015-2017 are searched.The results show the effectiveness of the proposed method and reveal the property of quasi-period of transfer opportunities between interplanetary halo orbits.

Trajectory design for the Moon departure libration point mission in full ephemeris model

The lunar probe may still have some remaining fuel after completing its predefined Moon exploration mission and is able to carry out some additional scientific or technological tasks after escaping from the Moon orbit.The Moon departure mission for the lunar probe is the focus of this paper.The possibility of the spacecraft orbiting the Moon to escape the Moon's gravitational pull is analyzed.The trajectory design for the Earth-Moon system libration point mission is studied in a full ephemeris dynamical model,which considers the non-uniform motion of the Moon around the Earth,the gravity of the Sun and planets and the finite thrust of the onboard engine.By applying the Particle Swarm Optimization algorithm,the trajectory design for the transfer from the Moon-centered orbit to the L1 halo orbit,the station-keeping strategies for the Earth-Moon halo orbit and the construction of homoclinic and heteroclinic orbits are investigated.Taking the tracking conditions and engineering constraints into account,two feasible schemes for the Moon departure libration point mission for the lunar probe are presented.

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.

A virtual reference satellite differential method for relative correction of satellite ephemeris errors

In order to solve the problems that the novel wide area differential method on the satellite clock and ephemeris relative correction (CERC) in the non-geostationary orbit satellite constellation, a virtual reference satellite (VRS) differential principle using relative correction of satellite ephemeris errors is proposed. It is referred to be as the VRS differential principle, and the elaboration is focused on the construction of pseudo-range errors of VRS. Through qualitative analysis, it can be found that the impact of the satellite’s clock and ephemeris errors on positioning can basically be removed and the users’ positioning errors are near zero. Through simulation analysis of the differential performance, it is verified that the differential method is universal in all kinds of satellite navigation systems with geostationary orbit (GEO) constellation, Medium orbit (MEO) constellation or hybrid orbit constellation, and it has insensitivity to abnormal aspects of a satellite ephemeris and clock. Moreover, the real time positioning accuracy of differential users can be maintained within several decimeters after the pseudo-range measurement noise is effectively weakened or eliminated.

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.

Performance analysis of SBAS ephemeris corrections and integrity algorithms in China region

Satellite Based Augmentation Systems(SBASs)improve the positioning accuracy and integrity by broadcasting to the civil aviation community the corrections and integrity parameters.A snapshot algorithm based on the minimum variance estimation is investigated in this study to calculate the satellite clock and orbit corrections.A chi-square test is performed on the remaining errors in the corrected ephemeris to guarantee the integrity.User Differential Range Error(UDRE)and scaling matrix contained in Message Type 28 are derived using the covariance information based on the assumption that one of the reference stations failed.A software package is developed and applied in the real data collected at 26 stations.International GNSS(Global Navigation Satellite System)Service(IGS)precise clock and orbit products are taken as the references to assess the accuracy of corrections.For both Global Positioning System(GPS)and BeiDou Navigation Satellite System(BDS),the range accuracy of 0.10 m can be achieved with the employment of the derived corrections.No obvious performance difference between GPS and BDS is found.UDREs for all visible satellites are generated with the maximum index of 12 and minimum index of 3.The geometric range differences calculated with IGS precise products and broadcast ephemeris are employed to assess the integrity of UDRE.It is found that the UDRE is able to bound the residuals with 99.9%confidence which meet the requirement of aviation users.With ionospheric delay corrected by Global Ionosphere Map(GIM),the positioning accuracy of 0.98 m with GPS corrections and 0.80 m with multi-constellation augmentation can be achieved which indicates a significant improvement of GPS standalone results.

GPS-Meteorology Network in Wuhan Region

There are three aspects in the study of GPS meteorology network in the Wuhan region. The first is the comparison of the GPS precipitable water vapor between final ephemeris and ultra-rapid ephemeris for which the relative coefficient is 99.97 and the root mean squares is 0.048 mm. It can be concluded that ultra-rapid ephemeris can be used to get the GPS precipitable water vapor for the real-time prediction. The second is the comparison of precipitable water vapor of GPS stations and the distribution of water vapor in the Wuhan region is acquired. The change of GPS precipitable water vapor and rainfall in a rainfall process are compared and analyzed. The change of GPS precipitable water vapor can reflect and predict the process of rainfall.

The Quality Assessment of Non-Integer-Hour Data in GPS Broadcast Ephemerides and Its Impact on the Accuracy of Real- Time Kinematic Positioning Over the South China Sea

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.

Digital IF GPS Signal Simulator Design

In order to test the static and dynamic performance of a Global Positioning System(GPS) receiver,a GPS signal simulator is required to generate real satellite signals in various environments. The software simulator is widely used because of the advantages of being flexible and reprogrammable. Therefore, a digital intermediate frequency GPS signal software simulator which implemented using MATLAB software is proposed. It is a method to calculate the satellite ephemeris parameters by using the anchor point, satellite elevation angle and azimuth angle, and to achieve navigation information transmission delay by modifying the C/A code frequency based on analyzing the positional relationship between the satellite and the receiver. The simulation results show that the simulator is correct and effective. When the receiver is stationary and the satellite is moving, the receiver positioning error is less than 1 m.

Leonardo 500 Years: Digital Experiences in Milan, Rio de Janeiro and São Paulo

The object of this study is the impact of technology in four exhibitions held to celebrate the 500 years of the death of Leonardo da Vinci on 2019.Two exhibitions took place in Milan,Italy,one took place in Rio de Janeiro,Brazil and the last one took place in São Paulo,also in Brazil.This study aims to explore the empirical evidences found during the field research in three of the four exhibitions object of this study(one of the exhibitions could not be observed to the museum being closed as a result of the pandemic caused by the coronavirus).This study is based on references and recent secondary researches that analyzed the aspects of quantity and quality in exhibitions sites,and also on other data available on websites and in the media.This study aims to question the importance of the original work in digital exhibitions and a possibly a further extension on the word“experience”not specifically through technological immersion.Lastly,these subjects are revisited once we look at the museums amid the world pandemic.

A long time span relativistic precession model of the Earth

A numerical solution to the Earth＇s precession in a relativistic framework for a long time span is presented here. We obtain the motion of the solar system in the Barycentric Celestial Reference System by numerical integration with a symplectic in- tegrator. Special Newtonian corrections accounting for tidal dissipation are included in the force model. The part representing Earth＇s rotation is calculated in the Geocentric Celestial Reference System by integrating the post-Newtonian equations of motion published by Klioner et al. All the main relativistic effects are included following Klioner et al. In particular, we consider several relativistic reference systems with cor- responding time scales, scaled constants and parameters. Approximate expressions for Earth＇s precession in the interval ~1 Myr around J2000.0 are provided. In the interval 4-2000 years around J2000.0, the difference compared to the P03 precession theory is only several arcseconds and the results are consistent with other long-term precession theories.

OBSERVATIONS OF COMET HALE-BOPP IN SPRINGS OF 1996 AND 1997

In the springs of 1996 and 1997, we used a new developed 1024×1024 CCD camera attached to the 1-meter telescope at Yunnan Observatory, to take photometric observations for the Comet Hale-Bopp. In addition, a 35-cm telescope, a 22-cm telescope and a common camera were also used for the observations, since this comet may become the brightest comet in our century. A lot of pictures had been obtained. They show us a "fan" and "shell" structure, also plentiful of phenomena in the plasma tail and dust tail with their variation. The positions and luminosity variations in 1996 have been measured accurately.

POSITION OBSERVATIONS OF THE COMET HYAKUTAKE

On March 16 of 1996, we used a new developed 1024×1024 CCD camera attached to the 1 meter telescope at Yunnan Observatory, to take photometric observations for the Comet Hyakutake. The positions have been measured accurately. Our result clearly states that even a new ephemeris of this comet just given by EMPC on February 29 of 1996 still has obvious systematical deviation with our observations. From images observed, we can clearly see that the cometary coma is very large and basically symmetric with a peach shape. It means that there is material flowing along the cometary tail which opposited the solar direction.

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.