TLE orbit determination using simplex method

Two-Line Element(TLE)datasets are the only orbital data source of Earth-orbiting space objects for many civil users for their research and applications.The datasets have uneven qualities that may affect the reliability of the propagated positions of space objects using a single TLE.The least squares approach to use multiple TLEs also suffers from the poor quality of some TLEs,and reliable error information cannot be available.This paper proposes a simplex algorithm to estimate an optimal TLE from multiple TLEs and obtain the uncertainty of each element.It is a derivative-free technique that can deal with various orbit types.Experiments have demonstrated that using the TLE estimated from the simplex method is more reliable,stable,and effective than those from the batch least squares method.As an application example,the optimal TLE and its uncertainty are used for predicting the fallen area,keeping the actual fallen site in the prediction areas.

Influence of higher-order ionospheric delay correction on GPS precise orbit determination and precise positioning

At present, Global Navigation Satellite Systems（GNSS） users usually eliminate the influence of ionospheric delay of the first order items by dual-frequency ionosphere-free combination. But there is still residual ionospheric delay error of higher order term. The influence of the higher-order ionospheric corrections on both GPS precision orbit determination and static Precise Point Positioning（PPP） are studied in this paper. The influence of higher-order corrections on GPS precision orbit determination, GPS observations and static PPP are analyzed by neglecting or considering the higher-order ionospheric corrections by using a globally distributed network which is composed of International GNSS Service（IGS） tracking stations. Numerical experimental results show that, the root mean square（RMS） in three dimensions of satellite orbit is 36.6 mme35.5 mm. The maximal second-order ionospheric correction is 9 cm, and the maximal third-order ionospheric correction is 1 cm. Higher-order corrections are influenced by latitude and station distribution. PPP is within 3 mm in the directions of east and up. Furthermore, the impact is mainly visible in the direction of north, showing a southward migration trend, especially at the lower latitudes where the influence value is likely to be bigger than 3 mm.

Impact Analysis of Solar Irradiance Change on Precision Orbit Determination of Navigation Satellites

Solar radiation pressure is the main driving force and error source for precision orbit determination of navigation satellites.It is proportional to the solar irradiance,which is the"sun constant".In regular calculation,the"solar constant"is regard as a constant.However,due to the existence of sunspots,flares,etc.,the solar constant is not fixed,the change in the year is about 1%.To investigate the variation of solar irradiance,we use interpolation and average segment modeling of total solar irradiance data of SORCE,establishing variance solar radiation pressure(VARSRP)model and average solar radiation pressure(AVESRP)model based on the built solar pressure model(SRPM)(constant model).According to observation data of global positioning system(GPS)and Beidou system(BDS)in 2015 and comparing the solar pressure acceleration of VARSRP,AVESRP and SRPM,the magnitude of change can reach 10-10 m/s^2.In addition,according to the satellite precise orbit determination,for GPS satellites,the results of VARSRP and AVESRP are slightly smaller than those of the SRPM model,and the improvement is between 0.1 to 0.5 mm.For geosynchronous orbit(GEO)satellites of BDS,The AVESRP and VARSRP have an improvement of 3.5 mm and 4.0 mm,respectively,based on overlapping arc,and SLR check results show the AVESRP model and the VARSRP model is improved by 2.3 mm and 3.5 mm,respectively.Moreover,the change of inclined geosynchronous orbit(IGSO)satellites and medium earth orbit(MEO)satellites is relatively small,and the improvement is smaller than 0.5 mm.

Orbit Determination Using Satellite-to-Satellite Tracking Data

Satellite-to-Satellite tricking (SST) data can be used to determine the orbits of spacecraft in two ways. One is combined orbit determination, which combines SST data with ground-based tracking data and exploits the enhanced tracking geometry. The other is the autonomous orbit determination, which uses only SST. The latter only fits some particular circumstances since it suffers the rank defect problem in other circumstances. The proof of this statement is presented. The nature of the problem is also investigated in order to find an effective solution. Several. methods of solution are discussed. The feasibility of the methods is demonstrated by their application to a simulation.

An Orbit Determination Using SGP4 Propagator and Doppler Shifts for CubeSats

The two line elements(TLEs),released by the North American Aerospace Defense Command(NORAD),are chosen for CubeSats' mission operators.Unfortunately,they have errors and other accompanied problems,which cause large deviations in the in-track component.When a TLE value is available at a certain epoch,the dominant error is the angular error.It is proposed to correct the angular error by solving-for the mean argument of latitude at the desired epoch.A batch least squares technique and range rate measurements are used for the correction process.With the assistance of satellite tool kit(STK)software and Matlab,a simulation to verify the orbit determination(OD)technique is implemented.This paper provides an angular correction low cost OD method and presents a complete analysis for various test cases.This approach maintains high accuracy in cross-track and radial and makes great improvement in in-track at the same time,but it is exclusive for circular orbits.When it is applied to an elliptical orbit,the error will be unacceptable.Therefore,the angular error is corrected using the longitude of periapsis which totally mitigates the error at the epoch under consideration.For inclinations less than 20 o,the mean longitude is preferred for the angular correction as it provides more accuracy compared with the mean argument of latitude.

Precise Orbit Determination for the FY-3C Satellite Using Onboard BDS and GPS Observations from 2013, 2015, and 2017

Using the FengYun-3C(FY-3C)onboard BeiDou Navigation Satellite System(BDS)and Global Positioning System(GPS)data from 2013 to 2017,this study investigates the performance and contribution of BDS to precise orbit determination(POD)for a low-Earth orbit(LEO).The overlap comparison result indicates that code bias correction of BDS can improve the POD accuracy by 12.4%.The multi-year averaged one-dimensional(1D)root mean square(RMS)of the overlapping orbit differences(OODs)for the GPS-only solution is 2.0,1.7,and 1.5 cm,respectively,during the 2013,2015,and 2017 periods.The 1D RMS for the BDS-only solution is 150.9,115.0,and 47.4 cm,respectively,during the 2013,2015,and 2017 periods,which is much worse than the GPS-only solution due to the regional system of BDS and the few BDS channels of the FY-3C receiver.For the BDS and GPS combined solution(also known as the GC combined solution),the averaged 1D RMS is 2.5,2.3,and 1.6 cm,respectively,in 2013,2015,and 2017,while the GC combined POD presents a significant accuracy improvement after the exclusion of geostationary Earth orbit(GEO)satellites.The main reason for the improvement seen after this exclusion is the unfavorable satellite tracking geometry and poor orbit accuracy of GEO satellites.The accuracy of BDS-only and GC combined solutions have gradually improved from 2013 to 2017,thanks to improvements in the accuracy of International GNSS Service(IGS)orbit and clock products in recent years,especially the availability of a high-frequency satellite clock product(30 s sampling interval)since 2015.Moreover,the GC POD(without GEO)was able to achieve slightly better accuracy than the GPS-only POD in 2017,indicating that the fusion of BDS and GPS observations can improve the accuracy of LEO POD.GC combined POD can significantly improve the reliability of LEO POD,simply due to system redundancy.An increased contribution of BDS to LEO POD can be expected with the launch of more BDS satellites and with further improvements in the accuracy of BDS satellite products in the near future.

Initial orbit determination of BDS-3 satellites based on new code signals

For the two newly launched satellites(PRN number 27 and 28) of the future global BeiDou navigation satellite system(BDS-3), there is no available broadcast ephemeris data and other initial orbit information, but the initial orbit is the fundamental of the comprehensive analysis of the satellites and their signals. Precise orbit determination(POD) also requires determination of a priori initial value with a certain precision in order to avoid problems such as filter divergence during POD. Compared with the Newton iteration method, which relies on the initial value, this study utilizes the Bancroft algorithm to directly solve the nonlinear equations with the advantage of numerical stability. The initial orbits of these two satellites are calculated based on new code signals, and their results are analyzed and discussed. The experimental results show that, with the exception of very few epochs, when the new code signal is utilized, the median and robust variance factor of the observed residuals computed using pseudo-range observations and the solved initial orbits are less than 4 and 2 m, respectively. It also shows that this solution can be used for rapid initial orbit recovery after maneuvers of the new BeiDou satellites.

CubeSat Autonomous Orbit Determination Based on Magnetometer and Sun Sensor Data

CubeSats have evolved from purely educational tools to a standard platform for technology demonstration,scientific instrumentation and application in less than a decade.They open the door to new challenges and interplanetary missions which lead to the direct realization of autonomous orbit determination(AOD)which has been investigated before with different integrated sensors combined with various filters.Mostly these studies were carried out for larger satellites with more accurate sensors.Magnetometer and sun sensor combined with extended Kalman filter(EKF)are chosen to complete AOD task considering their light weight.For the purpose of AOD and the computational cost requirements imposed on CubeSats,it is important to develop and apply low cost on-board models.In this perspective,a magnetic model based on a table look up is proposed to generate the reference magnetic field with a low computational burden.In current article the simulations through Matlab and Satellites Tool Kit(STK)especially focus on the accuracy of the AOD system provided by this model.For analysis three EKFs are carried out with different calculation models and data types.The system based on the proposed model is fully autonomous,low-cost and has moderate-accuracy required by most CubeSats missions.The AOD system can be applied as main or backup system depending on the space missions′demands.

Autonomous orbit determination for the probe around small body

The algorithm of autonomous orbit determination for the probe around small body is studied. In the algorithm, first, the observed images of the body are compared with its pre-computed model of the body to obtain the location of the limb features of the body in the inertial coordinate. Second, the information of the images and features in utilized to obtain the position of the probe using the Levenberg-Marquardt algorithm. The position is then input to an extended Kalman filter which determines the real time orbit of the probe. Finally, considering the effective of the irregular small body shape perturbation and the small body model parameter error on the orbit determination precise, the procedure of autonomous orbit determination is validated using digital simulation.

Relative orbit determination algorithm of space targets with passive observation

Angles-only relative orbit determination for space non-cooperative targets based on passive sensor is subject to weakly observable problem of the relative state between two spacecraft. Previously, the evidence for angles-only observability was found by using cylindrical dynamics, however, the solution of orbit determination is still not provided. This study develops a relative orbit determination algorithm with the cylindrical dynamics based on differential evolution. Firstly, the relative motion dynamics and line-of-sight measurement model for nearcircular orbit are established in cylindrical coordinate system.Secondly, the observability is qualitatively analyzed by using the dynamics and measurement model where the unobservable geometry is found. Then, the angles-only relative orbit determination problem is modeled into an optimal searching frame and an improved differential evolution algorithm is introduced to solve the problem. Finally, the proposed algorithm is verified and tested by a set of numerical simulations in the context of highEarth and low-Earth cases. The results show that initial relative orbit determination(IROD) solution with an appropriate accuracy in a relative short span is achieved, which can be used to initialize the navigation filter.

Consistency of MGEX Orbit and Clock Products

The analysis centers of the Multi-GNSS Pilot Project of the International GNSS Service provide orbit and clock products for the global navigation satellite systems(GNSSs)Global Positioning System(GPS),GLONASS,Galileo,and BeiDou,as well as for the Japanese regional Quasi-Zenith Satellite System(QZSS).Due to improved solar radiation pressure modeling and other more sophisticated models,the consistency of these products has improved in recent years.The current orbit consistency between different analysis centers is on the level of a few centimeters for GPS,around one decimeter for GLONASS and Galileo,a few decimeters for BeiDou-2,and several decimeters for QZSS.The clock consistency is about 2 cm for GPS,5 cm for GLONASS and Galileo,and 10 cm for BeiDou-2.In terms of carrier phase modeling error for precise point positioning,the various products exhibit consistencies of 2–3 cm for GPS,6–14 cm for GLONASS,3–10 cm for Galileo,and 10–17 cm for BeiDou-2.

Analytic Initial Relative Orbit Solution for Angles-Only Space Rendezvous Using Hybrid Dynamics Method

A closed-form solution to the angles-only initial relative orbit determination(IROD)problem for space rendezvous with non-cooperated target is developed,where a method of hybrid dynamics with the concept of virtual formation is introduced to analytically solve the problem.Emphasis is placed on developing the solution based on hybrid dynamics(i.e.,Clohessy-Wiltshire equations and two-body dynamics),obtaining formation geometries that produce relative orbit state observability,and deriving the approximate analytic error covariance for the IROD solution.A standard Monte Carlo simulation system based on two-body dynamics is used to verify the feasibility and evaluate the performance proposed algorithms.The sensitivity of the solution accuracy to the formation geometry,observation numbers is presented and discussed.

Computation of satellite clock-ephemeris augmentation parameters for dual-frequency multi-constellation satellite-based augmentation system

Dual-frequency multi-constellation(DFMC) satellitebased augmentation system(SBAS) does not broadcast fast correction, which is important in reducing range error in L1-only SBAS.Meanwhile, the integrity bound of a satellite at low elevation is so loose that the service availability is decreased near the boundary of the service area. Therefore, the computation of satellite clockephemeris(SCE) augmentation parameters needs improvement.We propose a method introducing SCE prediction to eliminate most of the SCE error resulting from global navigation satellite system GNSS broadcast message. Compared with the signal-inspace(SIS) after applying augmentation parameters broadcast by the wide area augmentation system(WAAS), SIS accuracy after applying augmentation parameters computed by the proposed algorithm is improved and SIS integrity is ensured. With global positioning system(GPS) only, the availability of category-I(CAT-I)with a vertical alert level of 15 m in continental United States is about 90%, while the availability in the other part of the WAAS service area is markedly improved. With measurements made by the stations from the crustal movement observation network of China,users in some part of China can obtain CAT-I(vertical alert limit is 15 m) service with GPS and global navigation satellite system(GLONASS).

Solar Radiation Pressure Modeling and Application of BDS Satellites

Solar radiation pressure(SRP)model is the basis of high precise orbit determination and positioning of navigation satellites.At present,it is common to see the study of SRP model of BDS satellites.However,the establishment and application of a comprehensive analytical SRP model based on satellite physical parameters are rare.Different from other conservative forces and non-conservative forces,SRP is closely related to the satellite’s physical parameters and in-orbit state.On the basis of the physical mechanism of solar radiation,BDS satellite physical parameters,in-orbit attitude control mode,and so on,a comprehensive analytical model has been studied in this paper.Based on precise ephemeris and satellite laser ranging(SLR)data,the precision of a comprehensive analytical model has been verified.And the precision of orbit determination is at the decimeter level using this comprehensive analytical SRP model.According to the satellite conservation theorem of angular momentum and change of in-orbit telemetry parameters,the difference between a comprehensive analytical model and the actual in-orbit interference force has been analyzed and calculated.The addition of empirical items on the comprehensive analytical model has been proposed.SLR validations demonstrated that the orbit precision of BDS C08 and C10 can be achieved at 0.078 m and 0.084 m respectively.Compared with using the improved CODE empirical model,precision orbit accuracy of them has increased by 0.021 m and 0.045 m respectively.

Precise orbit determination of Haiyang‑2D using onboard BDS‑3 B1C/B2a observations with ambiguity resolution

The Haiyang-2D altimetry mission of China is one of the first Low Earth Orbit(LEO)satellites that can receive new B1C/B2a signals from the BeiDou-3 Navigation Satellite System(BDS-3)for Precise Orbit Determination(POD).In this work,the achievable accuracy of the single-receiver ambiguity resolution for onboard LEO satellites is studied based on the real measurements of new BDS-3 frequencies.Under normal conditions,six BDS-3 satellites on average are visible.However,the multipath of the B1C/B2a code observations presents some patchy patterns that cause near-field variations with an amplitude of approximately 40 cm and deteriorate the ambiguity-fixed rate.By modeling those errors,for the B2a code,a remarkable reduction of 53%in the Root Mean Square(RMS)is achieved at high elevations,along with an increase of 8%in the ambiguity-fixed rates.Additionally,an analysis of the onboard antenna’s phase center offsets reveals that when compared to the solutions with float ambiguities,the estimated values in the antenna’s Z direction in the solutions with fixed ambiguities are notably smaller.The independent validation of the resulting POD using satellite laser ranging at 16 selected high-performance stations shows that the residuals are reduced by a minimum of 15.4%for ambiguity-fixed solutions with an RMS consistency of approximately 2.2 cm.Furthermore,when compared to the DORIS-derived orbits,a 4.3 cm 3D RMS consistency is achieved for the BDS-3-derived orbits,and the along-track bias is reduced from 2.9 to 0.4 cm using ambiguity fixing.

A method to realize NAVSOP by utilizing GNSS authorized signals

Navigation via signals of opportunity(NAVSOP)is able to realize positioning by making use of hundreds of different signals that are all around us.A method to realize NAVSOP for low earth orbit(LEO)satellites is proposed in this paper,in which the global navigation satellite system(GNSS)authorized signals are utilized as the signal of opportunity(SOP).At first,the carrier recovery technique is studied under the premise that the pseudo-code is unknown.Secondly,a method based on characteristics of Doppler frequency shift is proposed to recognize the navigation satellites.Thirdly,the extended Kalman filter(EKF)is utilized to estimate the orbital parameters by using carrier phase measurements.Finally,the proposed method is evaluated by using signals generated by a satellite navigation data simulator.The simulation results show that the proposed method can successfully realize navigation via GNSS authorized signals.

Precise orbit determination for TH02-02 satellites based on BDS3 and GPS observations

The Tianhui-202(TH02-02)satellite formation,as a supplement to the microwave mapping satellite system Tianhui-201(TH02-01),is the first Interferometric Synthetic Aperture Radar(InSAR)satellite formation-flying system that supports the tracking of BeiDou global navigation Satellite system(BDS3)new B1C and B2a signals.Meanwhile,the twin TH02-02 satellites also support the tracking of Global Positioning System(GPS)L1&L2 and BDS B1I&B3I signals.As the spaceborne receiver employs two independent boards to track the Global Navigation Satellite System(GNSS)satellites,we design an orbit determination strategy by estimating independent receiver clock offsets epoch by epoch for each GNSS to realize the multi-GNSS data fusion from different boards.The performance of the spaceborne receiver is evaluated and the contribution of BDS3 to the kinematic and reduced-dynamic Precise Orbit Determination(POD)of TH02-02 satellites is investigated.The tracking data onboard shows that the average number of available BDS3 and GPS satellites are 8.7 and 9.1,respectively.The carrier-to-noise ratio and carrier phase noise of BDS3 B1C and B2a signals are comparable to those of GPS.However,strong azimuth-related systematic biases are recognized in the pseudorange multipath errors of B1C and B3I.The pseudorange noise of BDS3 signals is better than that of GPS after eliminating the multipath errors from specific signals.Taking the GPS-based reduced-dynamic orbit with single-receiver ambiguity fixing technique as a reference,the results of BDS3-only and BDS3+GPS combined POD are assessed.The Root Mean Square(RMS)of orbit comparison of BDS3-based kinematic and reduced-dynamic POD with reference orbit are better than 7 cm and 3 cm in three-Dimensional direction(3D).The POD performance based on B1C&B2a data is comparable to that based on B1I&B3I.The precision of BDS3+GPS combined kinematic orbit can reach up to 3 cm(3D RMS),which has a more than 25%improvement relative to the GPS-only solution.In addition,the consistency between the BDS3+GPS combined reduced-dynamic orbit and the GPS-based ambiguity-fixed orbit is better than 1.5 cm(3D RMS).

Integrating BDS and GPS for precise relative orbit determination of LEO formation flying

Low-Earth-Orbit（LEO） formation-flying satellites have been widely applied in many kinds of space geodesy. Precise Relative Orbit Determination（PROD） is an essential prerequisite for the LEO formation-flying satellites to complete their mission in space. The contribution of the BeiDou Navigation Satellite System（BDS） to the accuracy and reliability of PROD of LEO formation-flying satellites based on a Global Positioning System（GPS） is studied using a simulation method. Firstly, when BDS is added to GPS, the mean number of visible satellites increases from9.71 to 21.58. Secondly, the results show that the 3-Dimensional（3 D） accuracy of PROD, based on BDS-only, GPS-only and BDS ＋ GPS, is 0.74 mm, 0.66 mm and 0.52 mm, respectively. When BDS co-works with GPS, the accuracy increases by 29.73%. Geostationary-Earth-Orbit（GEO） satellites and Inclined Geosynchronous-Orbit（IGSO） satellites are only distributed over the Asia-Pacific region; however, they could provide a global improvement to PROD. The difference in PROD results between the Asia-Pacific region and the non-Asia-Pacific region is not apparent. Furthermore, the value of the Ambiguity Dilution Of Precision（ADOP）, based on BDS ＋ GPS, decreases by 7.50% and 8.26%, respectively, compared with BDS-only and GPS-only. Finally, if the relative position between satellites is only a few kilometres, the effect of ephemeris errors on PROD could be ignored. However, for a several-hundred-kilometre separation of the LEO satellites, the SingleDifference（SD） ephemeris errors of GEO satellites would be on the order of centimetres. The experimental results show that when IGSO satellites and Medium-Earth-Orbit（MEO） satellites co-work with GEO satellites, the accuracy decreases by 17.02%.

Autonomous orbit determination using epoch-differenced gravity gradients and starlight refraction

Autonomous orbit determination via integration of epoch-differenced gravity gradients and starlight refraction is proposed in this paper for low-Earth-orbiting satellites operating in GPSdenied environments. Starlight refraction compensates for the significant along-track position error that occurs from only using gravity gradients and benefits from integration in terms of improved accuracy in radial and cross-track position estimates. The between-epoch differencing of gravity gradients is employed to eliminate slowly varying measurement biases and noise near the orbit revolution frequency. The refraction angle measurements are directly used and its Jacobian matrix derived from an implicit observation equation. An information fusion filter based on a sequential extended Kalman filter is developed for the orbit determination. Truth-model simulations are used to test the performance of the algorithm, and the effects of differencing intervals and orbital heights are analyzed. A semi-simulation study using actual gravity gradient data from the Gravity field and steady-state Ocean Circulation Explorer（GOCE） combined with simulated starlight refraction measurements is further conducted, and a three-dimensional position accuracy of better than 100 m is achieved.

Reduced Dynamic Orbit Determination Using Differenced Phase in Adjacent Epochs for Spaceborne Dual-frequency GPS

We study on reduced dynamic orbit determination using differenced phase in adjacent epochs for spacebome dual-frequency GPS. This method not only overcomes the shortcomings that the epoch-difference kinematic method cannot be used when observation geometry is poor or observations are insufficient, but also avoids solving the ambiguity in the zero-difference reduced dynamic method. As the epoch-difference method is not sensitive to the impact of phase cycle slips, it can lower the difficulty of slip detection in phase observation preprocessing. In the solution strategies, we solve the high-dimensional matrix computation problems by decomposing the long observation arc into a number of short arcs. By gravity recovery and climate experiment （GRACE） satellite orbit determination and compared with GeoForschungsZentrum （GFZ） post science orbit, for epoch-difference reduced dynamic method, the root mean squares （RMSs） of radial, transverse and normal components are 1.92 cm, 3.83 cm and 3.80 cm, and the RMS in three dimensions is 5.76 cm. The solution＇s accuracy is comparable to the zero-difference reduced dynamic method.