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.

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.

On simulation of precise orbit determination of HY-2 with centimeter precision based on satellite-borne GPS technique

The HY-2 satellite carrying a satellite-borne GPS receiver is the first Chinese radar altimeter satellite, whose radial orbit determination precision must reach the centimeter level. Now HY-2 is in the test phase so that the observations are not openly released. In order to study the precise orbit determination precision and procedure for HY-2 based on the satellite- borne GPS technique, the satellite-borne GPS data are simulated in this paper. The HY-2 satellite-borne GPS antenna can receive at least seven GPS satellites each epoch, which can validate the GPS receiver and antenna design. What＇s more, the precise orbit determination processing flow is given and precise orbit determination experiments are conducted using the HY-2-borne GPS data with both the reduced-dynamic method and the kinematic geometry method. With the 1 and 3 mm phase data random errors, the radial orbit determination precision can achieve the centimeter level using these two methods and the kinematic orbit accuracy is slightly lower than that of the reduced-dynamic orbit. The earth gravity field model is an important factor which seriously affects the precise orbit determination of altimeter satellites. The reduced-dynamic orbit determination experiments are made with different earth gravity field models, such as EIGEN2, EGM96, TEG4, and GEMT3. Using a large number of high precision satellite-bome GPS data, the HY-2 precise orbit determination can reach the centimeter level with commonly used earth gravity field models up to above 50 degrees and orders.

High Precision Orbit Determination of CHAMP Satellite

The precision orbit determination of challenging minisatellite payload(CHAMP) satellite was done based on position and navigation data analyst(PANDA) software which is developed in Wuhan University, using the onboard GPS data of year 2002 from day 126 to 131. The orbit accuracy was assessed by analyzing the difference from GFZ post-processed science orbits (PSO), the GPS carrier and pseudo-range data residuals and the satellite laser ranging (SLR) residuals.

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.

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.

Reducing Influence of Gravity Model Error in Precise Orbit Determination of Low Earth Orbit Satellites

Based on the orbit integration and orbit fitting method, the influence of the characters of the gravity model, with different precisions, on the movement of low Earth orbit satellites was studied. The way and the effect of absorbing the influence of gravity model error on CHAMP and GRACE satellite orbits, using linear and periodical empirical acceleration models and the so-called "pseudo-stochastic pulses" model, were also analyzed.

Geomagnetic Orbit Determination Using Fuzzy Regulating Unscented Kalman Filter

Geomagnetic orbit determination fits for nanosatellites which pursue low cost and high-density ratio,but one of its disadvantages is the poor position accuracy introduced by magnetic bias.Here,a new method,named the fuzzy regulating unscented Kalman filter(FRUKF),is proposed.The magnetic bias is regarded as a random walk model,and a fuzzy regulator is designed to estimate the magnetic bias more accurately.The input of the regulator is the derivative of magnetic bias estimated from unscented Kalman filter(UKF).According to the fuzzy rule,the process noise covariance is adaptively determined.The FRUKF is evaluated using the real-flight data of the SWARMA.The experimental results show that the root-mean-square(RMS)position error is 3.1 km and the convergence time is shorter than the traditional way.

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.

Research on Autonomous Orbit Determination of Navigation Satellite Based on Crosslink Range and Orientation Parameters Constraining

Autonomous navigation of navigation satellite is discussed. The method of auto-orbit determination using the erosslink range and orientation parameters constraining is put forward. On the basis of the analysis of its feasibility, some useful conclusions are given.

Atmospheric Drag Perturbation in an Autonomous Orbit Determination for Satellite

In this paper, an autonomous orbit determination method for satellite using a large field of view star sensor is presented. The simulation of orbit under atmospheric drag perturbation are given with expanded Kalman filtering. The large field of view star sensor has the same precision as star sensor and a sufficient filed of view. Therefore ,the refraction stars can be observed more accurately in real time. The geometric relation between the refracted starlight and the earth can be determined by tangent altitude of the refraction starlight. And then the earth center can be determined in satellite body frame. The simulation shows that the precision of the mean square deviation of satellite’s position and velocity is 5m and 0.01m/s respectively. The calculated decrement of the semi-major axis in one day is close to the theoretical result, and the absolute error is in the range of decimeter when the altitude of orbit is 750 km. The simu- lateion of orbit of different initial semi-major axis shows that the higher the altitude of orbit is, the smaller the dec- rement of the semi-major axis is, and when the altitude of orbit is 1700 km the decimeter of the semi-major axis is 10-7 km.

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.

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.

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.

Spaceborne and ground-based sensor collaboration:Advancing resident space objects’orbit determination for space sustainability

The limited space around the Earth is getting cluttered with leftover fragments from old missions,creating a real challenge.As more satellites are launched,even debris pieces as small as 5 mm must be tracked to avoid collisions.However,it is an arduous and challenging task in space.This paper presents a technical exploration of ground-based and in-orbit space debris tracking and orbit determination methods.It highlights the challenges faced during on-ground and in-orbit demonstrations,identifies current gaps,and proposes solutions following technological advancements,such as low-power pose estimation methods.Owing to the numerous atmospheric barriers to ground-based sensors,this study emphasizes the significance of spaceborne sensors for precise orbit determination,complemented by advanced data processing algorithms and collaborative efforts.The ultimate goal is to create a comprehensive catalog of resident space objects(RSO)around the Earth and promote space environment sustainability.By exploring different methods and finding innovative solutions,this study contributes to the protection of space for future exploration and the creation of a more transparent and precise map of orbital objects.

Initial orbit determination of some cislunar orbits based on short-arc optical observations

Ground-and space-based optical observation is an efficient way to catalog objects in the cislunar space.Initial orbit determination based on optical data is still an open problem for cislunar objects.The motion of these objects usually follows the law of three bodies instead of the two-body one,so current algorithms based on the two-body relation should be revised.Moreover,due to the long duration of most cislunar objects,optical observations of even hours can cover only a small fraction of one orbit,making the initial orbit determination of these objects a typical too-short-arc problem,which is difficult.A way to address this problem is to use the admissible region.In this study,an efficient algorithm constrained by the admissible region is proposed.It is easy to implement because it uses only simple iterations.Its efficiency is proven by comparing it with that of one traditional initial orbit determination algorithm.

Perturbed initial orbit determination

An algorithm for robust initial orbit determination (IOD) under perturbed orbital dynamics is presented. By leveraging map inversion techniques defined in the algebra of Taylor polynomials, this tool returns a highly accurate solution to the IOD problem and estimates a range centered on the aforementioned solution in which the true orbit should lie. To meet the specified accuracy requirements, automatic domain splitting is used to wrap the IOD routines and ensure that the local truncation error, introduced by a polynomial representation of the state estimate, remains below a predefined threshold. The algorithm is presented for three types of ground-based sensors, namely range radars, Doppler-only radars, and optical telescopes, by considering their different constraints in terms of available measurements and sensor noise. Finally, the improvement in performance with respect to a Keplerian-based IOD solution is demonstrated using large-scale numerical simulations over a subset of tracked objects in low Earth orbit.

Precise orbit determination for Tianwen-1 during mapping phase

The mapping phase is a key stage of the Tianwen-1 orbiter. It has the longest exploration time and gathers abundant radio tracking data via the Chinese deep space network. Thus, it also provides opportunities for radio science research topics such as the Mars gravity field model, ephemeris, and radio occultation experiments. At this stage, the need for imaging takes the highest priority, leading to frequent attitude adjustments for the spacecraft, which presents challenges for Precise Orbit Determination (POD). To improve the accuracy of the spacecraft’s orbit, this study analyzes the effects of arc length, the empirical acceleration, and the solar radiation pressure parameters on POD, considering the limited number of radio tracking observations. For one-day arcs, the POD is not able to adequately account for wheel off-loading and a few unknown forces with limited observations, but reasonable fitting is performed for the wheel off-loading occurring during tracking periods or the gap between two tracking periods. When extending the POD arc to three days, the estimated empirical acceleration can be well-fitted and reflects the aggregation feature, but the solar radiation pressure parameter has little impact on POD results. The root mean square of two-way range-rate residuals after POD is about 0.18-0.35 mm/s;the orbital position accuracy of 60% of the arcs is better than 100 m.