Precise orbit determination for LEO satellites:single-receiver ambiguity resolution using GREAT products

In recent years,the large Low Earth Orbit(LEO)constellations have become a hot topic due to their great potential to improve the Global Navigation Satellite Systems(GNSS)positioning performance.One of the important focus is how to obtain the accurate and reliable orbits for these constellations with dozens of LEO satellites.The GNSS-based Precise Orbit Determination(POD)will be exclusively performed to achieve this goal,where the Integer Ambiguity Resolution(IAR)plays a key role in acquiring high-quality orbits.In this study,we present a comprehensive analysis of the benefit of the single-receiver IAR in LEO POD and discuss its implication for the future LEO constellations.We perform ambiguity-fixed LEO POD for four typical missions,including Gravity Recovery and Climate Experiment(GRACE)Follow-On(GRACE-FO),Swarm,Jason-3 and Sentinel-3,using the Uncalibrated Phase Delay(UPD)products generated by our GREAT(GNSS+REsearch,Application and Teaching)software.The results show that the ambiguity fixing processing can significantly improve the accuracy of LEO orbits.There are negligible differences between our UPD-based ambiguity-fixed orbits and those based on the Observable Signal Bias(OSB)and Integer Recovery Clock(IRC)products,indicating the good-quality of UPD products we generated.Compared to the float solution,the fixed solution presents a better consistency with the external precise science orbits and the largest accuracy improvement of 5 mm is achieved for GRACE-FO satellites.Meanwhile,the benefit can be observed in laser ranging residuals as well,with a Standard Deviation(STD)reduction of 3–4 mm on average for the fixed solutions.Apart from the absolute orbits,the relative accuracy of the space baseline is also improved by 20–30%in the fixed solutions.The result demonstrates the superior performance of the ambiguity-fixed LEO POD,which appears as a particularly promising technique for POD of future LEO constellations.

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.

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.

Results and Analyses of BDS Precise Orbit Determination with the Enhancement of Fengyun-3C

Global navigation satellite system occultation sounder (GNOS) Fengyun-3C was launched successfully on September 23, 2013, which carried GPS/BDS receiver for the first time. This provides the convenience to study the enhancement results of low earth orbiter satellite (LEO) to BDS precise orbit determination (POD). First the data characteristic and code observation noise of GNOS are analyzed. Then the enhancement experiments in the case of global and regional ground observation stations layout are processed with four POD schemes: BDS single system, GPS/BDS double system, BDS single system with GNOS observations, GPS/BDS double system with GNOS observations. The precision of BDS orbits and clocks are compared via overlapping arcs. Results show that in the case of global station layout the along directional precision of GEO satellite has the biggest improvement, with the improvement percentage 60%. Then the precision of cross direction and the along direction of remaining satellites shows the second biggest improvement. The orbit precision of BDS-only POD in part of observation arcs some satellite even suffers a slight decline. The root mean square (RMS) of overlapping clock difference of visible arcs in GPS/BDS POD experiments improves by 0.1 ns level. As to the experiments of regional station layout with 7 ground stations, the orbit and clock overlapping precision and orbit predicting precision are analyzed. Results show that the predicting precision of BDS GEO satellites in the along direction improves by 85%. The remaining also has a substantial improvement, with the average percentage 21.7%. RMS of overlapping clock difference of visible arcs improves by 0.5 ns level.

Precise orbit determination for low Earth orbit satellites using GNSS:Observations,models,and methods

Spaceborne global navigation satellite system(GNSS)has significantly revolutionized the development of autonomous orbit determination techniques for low Earth orbit satellites for decades.Using a state-of-the-art combination of GNSS observations and satellite dynamics,the absolute orbit determination for a single satellite reached a precision of 1 cm.Relative orbit determination(i.e.,precise baseline determination)for the dual satellites reached a precision of 1 mm.This paper reviews the recent advancements in GNSS products,observation processing,satellite gravitational and non-gravitational force modeling,and precise orbit determination methods.These key aspects have increased the precision of the orbit determination to fulfill the requirements of various scientific objectives.Finally,recommendations are made to further investigate multi-GNSS combinations,satellite high-fidelity geometric models,geometric offset calibration,and comprehensive orbit determination strategies for satellite constellations.

Basic performance of BeiDou-2 navigation satellite system used in LEO satellites precise orbit determination

The visibility for low earth orbit（LEO） satellites provided by the BeiDou-2 system is analyzed and compared with the global positioning system（GPS）. In addition, the spaceborne receivers＇ observations are simulated by the BeiDou satellites broadcast ephemeris and LEO satellites orbits. The precise orbit determination（POD） results show that the along-track component accuracy is much better over the service area than the non-service area, while the accuracy of the other two directions keeps at the same level over different areas. However, the 3-dimensional（3D） accuracy over the two areas shows almost no difference. Only taking into consideration the observation noise and navigation satellite ephemeris errors, the 3D accuracy of the POD is about30 cm. As for the precise relative orbit determination（PROD）, the 3D accuracy is much better over the eastern hemisphere than that of the western hemisphere. The baseline length accuracy is 3.4 mm over the service area, and it is still better than 1 cm over the non-service area. This paper demonstrates that the BeiDou regional constellation could provide global service to LEO satellites for the POD and the PROD. Finally, the benefit of geostationary earth orbit（GEO） satellites is illustrated for POD.

Precise orbit determination for a large LEO constellation with inter-satellite links and the measurements from different ground networks:a simulation study

Geodetic applications of Low Earth Orbit(LEO)satellites requires accurate satellite orbits.Instead of using onboard Global Navigation Satellite System observations,this contribution treats the LEO satellite constellation independently,using Inter-Satellite Links and the measurements of different ground networks.Due to geopolitical and geographical reasons,a ground station network cannot be well distributed.We compute the impact of different ground networks(i.e.,global networks with different numbers of stations and regional networks in different areas and latitudes)on LEO satellite orbit determination with and without the inter-satellite links.The results are based on a simulated constellation of 90 LEO satellites.We find that the orbits determined using a high latitude network is worse than using a middle or low latitude network.This is because the high latitude network has a poorer geometry even if the availability of satellite measurements is higher than for the other two cases.Also,adding more stations in a regional network shows almost no improvements on the satellite orbits if the number of stations is more than 16.With the help of ISL observations,however,the satellite orbits determined with a small regional network can reach the same accuracy as that with the global network of 60 stations.Furthermore,satellite biases can be well estimated(less than 0.6 mm)and have nearly no impact on satellite orbits.It does thus not matter if they are not physically calibrated for estimating precise orbits.

LEO星载GPS实时精密定轨伪模糊度随机过程参数优化

提出在定轨策略及其他变量不变的情况下,使用一种数值步进的搜索比较方法,以确定伪模糊度随机过程参数的最优设置。使用GRACE-C、SWARM-A两颗LEO卫星2021年doy92~101共10 d的GPS数据及同时段的CNT、MADOCA两种实时精密星历产品,以模拟在轨实时精密定轨的方式,对伪模糊度随机过程参数开展优化实验。结果表明,在伪模糊度参数最优值方案下,两颗LEO卫星的实时精密定轨三维位置误差(RMS)约为4.62~7.56 cm,相比于传统模糊度浮点解方案,使用CNT和MADOCA产品的实时定轨精度分别平均提升约39.15%和29.61%。

LEO卫星通信终端的RTT定位技术

低地球轨道(LEO)卫星通信互联网是未来满足万物智联、天空地一体化网络连接的6G移动通信网络重要组成部分。LEO卫星通信终端的移动性管理是LEO卫星网络运行管理的基本功能,而获取卫星终端的位置是实现移动性管理的基础。目前,全球卫星导航系统(GNSS)能够提供比较高的定位精度,但是当GNSS位置服务在受到环境遮蔽、外部干扰时可能失效,因此卫星通信终端需要一种独立于外部GNSS服务的自主定位方案。以未来LEO卫星互联网的通信信号为背景,提出一种基于往返时延(Round Trip Time,RTT)测量的LEO卫星通信终端自主定位体制,对OFDM卫星互联网信号的时延估计算法精度以及定位误差进行了理论计算和数字仿真,获得了本定位方案的均方根误差(RMSE)和几何稀度因子(GDOP),计算结果表明可以实现百米量级的快速定位,满足了移动性管理所需的千米量级位置信息的应用需求。

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%.

Zero-difference and single-difference precise orbit determination for LEO using GPS

Various methods for precise orbit determination (POD) of low earth orbiters (LEO) are briefly intro-duced in this paper. Based on the software named SHORD-Ⅲ developed by our institute,sin-gle-difference (SD) and zero-difference (ZD) dynamic POD based on LEO carrying an on-board GPS receiver is mainly discussed. The approaches are tested using real GRACE data (November 5―25,2002) and independently validated with Satellite Laser Ranging (SLR) measurements over the same 21 days. Comparisons with the scientific orbits provided by GFZ indicate that the SD POD RMS accuracy can achieve 5,10 and 6 cm in radial,along and cross the track,and the ZD POD RMS accuracy can achieve 4,8 and 4 cm in radial,along and cross the track. SLR validation shows that SD POD accuracy is better than 8 cm in distance,and ZD POD accuracy is better than 6 cm.

LEO卫星单频精密定轨电离层模型改进算法

电离层延迟的有效改正是LEO卫星单频精密定轨的关键所在。目前主要采用电离层比例因子法进行LEO卫星电离层延迟改正,但该方法在电子密度峰值高度确定时未考虑太阳活动、经纬度、昼夜变化、季节等因素的影响。IRI2012模型虽然考虑了上述因素对电子密度峰值高度的影响,但因其与电离层薄层高度选择的标准不一致,通常它们之间存在系统性偏差而无法直接使用。为此本文提出将电离层薄层高度作为约束条件对IRI2012模型确定的电子密度峰值高度的均值进行参数约束估计,得到一种改进的电离层模型算法,并利用Swarm卫星GPS观测数据对其进行验证。结果表明:改进的电离层模型对Swarm卫星径向、切向和法向定轨精度均有不同程度的提高,尤其对轨道径向和法向精度改善最为明显,分别提高了31.6%和32.0%;同时较大幅度地降低了轨道的系统性偏差,尤其是在径向和法向,分别平均降低了65.0%和54.7%。

附加先验轨道约束的LEO几何法实时精密定轨验证分析

低轨卫星的实时精密定轨能够极大拓展其完成复杂科学任务的能力,例如实时环境监测、机动控制和卫星自主导航等.本文根据几何法实时精密定轨模型,提出了附加LEO先验轨道约束从而改善实时定轨的精度、收敛速度和稳定性的构想.分别采用广播星历、超快速星历预报部分和实时精密星历,设计了6种实时定轨方案,并利用Swarm-A, B, C星7天的观测数据进行方案验证与分析.结果表明,使用广播星历、IGU和IGC星历的方案精度递增,附加先验轨道约束能够进一步提升精度.使用IGC星历并附加标准差为1m的先验轨道约束后,在径向、切向和法向的定轨精度分别达到6.12 cm,5.55 cm和4.98 cm.此外,附加先验轨道约束能够显著提升收敛速度,使用IGC星历平均收敛时间约为31 min,附加标准差为1m的先验轨道约束后收敛仅需约4 min.

Precise orbit determination of a maneuvered GEO satellite using CAPS ranging data

Wheel-off-loadings and orbital maneuvers of the GEO satellite result in additional accelerations to the satellite itself. Complex and difficult to model, these time varying accelerations are an important error source of precise orbit determination (POD). In most POD practices, only non-maneuver orbital arcs are treated. However, for some applications such as satellite navigation RDSS services, uninterrupted orbital ephemeris is demanded, requiring the development of POD strategies to be processed both during and after an orbital maneuver. We in this paper study the POD for a maneuvered GEO satellite, using high precision and high sampling rate ranging data obtained with Chinese Area Positioning System (CAPS). The strategy of long arc POD including maneuver arcs is studied by using telemetry data to model the maneuver thrust process. Combining the thrust and other orbital perturbations, a long arc of 6 days’ CAPS ranging data is analyzed. If the telemetry data are not available or contain significant errors, attempts are made to estimate thrusting parameters using CAPS ranging data in the POD as an alternative to properly account for the maneuver. Two strategies achieve reasonably good data fitting level in the tested arc with the maximal position difference being about 20 m.

Orbit determination for geostationary satellites with the combination of transfer ranging and pseudorange data

Geostationary satellites(GEOs) play a significant role in the regional satellite navigation system.Simulation experiments show that the clock corrections could be mitigated through a single strategy or double differencing strategies for a navigation constellation,but for the mode of individual GEO orbit determination,high precision orbit and clock correction could not be obtained in the orbit determination based on the pseudorange data.A new GEO combined precise orbit determination(POD) strategy is studied in this paper,which combines pseudorange data and C-band transfer ranging data.This strategy overcomes the deficiency of C-band transfer ranging caused by limited stations and tracking time available.With the combination of transfer ranging and pseudorange data,clock corrections between the GEO and the stations can be estimated simultaneously along with orbital parameters,maintaining self-consistency between the satellite ephemeris and clock correction parameters.The error covariance analysis is conducted to illuminate the contributions from the transfer ranging data and the psudoranging data.Using data collected for a Chinese GEO satellite with 3 C-band transfer ranging stations and 4 L-band pseudorange tracking stations,POD experiments indicate that a meter-level accuracy is achievable.The root-mean-square(RMS) of the post-fit C-band ranging data is about 0.203 m,and the RMS of the post-fit pseudorange is 0.408 m.Radial component errors of the POD experiments are independently evaluated with the satellite laser ranging(SLR) data from a station in Beijing,with the residual RMS of 0.076 m.The SLR evaluation also suggests that for 2-h orbital predication,the predicted radial error is about 0.404 m,and the clock correction error is about 1.38 ns.Even for the combination of one C-band transfer ranging station and 4 pseudorange stations,POD is able to achieve a reasonable accuracy with the radial error of 0.280 m and the 2-h predicted radial error of 0.888 m.Clock synchronization between the GEO and tracking stations is achieved with an estimated accuracy of about 1.55 ns,meeting the navigation service requirements.

Precise orbit determination of Haiyang-2 using satellite laser ranging

With the successful launch and official commissioning of China's first dynamic ocean environment satellite Haiyang-2(HY-2),China's capabilities for oceanic environment monitoring and oceanic resource detecting have been further improved and enhanced.Precise tracking and orbit determination are not only key technical concerns in the ocean dynamic environment satellite project but also necessary conditions for carrying out related oceanic science research using observational data obtained using spaceborne instruments including radar altimeter.In this study,the current available status of international satellite laser ranging(SLR) monitoring on HY-2 was introduced.Six-months of SLR data from HY-2 were processed to obtain precise satellite orbit information using the dynamic orbit determination method.We carried out a detailed assessment of the SLR orbit accuracy by internal evaluation,comparisons with the orbit derived by the French Doppler orbitography and radio-positioning integrated by satellite(DORIS) system,and station-satellite distance validation.These assessments indicate that the three-dimensional orbital accuracy of HY-2 is about 12.5 cm,and the radial accuracy is better than 3 cm.It provides a good example of the application of international SLR monitoring and precise orbit determination in China's earth observation satellite project.

顾及不同LEO卫星数量及轨道误差的GPS/LEO联合PPP

为解决现有单系统GPS PPP收敛速度较慢的问题,选取不同卫星数量构成的LEO星座系统,根据观测值仿真原理得到待估点来自低轨卫星的伪距观测值和相位观测值;选取CPVG、WUH2、KOUG、IISC、FUCN测站,利用GPS及仿真附加轨道误差的LEO星座观测数据进行静态精密单点定位,以分析LEO星座的增强效果。结果表明:1)在原有GPS系统中加入LEO星座后,3种组合场景下平均可见卫星数量分别增加9.7、19.4、31.3颗,PDOP值分别减少0.7、0.9、1.1;2)收敛时间快速缩短,由单系统GPS卫星的17.1 min分别降至4.7 min、2.1 min、1.5 min,收敛时间分别缩短67.3%、84.4%、89.5%;3)E方向上的RMS值分别提升34.4%、59.4%、72.9%,N方向上分别提升37.4%、60.3%、67.3%,U方向上分别提升55.9%、71.7%、79.6%。LEO星座对GPS PPP的性能提升巨大,对于指导LEO星座增强GPS系统设计及拓展精密单点定位的应用场景具有一定价值。

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.

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.