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.

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.

HOI延迟对LEO卫星简化动力学POD的影响

通常使用无电离层(IF)线性组合(LC)消除低地球轨道(LEO)卫星简化动力学精密定轨(POD)一阶电离层延迟误差,忽略了高阶电离层(HOI)延迟误差。随着LEO卫星POD技术的发展,计算不同轨道高度的HOI延迟并探索其变化已成为进一步提高POD精度的重要手段。首先,使用国际参考电离层-2016(IRI-2016)和国际地磁参考场第13代(IGRF-13)模型,计算电离层穿刺点(IPP)位置和地磁场强度。其次,使用平滑星载GNSS数据计算电离层斜路径总电子含量(STEC)。然后,分别计算GOCE、GRACE-A和SWARM-A/B卫星的二阶和三阶电离层延迟。最后,评估了HOI延迟对LEO卫星重叠轨道分析、卫星激光测距(SLR)检核和精密科学轨道(PSO)比较结果的影响。实验结果表明:HOI延迟对LEO卫星简化动力学POD的影响大约在毫米至厘米的数量级上;HOI延迟对LEO卫星简化动力学POD外符合精度的影响分别达到0.92,0.22,0.21和0.18 mm;随着LEO卫星轨道高度的增加,HOI延迟对LEO卫星简化动力学POD的影响减小。

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.

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%。

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.

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。

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.

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.

面向导航增强的低轨卫星钟差确定及预报方法研究

低轨导航增强是未来导航发展的重要趋势,而高精度低轨卫星钟差是实现低轨导航增强的必要条件。基于Sentinel-6A卫星,对低轨卫星钟差特性进行了分析,给出了钟差确定方法及影响因素,介绍了顾及钟差特性的低轨卫星钟差预报方法。实验表明,低轨卫星钟差含有多个周期项,给低轨卫星建模和预报带来了困难。与使用运动学定轨模型相比,基于简化动力学的定轨模型可显著提升低轨卫星钟差精度;当基于运动学模型确定低轨卫星钟差时,相较于使用GPS单系统数据,多GNSS观测数据可提升低轨卫星钟差精度。研究表明,基于GPS和Galileo观测的Sen-tinel-6A卫星钟差精度相较于GPS单系统钟差精度改善了36%,同时,所使用的GNSS产品精度与低轨卫星钟差精度密切相关。利用顾及卫星钟差特性的低轨卫星钟差预报方法,当预报时长小于1min,低轨卫星钟差预报精度(预报与解算值之差的RMSE)在0.1ns之内,当预报时长小于5min,预报精度在0.3ns之内,随着预报时长的增长,预报精度显著下降。

一种基于偏航导引的SAR卫星成像参数更新方法

为了解决低轨合成孔径雷达(SAR)卫星在开启偏航导引情况下缺乏参数计算方法的问题,从现有某卫星的实际任务规划需求出发,分析了升降轨、左右侧视等情况下偏航导引对目标可视情况的影响,提出了一种面向低轨道SAR卫星偏航导引更新成像参数的计算方法,达到对指定目标位置准确成像的效果.仿真结果表明,地球自转引起的偏航对成像中心时刻和斜距影响较大.

双线程滑动窗口多系统GNSS超快精密定轨实现及评估

全球导航卫星系统(GNSS)超快精密定轨为GNSS实时应用提供了高精度空间基准。基于天地协同定位、导航与授时(PNT)网络服务中心实现了四系统GNSS卫星超快精密定轨,并对定轨结果进行精度评价。介绍了天地协同PNT网络的概念内涵以及网络服务中心部署的超快精密定轨软件架构和详细功能,并针对实时应用需求提出了一种双线程滑动窗口超快精密定轨策略。最后利用重叠弧段比较、与外部轨道产品比较以及卫星激光测距(SLR)检核3种方式对定轨结果进行了精度评价。结果表明,与武汉大学分析中心的最终事后精密轨道产品相比,四系统GNSS MEO卫星预报6 h弧段的径向均方根(RMS)误差整体在2~5 cm水平,BDS2 IGSO卫星最小一维RMS误差在10~15 cm水平;GPS和Galileo卫星的SLR检核残差均值在1~3 cm水平,标准差在3~6 cm水平,能够满足后续厘米级实时应用对空间基准的精度需求。

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%。

低轨卫星下行仿真数据精密定轨研究

低轨卫星导航定位是新一代卫星导航技术发展的重要方向,使用低轨卫星提供高精度定位、导航与授时(positioning,navigation and timing,PNT)服务,需要能够利用下行数据对其进行精密定轨.目前低轨卫星定轨相关研究多以星载GNSS数据和星间链路数据为研究对象,缺少针对低地球轨道(low earth orbit,LEO)下行数据定轨能力的分析.为分析低轨卫星下行数据定轨性能,模拟仿真了轨道高度1000 km、轨道倾角48°的Walker 90/10/1低轨卫星导航星座、150个地面测站及相应轨道、钟差和观测数据.分别使用测站数为60、90、120和150的全球测站网络观测数据进行LEO卫星精密定轨,并对定轨精度和可视测站卫星位置精度衰减因子(satellite position dilution of precision,SPDOP)值进行分析.结果表明:测站数从60增加至150可使LEO卫星轨道1d均方根(root mean square,RMS)从117.5 mm提升至39.8 mm;当测站稀疏时,LEO卫星定轨精度降低迅速;增加测站可以有效改善陆地范围可视测站SPDOP和LEO卫星定轨精度,但由于测站跟踪范围有限,海洋区域可视测站SPDOP和LEO卫星定轨精度难以获得改善,需引入新的观测数据源.研究结果可为低轨导航卫星系统建设提供支持.

BDS-3全球短报文2种低轨卫星几何法定轨

针对低轨卫星实时在线精密定轨难以获取实时改正数问题,提出基于北斗三号全球卫星导航系统(BDS-3)全球短报文播发距离改正数和状态空间表达(SSR)改正数的低轨卫星精密定轨方法。基于提出的距离改正数和SSR改正数编码播发方案,利用Swarm A卫星7 d星载全球卫星导航系统(GNSS)数据进行验证,从定轨精度以及处理效率2方面进行分析,结果表明:基于BDS-3全球短报文播发的改正数可以实现低轨卫星几何法定轨精度约为0.1 m,且基于SSR改正数的低轨卫星定轨精度优于距离改正数。非差非组合模型的定轨精度略优于无电离层(IF)组合定轨精度;当BDS-3全球短报文通信成功率为90%时,定轨精度下降约15%。在处理效率上,IF组合较非差非组合提升明显,2种方法在主频为1.6 GHz的个人笔记本上单历元处理时间均小于0.003 s。

基于北斗卫星导航系统的低轨卫星精密定轨精度分析

随着北斗卫星导航系统的建成运行,基于北斗卫星导航系统的低轨卫星精密定轨得以广泛应用。为有效评估基于北斗卫星导航系统的低轨卫星精密定轨精度,本文分别基于运动学法、动力学法和简化动力学法对低轨星载北斗观测数据进行了精密定轨处理,并通过重叠弧段法进行内符合精度评价,然后采用不同定轨方法对比的方式对精密定轨结果进行了验证分析。试验结果表明,3种精密定轨结果的位置互差均方根误差为1.4 cm,最大位置互差7 cm,说明基于北斗卫星导航系统的精密定轨精度可达到厘米级。