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.

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.

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.

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.

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.

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.

Satellite Positioning and Orbit Determination System(SPODS):Introduction and Evaluation

The Satellite Positioning and Orbit Determination System(SPODS)is a software package for GNSS positioning/orbit determination,developed by the Xi’an Research Institute of Surveying and Mapping.So far it has been able to analyse GPS data and has the capability of high precision GPS positioning and orbit determination.The underlying theory and the performance evaluation are briefly addressed in this paper.The experiments are carried out with GPS data collected from about 127 IGS stations during 4~10 January 2009.The results show that the RMS 1D difference is 1.1 cm between SPODS orbits and final IGS combined orbits,and that the repeatability of daily solutions of station coordinates is 1.5 mm for horizontal components,and 4.5 mm for vertical component,and that the consistency of ERP solutions with IGS final products is 0.025 mas,0.093 mas and 0.013 ms/d respectively for pole coordinates and LOD.

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.

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.

A review of real-time multi-GNSS precise orbit determination based on the filter method

Stable and reliable high-precision satellite orbit products are the prerequisites for the positioning services with high performance.In general,the positioning accuracy depends strongly on the quality of satellite orbit and clock products,especially for absolute positioning modes,such as Precise Point Positioning(PPP).With the development of real-time services,real-time Precise Orbit Determination(POD)is indispensable and mainly includes two methods:the ultra-rapid orbit prediction and the real-time filtering orbit determination.The real-time filtering method has a great potential to obtain more stable and reliable products than the ultra-rapid orbit prediction method and thus has attracted increasing attention in commercial companies and research institutes.However,several key issues should be resolved,including the refinement of satellite dynamic stochastic models,adaptive filtering for irregular satellite motions,rapid convergence,and real-time Ambiguity Resolution(AR).This paper reviews and summarizes the current research progress in real-time filtering POD with a focus on the aforementioned issues.In addition,the real-time filtering orbit determination software developed by our group is introduced,and some of the latest results are evaluated.The Three-Dimensional(3D)real-time orbit accuracy of GPS and Galileo satellites is better than 5 cm with AR.In terms of the convergence time and accuracy of kinematic PPP AR,the better performance of the filter orbit products is validated compared to the ultra-rapid orbit products.

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.

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).

顾及BDS-3星钟约束的GNSS超快速轨道钟差解算方法

BDS-3高稳定星载原子钟作为北斗星座的显著技术优势,在GNSS数据处理中尚未得到充分利用。针对严格时效性限制下GNSS超快速轨道钟差参数精度受限问题,本文提出顾及BDS-3星钟约束的GNSS超快速轨道钟差解算方法。首先,以GNSS轨道钟差参数间相关性为基础,构建顾及BDS-3星钟参数特性的GNSS定轨模型;然后,基于GNSS精密钟差产品,分析星钟约束对GNSS轨道钟差参数精度的影响规律;最后,为克服预报钟差精度与约束筛选对定轨影响,建立BDS-3星钟建模与GNSS超快速轨道钟差估计的同步处理方法。试验结果表明,在BDS-3星钟参数最优约束下,BDS-3与GPS轨道钟差精度可分别提升27.5%、5.1%和20.2%、5.2%;且较传统BDS-3星钟单历元处理策略,基于BDS-3星钟建模与GNSS超快速定轨同步处理方法,GNSS超快速轨道钟差精度可分别提升至4.8%与34.2%,轨道精度实现了毫米级改善。因此,顾及BDS-3星钟约束的GNSS超快速轨道钟差解算方法可有效对BDS-3高稳星钟信息模型化,并实现GNSS超快速轨道钟差精度的优化处理。

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。

动量轮卸载对“天问一号”环火轨道影响分析

针对“天问一号”动量轮频繁喷气卸载对环火轨道的扰动问题,定性分析了动量轮卸载的摄动量级以及对环火段轨道的影响,在RTN(Radial Transverse Normal)坐标系下建立匀加速模型描述动量轮卸载产生的加速度,对环火中继段和遥感使命段分别采用2种策略计算分析,评估了不同飞行阶段的定轨预报精度。结果表明:频繁的动量轮卸载是影响环火段定轨精度的主要误差因素,目前条件下中继段定轨的位置精度为约150 m,在卸载更为频繁的遥感使命段,位置精度下降至约700 m。

近地小行星天地基协同监测和轨道确定试验

基于中国科学院国家天文台空间碎片试验望远镜,联合“仰望一号”“吉林一号”卫星,设计并开展了近地小行星天地基协同监测试验,利用图像处理和定轨方法,实现了天地基观测图像的目标检测和天文定位,完成了近地小行星轨道的精确确定。经分析,基于现有的天地基设备可实现对近地小行星的协同监测和轨道编目,为研判近地小行星撞击风险提供轨道数据支持。

Problem of algorithm in precision orbit determination

In orbit determination, the precision ephemeris and state transition matrix are usually obtained by solving two groups of ordinary differential equations with numerical integration method due to the complexity of the force models. A kind of simplified analytical method to compute the state transition matrix is given. The method is not only very efficient for the case where the orbit arc is not too long, but also can avoid the integration of two groups of ordinary differential equations at the same time. Some practical test examples also show the efficiency of the method.

基于国产ARM架构CPU的导航卫星精密定轨解算效率优化方法

以国产飞腾CPU为例,讨论在国产ARM架构CPU基础上的导航卫星精密定轨解算效率优化方法。基于导航卫星精密定轨解算流程中钟差约化和法方程求逆耗时较多,分别利用多线程和OpenBlas对上述2个过程进行优化。结果表明,优化后解算效率大幅提升。钟差约化方面,采用100个测站32颗导航卫星进行解算时,原始单历元平均耗时1.105 s,优化后为0.188 s;法方程求逆方面,原始求逆平均耗时2 264 s,优化后仅需78 s。

VLBI观测对转发式测距GEO卫星定轨精度的贡献分析

联合甚长基线干涉测量(very long baseline interferometry,VLBI)时延数据与转发式(orbit determination by transfer tracking,ODTT)测距数据能够有效提高地球静止轨道(geostationary earth orbit,GEO)卫星定轨精度。参照位置精度衰减因子(position dilution of precision,PDOP)的改变,研究不同VLBI基线时延数据与转发式测距数据的联合对GEO卫星定轨精度的改善,可为特定条件下联合观测时VLBI基线的最优选择提供参考。基于中国科学院国家授时中心宽带VLBI系统和转发式测轨系统的实测数据,开展中星12号GEO卫星的定轨试验。试验结果表明定轨精度的提高与PDOP的降低成正相关。相比于转发式单独定轨,联合VLBI系统中的喀什—三亚基线,PDOP降低了3.00,定轨精度提高了11.48%;联合VLBI系统中的吉林—喀什基线,PDOP降低了3.38,定轨精度提高了14.73%;联合VLBI系统中的吉林—三亚基线,PDOP降低了6.90,定轨精度提高了19.75%;联合VLBI系统中的吉林—三亚和吉林—喀什两条基线,PDOP降低了9.94,定轨精度提高了27.23%。