Near real-time BDS GEO satellite orbit determination and maneuver analysis with reversed point positioning

The Geostationary Earth Orbit (GEO) satellite is a crucial part of the BeiDou Navigation Satellite System (BDS) constellation. However, due to various perturbation forces acting on the GEO satellite, it drifts gradually over time. Thus, frequent orbit maneuvers are required to maintain the satellite at its designed position. During the orbit maneuver and recovery periods, the orbit quality of the maneuvered satellite computed with broadcast navigation ephemeris will be significantly degraded. Furthermore, the conventional dynamic Precise Orbit Determination (POD) approach may not work well, because of a lack of publicly available satellite information for modeling the thrust forces. In this paper, a near real-time approach free of thrust forces modeling is proposed for BDS GEO satellite orbit determination and maneuver analysis based on the Reversed Point Positioning (RPP). First, the station coordinates and receiver clock offsets are estimated by GPS/BDS combined Single Point Positioning (SPP) with single-frequency phase-smoothed pseudorange observations. Then, with the fixed station coordinates and receiver clock offsets, the RPP method can be conducted to determine the GEO satellite orbits. When no orbit maneuvers occur, the proposed method can obtain orbit accuracies of 0.92, 2.74, and 8.30?m in the radial, along-track, and cross-track directions, respectively. The average orbit-only Signal-In-Space Range Error (SISRE) is 1.23?m, which is slightly poorer than that of the broadcast navigation ephemeris. Using four days of GEO maneuvered datasets, it is further demonstrated that the derived orbits can be employed to characterize the behaviors of GEO satellite maneuvers, such as the time span of the maneuver as well as the satellite thrusting accelerations. These results prove the efficiency of the proposed method for near real-time GEO satellite orbit determination during maneuvers.     

Analysis on navigation accuracy of high orbit spacecraft based on BDS GEO and IGSO satellites

To make up for the insufficiency of earth-based TT&C systems, the use of GNSS technology for high-orbit spacecraft navigation and orbit determination has become a new technology. It is of great value to applying Geosynchronous Earth Orbit (GEO) and Inclined GeoStationary Orbit (IGSO) navigation satellites for supporting the navigation of high-orbit spacecraft since there are three different types of navigation satellites in BeiDou Navigation Satellite System (BDS): Medium Earth Orbit (MEO), GEO and IGSO. This paper conducts simulation experiments based on Two-Line Orbital Element (TLE) data to analyze and demonstrate the role of these satellites in the navigation of high-orbit spacecraft. Firstly, the spacecraft in GEO was used as the target satellite to conduct navigation experiments. Experiments show that for the spacecraft on the GEO orbit, after adding GEO and IGSO respectively on the basis of receiving MEO navigation satellite signals, the accuracies were improved by 7.22 % and 6.06 % respectively. When adding both GEO and IGSO navigation satellites at the same time, the accuracy can reach 16 m. In the second place, navigation and positioning experiments were carried out on three high elliptical orbit (HEO) satellites with different semimajor axis (32037.2 km, 42385.9 km, 67509.6 km). The experiments show that the number of visible satellites has been improved significantly after adding GEO and IGSO navigation satellites at the same time. The visible satellites in these three orbits were improved by 32.84 %, 41.12 % and 37.68 %, respectively compared with only observing MEO satellites.The RMS values of the navigation positioning errors of these three orbits are 25.59 m, 87.58 m and 712.48 m, respectively.     

Orbit determination of BDS-3 satellite based on regional ground tracking station and inter-satellite link observations

The BeiDou global navigation satellite system (BDS-3) has established the Ka-band inter-satellite link (ISL) to realize a two-way ranging function between satellites, which provides a new observation technology for the orbit determination of BDS-3 satellites. Therefore, this study presents a BDS satellite orbit determination model based on ground tracking station (GTS) observations and ISL ranging observations firstly to analyze the impact of the ISL ranging observations on the orbit determination of BDS-3 satellites. Subsequently, considering the data fusion processing, the variance component estimation (VCE) algorithm is applied to the parameter estimation process of the satellite orbit determination. Finally, using the measured data from China’s regional GTS observations and BDS-3 ISL ranging observations, the effects of ISL ranging observations on the orbit determination accuracy of BDS-3 satellites are analyzed. Moreover, the impact of the VCE algorithm on the fusion data processing is evaluated from the aspects of orbit determination accuracy, Ka-band hardware delay parameter stability, and ISL ranging observation residuals. The results show that for China’s regional GTSs, the addition of BDS-3 ISL ranging observations can significantly improve the orbit determination accuracy of BDS-3 satellites. The observed orbit determination accuracy of satellite radial component is improved from 48 cm to 4.1 cm. In addition, when the initial weight ratio between GTS observations and ISL ranging observations is not appropriate, the various indicators which include orbit determination accuracy, ISL hardware delay, and ISL observation residuals were observed to have improved after the adjustment of the VCE algorithm. These results validate the effectiveness of the VCE algorithm for the fusion data processing of the GTS observations and ISL ranging observations.     

Analysis of BDS-3 distributed autonomous navigation based on BeiDou system simulation platform

Satellite autonomous navigation is an important function of the BeiDou-3 navigation System (BDS-3). Satellite autonomous navigation means that the navigation satellite uses long-term forecast ephemeris and Inter-Satellite Link (ISL) measurements to determinate its own spatial position and time reference without the support of the ground Operation and Control System (OCS) for a long time to ensure that the navigation system can normally maintain the time and space reference. This paper aims to analyze the feasibility of distributed autonomous navigation algorithms. For the first time, a ground parallel autonomous navigation test system (GPANTS) is built. The performance of distributed autonomous navigation is then analyzed using the two-way ISL ranging of BDS-3 satellites. First, the BDS simulation platform and the GPANTS are introduced. Then, the basic principles of distributed satellite autonomous orbit determination and time synchronization based on ISL measurements are summarized. Preliminary evaluation of the performance of the BDS-3 constellation autonomous navigation service under ideal conditions through simulation data. Then the performance of autonomous navigation for 22 BeiDou-3 satellites using ISL measurements is evaluated. The results show that when satellites operate autonomously for 50 days without the support of any ground station, the User Range Error (URE) of autonomous orbit determination is better than 3 m, and the time synchronization accuracy is better than 4 ns.     

Instantaneous BeiDou–GPS attitude determination: A performance analysis

The advent of modernized and new global navigation satellite systems (GNSS) has enhanced the availability of satellite based positioning, navigation, and timing (PNT) solutions. Specifically, it increases redundancy and yields operational back-up or independence in case of failure or unavailability of one system. Among existing GNSS, the Chinese BeiDou system (BDS) is being developed and will consist of geostationary (GEO) satellites, inclined geosynchronous orbit (IGSO) satellites, and medium-Earth-orbit (MEO) satellites. In this contribution, a BeiDou–GPS robustness analysis is carried out for instantaneous, unaided attitude determination.     

基于机动力模型的GEO卫星恢复期间定轨

北斗卫星导航系统(BDS)中GEO卫星频繁的轨道机动对高精度、实时不间断的导 航服务需求提出了更高要求, 如何在短弧跟踪条件下提高GEO卫星轨道快速 恢复能力, 是提升导航系统服务精度的关键因素. 针对该问题, 本文提出了基 于机动力模型的动力学定轨方法, 尝试利用高精度的C波段转发式测距数据, 辅 以机动期间的遥测遥控信息建立机动力模型, 联合轨控前后的观测数据进行动 力学长弧定轨. 利用BDS中GEO卫星实测数据进行了定轨试验与分析, 结果表明, 恢复期间需要采用解算机动推力的定轨方法, 联合机动前、机动期间和机 动后4h数据定轨的轨道位置精度在20m量级, 径向精度优于2.5m. 该方 法克服了短弧跟踪条件下动力学法定轨和单点定位中的诸多问题, 提供了解决 GEO卫星机动后轨道快速恢复问题的技术方法.      

北斗GEO卫星CEI相时延解算方法研究

连线端站干涉测量(connected element interferometry，CEI)是高精度测角技术，在中高轨卫星、月球及深空航天器定轨定位中有良好的应用前景。基于CEI技术特点，提出了一种新的测量方法，即在相干测距模式下利用测距音和载波信号作为信号源进行连线端站干涉测量。构建了CEI试验系统对北斗GEO卫星进行观测，利用相干测距模式下的下行信号解算群时延、相时延。利用北斗GEO卫星精密星历计算的时延理论值，对北斗GEO卫星CEI群时延和相时延结果进行评估。结果表明，相干测距模式下CEI群时延和相时延残差均值分别为0.47ns、0.08ns，标准差(3σ)分别4.2ns、0.13ns。该项研究验证了相干测距模式下CEI相时延解算的可行性，可为共位地球同步卫星精密相对定位、月球探测器CEI测量提供技术参考。     

Design and performances of laser retro-reflector arrays for Beidou navigation satellites and SLR observations

Beidou is the regional satellite navigation system in China, consisting of three kinds of orbiting satellites, MEO, GEO and IGSO, with the orbital altitudes of 21500–36000 km. For improving the accuracy of satellites orbit determination, calibrating microwave measuring techniques and providing better navigation service, all Beidou satellites are equipped with laser retro-reflector arrays (LRAs) to implement high precision laser ranging. The paper presents the design of LRAs for Beidou navigation satellites and the method of inclined installation of LRAs for GEO satellites to increase the effective reflective areas for the regional ground stations. By using the SLR system, the observations for Beidou satellites demonstrated a precision of centimeters. The performances of these LRAs on Beidou satellites are very excellent.     

Satellite availability and positioning performance of uncombined precise point positioning using BeiDou-2 and BeiDou-3 multi-frequency signals

To realize the smooth transition from regional BeiDou Navigation Satellite System (BDS-2) to the global one (BDS-3), the integration of BDS-2 and BDS-3 is important for providing continuous, stable and reliable positioning, navigation and timing (PNT) services for global users. This work used 154 globally distributed multi-GNSS (Global Navigation Satellite System) experiment stations spanning 30 days to analyze the satellite availability and positioning performance of uncombined precise point positioning (UC-PPP) under current BDS-2 and BDS-3 constellations. We focused on three issues: the influence of BDS-3 receiver tracking abilities, the positioning performance among different areas, and the benefit of multi-frequency observations. The results show that the elliptical zone caused by poor BDS-2 satellite visibility is disappeared when the evenly distributed BDS-3 medium earth orbit satellites are introduced. When BDS-3 are integrated with BDS-2, the area with the Position Dilution of Precision (PDOP) less than 2 can be expanded to 75° S-75° N and 30° E-150° W. The positioning performance of BDS-3 and BDS-2/BDS-3 UC-PPP are seriously affected by the receiver tracking abilities of BDS-3 signals. When the maximum pseudo-random noise sequences (PRNs) of BDS-3 satellites tracked by stations are within 30 or 37, the positioning accuracy of static UC-PPP can be improved by 22.94% or 8.27% due to the integration of BDS-2 and BDS-3. Besides, the most improvement of BDS-2 and BDS-3 integration is achieved in Asia-Pacific regions, especially for the kinematic UC-PPP or the poor receiver tracking abilities of BDS-3. Similar to the multi-frequency BDS-2 UC-PPP, the benefit of multi-frequency signals for BDS-3 or BDS-2/BDS-3 UC-PPP is also non-vital. The three-dimensional positioning accuracy of BDS-2/BDS-3 multi-frequency UC-PPP in static mode and kinematic mode are 2.24 cm and 5.39 cm, while the corresponding convergence time are 49.62 min and 73.80 min, respectively. Compared with BDS-2, both the positioning accuracy and the convergence time of BDS-2/BDS-3 joint UC-PPP are improved by approximately over 50%, which indicates that BDS-3 has a great potential to provide high-quality PNT services as other global navigation satellite systems.     

Orbit determination and prediction of GEO satellite of BeiDou during repositioning maneuver

In order to establish a continuous GEO satellite orbit during repositioning maneuvers, a suitable maneuver force model has been established associated with an optimal orbit determination method and strategy. A continuous increasing acceleration is established by constructing a constant force that is equivalent to the pulse force, with the mass of the satellite decreasing throughout maneuver. This acceleration can be added to other accelerations, such as solar radiation, to obtain the continuous acceleration of the satellite. The orbit determination method and strategy are illuminated, with subsequent assessment of the orbit being determined and predicted accordingly. The orbit of the GEO satellite during repositioning maneuver can be determined and predicted by using C-Band pseudo-range observations of the BeiDou GEO satellite with COSPAR ID 2010-001A in 2011 and 2012. The results indicate that observations before maneuver do affect orbit determination and prediction, and should therefore be selected appropriately. A more precise orbit and prediction can be obtained compared to common short arc methods when observations starting 1 day prior the maneuver and 2 h after the maneuver are adopted in POD (Precise Orbit Determination). The achieved URE (User Range Error) under non-consideration of satellite clock errors is better than 2 m within the first 2 h after maneuver, and less than 3 m for further 2 h of orbit prediction.     

Precise orbit determination and precision comparison for FY3C and FY3D with receiver antenna GPS and BDS PCV using spaceborne BDS and GPS observation data

The FY3C and FY3D satellites were equipped with global navigation satellite occultation detector (GNOS) receivers that received both GPS and BDS-2 signals. For further improving precise orbit determination (POD) precisions, we estimated receiver GPS and BDS signal phase center variations (PCV) models with 2° and 5° resolutions and set the different weights for GPS and BDS-2 observations in the combined POD. The BDS-based POD precision using BDS-2 satellite antenna phase center offset (PCO) values from the China Satellite Navigation Office (CSNO) are not as accurate as those obtained from the International GNSS Service (IGS) Multi-GNSS experiments project (MGEX). The estimated receiver GPS and BDS PCV models with 2° and 5° resolutions were estimated from the GPS phase residuals of GPS-based POD and BDS phase residuals of combined POD, respectively. In most cases, the POD precisions using the estimated PCVs with 2° resolution are superior to those with 5° resolution. The precisions of the BDS-based POD and combined POD were both improved by introducing the receiver BDS PCV models. The weighting for GPS and BDS-2 observations can further improve the precision of the combined POD. The tested results of selected weights are better than those with equal weight in the combined POD. The experiment results show that orbital precisions of FY3C are worse than those of FY3D.     

基于北斗三号导航系统的卫星定位技术

对北斗三号体制下的传输链路、接收门限进行理论分析,得出捕获算法采用4次非相干累加,可以使捕获灵敏度达到-130 dBm,同时实现定位时间小于5 min的综合较优结果.接着以低轨太阳同步轨道卫星为例,利用STK建模进行全轨道周期仿真,结果显示全程收星数超过4颗,定位精度达到2.59 m,速度误差为0.00378 m/s....     

北斗卫星导航系统实时定轨与钟差处理策略

目前鲜有对北斗卫星导航系统（BeiDouNavigationSatelliteSystem,BDS）实时精密定轨与钟差确定的研究,文章提出了BDS实时轨道与实时钟差处理策略,包括了观测与动力学模型、实时轨道与实时钟差处理流程与评估方法。尤其对于实时钟差,为了提高计算效率,联合使用两个独立并行的线程估计非差绝对钟差和历元间相对钟差。利用多模全球卫星导航系统试验(MGEX)与全球连续检测评估系统（iGMAS）实测数据进行了北斗实时轨道与钟差解算,BDS实时轨道径向平均精度对于GEO卫星优于20cm,对于IGSO与MEO一般优于10cm;钟差精度对于GEO卫星为0.5~4.5ns,对于IGSO／MEO为0.2~2.0ns。基于目前的轨道与钟差结果,实时精密单点定位（PrecisePointPositioning,PPP）结果可以达到分米量级。     

GEO卫星快速发射入轨定点控制方法

提出了一种GEO卫星快速发射入轨定点方法,运载火箭将卫星发射进入GTO轨道后,由上面级或卫星自身在48h内快速定点到GEO轨道任意指定定点位置。考虑时间、测控等约束,在选定变轨策略基础上,以燃料消耗最小为目标,优化给出了快速入轨定点标称轨迹。采用无奇异的春分点根数描述轨道运动,基于最小二乘法给出了航天器在有限推力条件下变轨的闭环显式制导方法,控制航天器沿标称轨迹飞行。仿真算例表明,采用该变轨策略、轨道优化设计方法和制导律,可以完成GEO卫星快速入轨定点控制。     

BeiDou-3 orbit and clock quality of the IGS Multi-GNSS Pilot Project

Within the Multi-GNSS Pilot Project (MGEX) of the International GNSS Service (IGS), precise orbit and clock products for the BeiDou-3 global navigation satellite system (BDS-3) are routinely generated by a total of five analysis centers. The processing standards and specific properties of the individual products are reviewed and the BDS-3 orbit and clock product performance is assessed through direct inter-comparison, satellite laser ranging (SLR) residuals, clock stability analysis, and precise point positioning solutions. The orbit consistency evaluated by the signal-in-space range error is on the level of 4–8 cm for the medium Earth orbit satellites whereas SLR residuals have RMS values between 3 and 9 cm. The clock analysis reveals sytematic effects related to the elevation of the Sun above the orbital plane for all ACs pointing to deficiencies in solar radiation pressure modeling. Nevertheless, precise point positioning with the BDS-3 MGEX orbit and clock products results in 3D RMS values between 7 and 8 mm.     

The influence of orbital maneuver on autonomous orbit determination of an extended satellite navigation constellation

The right ascension of the ascending node is unobservable if only the inter-satellite ranging is used for autonomous orbit determination (AOD) of an Earth navigation constellation. However, if an Earth-Moon libration point satellite is added to the Earth navigation constellation to construct an extended navigation constellation, all the orbital elements can be determined with only the inter-satellite ranging. Furthermore, the extended navigation constellation can provide navigation information for interplanetary probes. For such an extended navigation constellation, orbital control needs to be considered due to the instability of the libration-point satellite orbit. This study concerns the influence of satellite orbital maneuver on the AOD of the extended navigation constellation. An AOD method under orbital maneuver is proposed. A low thrust controller is designed to achieve libration point satellite autonomous orbit maintenance by using AOD results. A navigation constellation consisting of three GPS satellites and one libration point satellite are designed for simulation. The simulation results show that libration point satellites can achieve autonomous navigation and autonomous orbit maintenance by only using inter-satellite ranging information. The rotation drift error of the Earth navigation constellation is also suppressed.     

Performance assessment of real-time orbit determination for the Haiyang-2D using onboard BDS-3/GPS observations

The Global Navigation Satellite System (GNSS) receivers equipped on the Haiyang-2D (HY-2D) satellite is capable of tracking the signals of both the third generation of BeiDou satellite navigation System (BDS-3) and the Global Positioning System (GPS), which make it feasible to assess the performance of real-time orbit determination (RTOD) for the HY-2D using onboard GNSS observations. In this study, the achievable accuracy and convergence time of RTOD for the HY-2D using onboard BDS-3 and GPS observations are analyzed. Benefiting from the binary-offset-carrier (BOC) modulation, the BDS-3 C1X signal includes less noise than the GPS C1C signal, which has the same signal frequency and chipping rate. The root mean squares (RMS) of the noises of C1X and C1C code measurements are 0.579 m and 1.636 m, respectively. Thanks to a ten-times higher chipping rate, the code measurements of BDS-3 C5P, GPS C1W and C2W are less noisy. The RMS of code noises of BDS-3 C5P, GPS C1W, and C2W are 0.044 m, 0.386 m, and 0.272 m, respectively. For the HY-2D orbit, the three-dimensional (3D) and radial accuracies can reach 31.8 cm and 7.5 cm with only BDS-3 observations, around 50 % better than the corresponding accuracies with GPS. Better performance of the BDS-3 in RTOD for the HY-2D is attributed to the high quality of its broadcast ephemeris. When random parameters are used to absorb ephemeris errors, substantial improvement is seen in the accuracy of HY-2D orbit with either BDS-3 or GPS. The 3D RMS of HY-2D orbit errors with BDS-3 and GPS are enhanced to 23.1 cm and 33.6 cm, and the RMS of the radial components are improved to 6.1 cm and 13.3 cm, respectively. The convergence time is 41.6 and 75.5 min for the RTOD with BDS-3 and GPS, while it is reduced to 39.2 and 27.4 min after the broadcast ephemeris errors are absorbed by random parameters. Overall, the achievable accuracy of RTOD with BDS-3 reaches decimeter level, which is even better than that with GPS, making real-time navigation using onboard BDS-3 observations a feasible choice for future remote sensing missions.     

An empirical solar radiation pressure model for satellites moving in the orbit-normal mode

We present a family of empirical solar radiation pressure (SRP) models suited for satellites orbiting the Earth in the orbit normal (ON) mode. The proposed ECOM-TB model describes the SRP accelerations in the so-called terminator coordinate system. The choice of the coordinate system and the SRP parametrization is based on theoretical assumptions and on simulation results with a QZS-1-like box-wing model, where the SRP accelerations acting on the solar panels and on the box are assessed separately. The new SRP model takes into account that in ON-mode the incident angle of the solar radiation on the solar panels is not constant like in the yaw-steering (YS) attitude mode. It depends on the elevation angle of the Sun above the satellite’s orbital plane. The resulting SRP vector acts, therefore, not only in the Sun-satellite direction, but has also a component normal to it. Both components are changing as a function of the incident angle. ECOM-TB has been used for precise orbit determination (POD) for QZS-1 and BeiDou2 (BDS2) satellites in medium (MEO) and inclined geosynchronous Earth orbits (IGSO) based on IGS MGEX data from 2014 and 2015. The resulting orbits have been validated with SLR, long-arc orbit fits, orbit misclosures, and by the satellite clock corrections based on the orbits. The validation results confirm that—compared to ECOM2—ECOM-TB significantly (factor 3–4) improves the POD of QZS-1 in ON-mode for orbits with different arc lengths (one, three, and five days). Moderate orbit improvements are achieved for BDS2 MEO satellites—especially if ECOM-TB is supported by pseudo-stochastic pulses (the model is then called ECOM-TBP). For BDS2 IGSOs, ECOM-TB with its 9 SRP parameters appears to be over-parameterized. For use with BDS2 IGSO spacecraft we therefore developed a minimized model version called ECOM-TBMP, which is based on the same axis decomposition as ECOM-TB, but has only 2 SRP parameters and is supported by pseudo-stochastic parameters, as well. This model shows a similar performance as ECOM-TB with short arcs, but an improved performance with (3-day) long-arcs. The new SRP models have been activated in CODE’s IGS MGEX solution in Summer 2018. Like the other ECOM models the ECOM-TB derivatives might be used together with an a priori model.     

混合星座导航卫星广播星历相关问题研究

GPS卫星广播星历参数具有参数少、物理意义明确以及精度高等特点,可以考虑将它应用于包含MEO、IGSO和GEO卫星的混合星座卫星导航系统。分析了采用GPs卫星广播星历参数时MEO、IGSO和GEO卫星的广播星历拟合精度,并且比较分析了在一个卫星的轨道周期内,广播星历参数拟合结果的变化规律。仿真结果表明,MEO、IGSO和GEO卫星的广播星历拟合误差最大在分米量级;MEO和IGSO卫星在一个轨道周期内星历参数拟合结果的变化规律相近,但是与GEO卫星的差异较大。