Evaluation of CHAMP satellite orbit with SLR measurements

The technique of Evaluating CHAMP satellite orbit with SLR measurements iS presented. As an independent evaluation of the orbit solution, SLR data observed from January 1 to 16, 2002 are processed to compute the residuals after fixing the GFZ＇s post science orbits solutions. The SLR residuals are computed as the differences of the SLR measurements minus the corresponding distances between the SLR station and the GPS-derived orbit positions. On the basis of the SLR residuals analysis, it is found that the accuracy of GFZ＇ s post science orbits is better than 10 cm and that there is no systematic error in GFZ＇s post science orbits.     

High precision orbit determination of CHAMP satellite

IntroductionCHAMP satellite was launched on July 15 ,2000 to study the earth gravity field, magneticfield, and at mosphere/ionosphere . CHAMPmission is managed by GeoForshungsZentrum(GFZ) Potsdam withinternational partners .In-cluding accelerometer ,star …     

CHAMP卫星cm级精密定轨

在卫星定位导航数据综合处理软件（PANDA软件）的基础上，解算了2002年年积日126～131d CHAMP卫星的精密轨道，并通过与GFZ精密轨道的比较、GPS观测值的验后残差和SLR观测值检验等3种方式进行了轨道精度的评估。结果显示，本文的轨道精度在径向为4～5cm，切向和法向为6～8cm。     

Swarm系列卫星非差运动学厘米级精密定轨

采用2015年5月24日—30日的Swarm星载GPS双频观测数据,基于Melbourne-Wübbena(MW)和消电离层线性组合,在精密单点定位技术的基础上,采用批处理最小二乘估计法对不同轨道高度的Swarm系列卫星进行非差运动学精密定轨。利用星载GPS相位观测值残差、与欧空局发布的简化动力学轨道对比,以及SLR检核3种方法对Swarm系列卫星非差运动学定轨结果进行精度评估。结果表明:①Swarm系列卫星星载GPS相位观测值残差RMS为6~7 mm;②与欧空局发布的简化动力学轨道进行求差,径向、切向及法向轨道差值RMS为2~4 cm;③与欧空局发布的运动学轨道进行求差,径向、切向及法向轨道差值RMS为1~2 cm;④SLR检核结果表明Swarm-A/B/C卫星轨道精度为3~4 cm。因此,采用非差运动学定轨方法与本文提供的定轨策略进行Swarm系列卫星精密定轨是切实可行的,定轨精度为厘米级。     

Initial results of centralized autonomous orbit determination of the new-generation BDS satellites with inter-satellite link measurements

Autonomous orbit determination is the ability of navigation satellites to estimate the orbit parameters on-board using inter-satellite link (ISL) measurements. This study mainly focuses on data processing of the ISL measurements as a new measurement type and its application on the centralized autonomous orbit determination of the new-generation Beidou navigation satellite system satellites for the first time. The ISL measurements are dual one-way measurements that follow a time division multiple access (TDMA) structure. The ranging error of the ISL measurements is less than 0.25 ns. This paper proposes a derivation approach to the satellite clock offsets and the geometric distances from TDMA dual one-way measurements without a loss of accuracy. The derived clock offsets are used for time synchronization, and the derived geometry distances are used for autonomous orbit determination. The clock offsets from the ISL measurements are consistent with the L-band two-way satellite, and time–frequency transfer clock measurements and the detrended residuals vary within 0.5 ns. The centralized autonomous orbit determination is conducted in a batch mode on a ground-capable server for the feasibility study. Constant hardware delays are present in the geometric distances and become the largest source of error in the autonomous orbit determination. Therefore, the hardware delays are estimated simultaneously with the satellite orbits. To avoid uncertainties in the constellation orientation, a ground anchor station that “observes” the satellites with on-board ISL payloads is introduced into the orbit determination. The root-mean-square values of orbit determination residuals are within 10.0 cm, and the standard deviation of the estimated ISL hardware delays is within 0.2 ns. The accuracy of the autonomous orbits is evaluated by analysis of overlap comparison and the satellite laser ranging (SLR) residuals and is compared with the accuracy of the L-band orbits. The results indicate that the radial overlap differences between the autonomous orbits are less than 15.0 cm for the inclined geosynchronous orbit (IGSO) satellites and less than 10.0 cm for the MEO satellites. The SLR residuals are approximately 15.0 cm for the IGSO satellites and approximately 10.0 cm for the MEO satellites, representing an improvement over the L-band orbits.     

基于星载GPS数据的Jason-3卫星简化动力学和运动学法精密定轨

利用Jason-3星载GPS观测数据,采用简化动力学方法和运动学方法对Jason-3卫星进行精密定轨研究. 通过载波相位残差、重叠轨道对比、参考轨道对比和卫星激光测距(SLR)轨道检核四种方式评定轨道精度. 计算相位残差均方根(RMS)值,简化动力学轨道的RMS值在0.7～0.8 cm,运动学轨道的RMS值在0.50～0.55 cm;简化动力学轨道重叠部分径向RMS值达到0.32 cm,运动学轨道重叠部分径向RMS值达到1.12 cm;与国际DORIS服务(IDS)官方提供的参考轨道对比,简化动力学轨道径向精度达到1.47 cm,运动学轨道径向精度达到4.36 cm;利用SLR观测数据进行核验,简化动力学轨道精度整体优于2.1 cm,运动学轨道精度整体优于3.3 cm. 通过实验证明:Jason-3卫星的简化动力学轨道和运动学轨道的精度均达到cm级.      

Validation of Galileo orbits using SLR with a focus on satellites launched into incorrect orbital planes

The space segment of the European Global Navigation Satellite System (GNSS) Galileo consists of In-Orbit Validation (IOV) and Full Operational Capability (FOC) spacecraft. The first pair of FOC satellites was launched into an incorrect, highly eccentric orbital plane with a lower than nominal inclination angle. All Galileo satellites are equipped with satellite laser ranging (SLR) retroreflectors which allow, for example, for the assessment of the orbit quality or for the SLR–GNSS co-location in space. The number of SLR observations to Galileo satellites has been continuously increasing thanks to a series of intensive campaigns devoted to SLR tracking of GNSS satellites initiated by the International Laser Ranging Service. This paper assesses systematic effects and quality of Galileo orbits using SLR data with a main focus on Galileo satellites launched into incorrect orbits. We compare the SLR observations with respect to microwave-based Galileo orbits generated by the Center for Orbit Determination in Europe (CODE) in the framework of the International GNSS Service Multi-GNSS Experiment for the period 2014.0–2016.5. We analyze the SLR signature effect, which is characterized by the dependency of SLR residuals with respect to various incidence angles of laser beams for stations equipped with single-photon and multi-photon detectors. Surprisingly, the CODE orbit quality of satellites in the incorrect orbital planes is not worse than that of nominal FOC and IOV orbits. The RMS of SLR residuals is even lower by 5.0 and 1.5 mm for satellites in the incorrect orbital planes than for FOC and IOV satellites, respectively. The mean SLR offsets equal \(-44.9, -35.0\), and \(-22.4\) mm for IOV, FOC, and satellites in the incorrect orbital plane. Finally, we found that the empirical orbit models, which were originally designed for precise orbit determination of GNSS satellites in circular orbits, provide fully appropriate results also for highly eccentric orbits with variable linear and angular velocities.     

利用SLR检核GPS35卫星精密轨道

论述了利用SLR检核IGS提供的GPS卫星精密轨道的方法。采用2005年9月1日到30日的SLR观测数据对IGS提供的GPS35卫星精密轨道进行了检核实验,实验结果表明,SLR观测站存在一定的系统偏差,IGS提供的精密轨道没有明显的系统偏差,其精度优于2 cm。     

Initial results of precise orbit and clock determination for COMPASS navigation satellite system

The development of the COMPASS satellite system is introduced, and the regional tracking network and data availability are described. The precise orbit determination strategy of COMPASS satellites is presented. Data of June 2012 are processed. The obtained orbits are evaluated by analysis of post-fit residuals, orbit overlap comparison and SLR (satellite laser ranging) validation. The RMS (root mean square) values of post-fit residuals for one month’s data are smaller than 2.0 cm for ionosphere-free phase measurements and 2.6 m for ionosphere-free code observations. The 48-h orbit overlap comparison shows that the RMS values of differences in the radial component are much smaller than 10 cm and those of the cross-track component are smaller than 20 cm. The SLR validation shows that the overall RMS of observed minus computed residuals is 68.5 cm for G01 and 10.8 cm for I03. The static and kinematic PPP solutions are produced to further evaluate the accuracy of COMPASS orbit and clock products. The static daily COMPASS PPP solutions achieve an accuracy of better than 1 cm in horizontal and 3 cm in vertical. The accuracy of the COMPASS kinematic PPP solutions is within 1–2 cm in the horizontal and 4–7 cm in the vertical. In addition, we find that the COMPASS kinematic solutions are generally better than the GPS ones for the selected location. Furthermore, the COMPASS/GPS combinations significantly improve the accuracy of GPS only PPP solutions. The RMS values are basically smaller than 1 cm in the horizontal components and 3–4 cm in the vertical component.     

Model improvements and validation of TerraSAR-X precise orbit determination

The radar imaging satellite mission TerraSAR-X requires precisely determined satellite orbits for validating geodetic remote sensing techniques. Since the achieved quality of the operationally derived, reduced-dynamic (RD) orbit solutions limits the capabilities of the synthetic aperture radar (SAR) validation, an effort is made to improve the estimated orbit solutions. This paper discusses the benefits of refined dynamical models on orbit accuracy as well as estimated empirical accelerations and compares different dynamic models in a RD orbit determination. Modeling aspects discussed in the paper include the use of a macro-model for drag and radiation pressure computation, the use of high-quality atmospheric density and wind models as well as the benefit of high-fidelity gravity and ocean tide models. The Sun-synchronous dusk–dawn orbit geometry of TerraSAR-X results in a particular high correlation of solar radiation pressure modeling and estimated normal-direction positions. Furthermore, this mission offers a unique suite of independent sensors for orbit validation. Several parameters serve as quality indicators for the estimated satellite orbit solutions. These include the magnitude of the estimated empirical accelerations, satellite laser ranging (SLR) residuals, and SLR-based orbit corrections. Moreover, the radargrammetric distance measurements of the SAR instrument are selected for assessing the quality of the orbit solutions and compared to the SLR analysis. The use of high-fidelity satellite dynamics models in the RD approach is shown to clearly improve the orbit quality compared to simplified models and loosely constrained empirical accelerations. The estimated empirical accelerations are substantially reduced by 30% in tangential direction when working with the refined dynamical models. Likewise the SLR residuals are reduced from \(-3\,\pm \,17\) to \(2\,\pm \,13\) mm, and the SLR-derived normal-direction position corrections are reduced from 15 to 6 mm, obtained from the 2012–2014 period. The radar range bias is reduced from \(-10.3\) to \(-6.1\) mm with the updated orbit solutions, which coincides with the reduced standard deviation of the SLR residuals. The improvements are mainly driven by the satellite macro-model for the purpose of solar radiation pressure modeling, improved atmospheric density models, and the use of state-of-the-art gravity field models.     

基于星载GPS数据的GRACE卫星动力学法定轨

利用GRACEA卫星的星载GPS观测数据,采用非差动力学低轨卫星定轨方法,解算了2012年1月11日至18日的卫星轨道,将得到的结果与GFZ发布的RSO轨道进行对比分析,并通过SLR观测数据进行轨道的校验。结果表明：定轨精度满足低轨卫星精密定轨的要求,与RSO轨道比较,在X、Y、Z方向的均方根误差的平均值分别为4．7cm、4．3cm和4．9cm;通过SLR观测数据进行校验,残差平均值为-1．6cm,均方根误差为4．7cm．     

GOCE: precise orbit determination for the entire mission

The Gravity field and steady-state Ocean Circulation Explorer (GOCE) was the first Earth explorer core mission of the European Space Agency. It was launched on March 17, 2009 into a Sun-synchronous dusk-dawn orbit and re-entered into the Earth’s atmosphere on November 11, 2013. The satellite altitude was between 255 and 225 km for the measurement phases. The European GOCE Gravity consortium is responsible for the Level 1b to Level 2 data processing in the frame of the GOCE High-level processing facility (HPF). The Precise Science Orbit (PSO) is one Level 2 product, which was produced under the responsibility of the Astronomical Institute of the University of Bern within the HPF. This PSO product has been continuously delivered during the entire mission. Regular checks guaranteed a high consistency and quality of the orbits. A correlation between solar activity, GPS data availability and quality of the orbits was found. The accuracy of the kinematic orbit primarily suffers from this. Improvements in modeling the range corrections at the retro-reflector array for the SLR measurements were made and implemented in the independent SLR validation for the GOCE PSO products. The satellite laser ranging (SLR) validation finally states an orbit accuracy of 2.42 cm for the kinematic and 1.84 cm for the reduced-dynamic orbits over the entire mission. The common-mode accelerations from the GOCE gradiometer were not used for the official PSO product, but in addition to the operational HPF work a study was performed to investigate to which extent common-mode accelerations improve the reduced-dynamic orbit determination results. The accelerometer data may be used to derive realistic constraints for the empirical accelerations estimated for the reduced-dynamic orbit determination, which already improves the orbit quality. On top of that the accelerometer data may further improve the orbit quality if realistic constraints and state-of-the-art background models such as gravity field and ocean tide models are used for the reduced-dynamic orbit determination.     

SLR资料精密测定GLONASS卫星轨道

将SLR资料计算的轨道与CODE轨道进行了比较，并将比较结果转换到RTN坐标系中。通过比较分析发现，两种轨道差值在轨道径向、法向和沿轨方向的精度分别优于10cm、50cm和45cm；SLR和微波资料确定的GLONASS卫星轨道在径向存在系统误差，该系统误差随卫星轨道面的不同而不同。     

The impact of accelerometry on CHAMP orbit determination

 The contribution of the STAR accelerometer to the CHAMP orbit precision is evaluated and quantified by means of the following results: orbital fit to the satellite laser ranging (SLR) observations, GPS reduced-dynamic vs SLR dynamic orbit comparisons, and comparison of the measured to the modeled non-gravitational accelerations (atmospheric drag in particular). In each of the four test periods in 2001, five CHAMP arcs of 2 days' length were analyzed. The mean RMS-of-fit of the SLR observations of the orbits computed with STAR data or the non-gravitational force model were 11 and 24 cm, respectively. If the accelerometer calibration parameters are not known at least at the few percent level, the SLR orbit fit deteriorates. This was tested by applying a 10% error to the along-track scale factor of the accelerometer, which increased the SLR RMS-of-fit on average to 17 cm. Reference orbits were computed employing the reduced-dynamic technique with GPS tracking data. This technique yields the most accurate orbit positions thanks to the estimation of a large number of empirical accelerations, which compensate for dynamic modeling errors. Comparison of the SLR orbits, computed with STAR data or the non-gravitational force model, to the GPS-based orbits showed that the SLR orbits employing accelerometer observations are twice as accurate. Finally, comparison of measured to modeled accelerations showed that the level of geomagnetic activity is highly correlated with the atmospheric drag model error, and that the largest errors occur around the geomagnetic poles. Received: 7 May 2002 / Accepted: 18 November 2002 Correspondence to: S. Bruinsma Acknowledgments. The TIGCM results were obtained from the CEDAR database. This study was supported by the Centre National d'Etudes Spatiales (CNES). The referees are thanked for their helpful remarks and suggestions.     

TOPEX/Poseidon orbit error assessment

This paper discusses the accuracy of TOPEX/Poseidon orbits computed at Delft University, Section Space Research & Technology (DUT/SSR&T), from several types of tracking data,i.e. SLR, DORIS, and GPS. To quantify the orbit error, three schemes are presented. The first scheme relies on the direct altimeter observations and the covariance of the JGM-2 gravity field. The second scheme is based on crossover difference residuals while the third scheme uses the differences of dynamic orbit solutions with the GPS reduced-dynamic orbit. All three schemes give comparable results and indicate that the radial orbit error of TOPEX/Poseidon is 3–4 cm. From the orbit comparisons with GPS reduced dynamic, both the along-track and cross-track errors of the dynamic orbit solutions were found to be within 10–15 cm.     

Reduced dynamic and kinematic precise orbit determination for the Swarm mission from 4 years of GPS tracking

Precise science orbits for the first 4 years of the Swarm mission have been generated from onboard GPS measurements in a systematic reprocessing using refined models and processing techniques. Key enhancements relate to the introduction of macro-models for a more elaborate non-gravitational force modeling (solar radiation pressure, atmospheric drag and lift, earth albedo), as well as carrier phase ambiguity fixing. Validation using satellite laser ranging demonstrates a 30% improvement in the precision of the reduced dynamic orbits with resulting errors at the 0.5–1 cm level (1D RMS). A notable performance improvement is likewise achieved for the kinematic orbits, which benefit most from the ambiguity fixing and show a 50% error reduction in terms of SLR residuals while differences with respect to reduced dynamic ephemerides amount to only 1.7 cm (median of daily 3D RMS). Compared to the past kinematic science orbits based on float-ambiguity estimates, the new kinematic position solutions exhibit a factor of reduction of two to three in Allan deviation at time scales of 1000s and higher, and promise an improved recovery of low-degree and -order gravity field coefficients in Swarm gravity field analyses.     

CODE’s five-system orbit and clock solution—the challenges of multi-GNSS data analysis

This article describes the processing strategy and the validation results of CODE’s MGEX (COM) orbit and satellite clock solution, including the satellite systems GPS, GLONASS, Galileo, BeiDou, and QZSS. The validation with orbit misclosures and SLR residuals shows that the orbits of the new systems Galileo, BeiDou, and QZSS are affected by modelling deficiencies with impact on the orbit scale (e.g., antenna calibration, Earth albedo, and transmitter antenna thrust). Another weakness is the attitude and solar radiation pressure (SRP) modelling of satellites moving in the orbit normal mode—which is not yet correctly considered in the COM solution. Due to these issues, we consider the current state COM solution as preliminary. We, however, use the long-time series of COM products for identifying the challenges and for the assessment of model-improvements. The latter is demonstrated on the example of the solar radiation pressure (SRP) model, which has been replaced by a more generalized model. The SLR validation shows that the new SRP model significantly improves the orbit determination of Galileo and QZSS satellites at times when the satellite’s attitude is maintained by yaw-steering. The impact of this orbit improvement is also visible in the estimated satellite clocks—demonstrating the potential use of the new generation satellite clocks for orbit validation. Finally, we point out further challenges and open issues affecting multi-GNSS data processing that deserves dedicated studies.     

HY2A卫星的GPS/DORIS/SLR数据精密定轨

采用HY2A卫星2013年2月的实测数据,研究了GPS、星载多谱勒无线电定轨定位系统(DORIS)及卫星激光测距(SLR)三种观测数据的单独和联合定轨问题。通过与法国CNES的精密轨道数据比较发现:分别采用GPS、DORIS和SLR数据进行单独定轨,GPS数据确定轨道的径向平均精度为1.3cm,三维位置约为6.2cm;DORIS定轨的径向平均精度为1.6cm,比GPS结果略差;SLR确定轨道的径向平均精度为2.3cm。用GPS、DORIS和SLR三种数据联合定轨,确定轨道的径向平均精度为1.2cm,三维位置约为6.5cm。与星载GPS定轨结果比较,三种观测数据的联合定轨在提高卫星轨道确定精度上不明显,但联合定轨有利于保持计算轨道精度相对稳定。用站星间高度角大于60°的SLR数据检验GPS/DORIS联合确定的轨道,两者在测距方向的均方差为2.5cm,可见基于HY2A的观测数据可以实现cm级的定轨需求。     

An a priori solar radiation pressure model for the QZSS Michibiki satellite

It has been noted that the satellite laser ranging (SLR) residuals of the Quasi-Zenith Satellite System (QZSS) Michibiki satellite orbits show very marked dependence on the elevation angle of the Sun above the orbital plane (i.e., the \(\beta \) angle). It is well recognized that the systematic error is caused by mismodeling of the solar radiation pressure (SRP). Although the error can be reduced by the updated ECOM SRP model, the orbit error is still very large when the satellite switches to orbit-normal (ON) orientation. In this study, an a priori SRP model was established for the QZSS Michibiki satellite to enhance the ECOM model. This model is expressed in ECOM’s D, Y, and B axes (DYB) using seven parameters for the yaw-steering (YS) mode, and additional three parameters are used to compensate the remaining modeling deficiencies, particularly the perturbations in the Y axis, based on a redefined DYB for the ON mode. With the proposed a priori model, QZSS Michibiki’s precise orbits over 21 months were determined. SLR validation indicated that the systematic \(\beta \)-angle-dependent error was reduced when the satellite was in the YS mode, and better than an 8-cm root mean square (RMS) was achieved. More importantly, the orbit quality was also improved significantly when the satellite was in the ON mode. Relative to ECOM and adjustable box-wing model, the proposed SRP model showed the best performance in the ON mode, and the RMS of the SLR residuals was better than 15 cm, which was a two times improvement over the ECOM without a priori model used, but was still two times worse than the YS mode.     

星蚀期北斗卫星轨道性能分析——SLR检核结果

星蚀期北斗卫星的轨道性能是北斗卫星导航系统性能分析的重要部分。了解北斗卫星导航系统星历中星蚀期轨道的精度,不仅可为系统服务性能评估提供支持,还有助于了解星蚀期精密定轨中相关模型可能存在的问题,进而为精密定轨函数模型改进提供参考。本文基于2014年1月至2015年7月的卫星激光测距资料,重点分析了星蚀期对北斗不同类型卫星轨道的影响,同时也对北斗广播星历和精密星历中整体轨道径向精度进行检核。结果表明:星蚀期内(尤其是偏航机动期间),IGSO/MEO卫星的广播星历和精密星历轨道均存在明显的精度下降;广播星历轨道径向误差达1.5~2.0m,精密星历轨道径向误差超过10.0cm。但仅从轨道径向残差序列中难以发现星蚀期对GEO卫星轨道是否有显著影响。非星蚀期间,IGSO/MEO卫星和GEO卫星的广播星历轨道径向精度分别优于0.5 m和0.9 m。IGSO/MEO卫星的精密星历轨道径向精度优于10.0cm,GEO卫星的轨道径向精度约50.0cm,且存在40.0cm左右的系统性偏差。