I: PRECISE ORBIT DETERMINATION AND GRAVITY FIELD MODELLING: Strategies for Precise Orbit Determination of Low Earth Orbiters Using the GPS

Considerable experience accumulated during the past decade in strategies for processing GPS data from ground-based geodetic receivers. First experience on the use of GPS observations from spaceborne receivers for orbit determination of satellites on low altitude orbits was gained with the launch of TOPEX/POSEIDON ten years ago. The launch of the CHAMP satellite in July 2000 stimulated a number of activities worldwide on improving the strategies and algorithms for orbit determination for Low Earth Orbiters (LEOs) using the GPS. Similar strategies as for ground-based receivers are applied to data from spaceborne GPS receivers to determine high precision orbits. Zero- and double-differencing techniques are applied to obtain kinematic and/or reduced-dynamic orbits with an accuracy which is today at the decimeter level. Further developments in modeling and processing strategies will continuously improve the quality of GPS-derived LEO orbits in the near future. A significant improvement can be expected from fixing double-difference phase ambiguities to integer numbers. Particular studies focus on the impact of a combined processing of LEO and GPS orbits on the quality of orbits and the reference frame realization. This revised version was published online in August 2006 with corrections to the Cover Date.     

地球静止卫星精密测定轨技术的现状及发展

介绍并分析了针对地球静止卫星的各种高精度测定轨跟踪技术.指出测距系统的校正误差是常规测距跟踪网定轨在沿迹方向和法向的主要误差源,为保证一致的卫星三维位置解算精度,应利用高分辨率的角度观测约束信息来有效地降低测距偏差对轨道确定的影响,或者利用天地基联合定轨的低轨卫星运动几何在轨道改进的同时精化测距偏差.     

磁暴下的LEO卫星精密轨道确定

对低轨卫星（LEO）,大气阻尼摄动是主要的定轨误差源.尤其在发生磁暴时,求解一个大气阻尼因子的定轨方法已不能充分吸收大气密度计算不准所造成的定轨误差,因而在标校统一S波段（USB）的测量系统差和随机差时往往计算失真.本文提出了一种求解折线型Cd因子的新方法,克服了动力学模型不准所带来的定轨误差,通过与独立的GPS数据比较,定轨精度有明显提高,同时给出的测量系统差和随机差更加真实可信.     

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.     

双星定位系统及其备份星在近地卫星联合定轨建模中的应用

建立了基于双星定位系统距离和观测数据的近地卫星联合定轨模型,设计了相应的数值融合联合定轨算法;为进一步提高近地卫星定轨精度,考虑融合双星及备份星距离和观测数据,建立了基于双星和备份星的近地卫星联合定轨模型及实现算法,并针对不同仿真条件进行了联合定轨仿真实验。仿真计算结果表明,联合定轨方式较传统近地卫星精密定轨方式可以更好地抑制双星星历误差对近地卫星定轨精度的影响,近地卫星和双星的定轨精度均得到了一定程度的提高;同时,融合备份星观测数据的近地卫星联合定轨精度得到进一步改善,达到5.17m。     

轨道预测辅助GPS载波跟踪技术用于低轨道卫星定位研究

针对低轨道卫星及其特定的运动环境,研究了星载GPS接收机载波跟踪问题。基于卫星轨道可模化、可预测的特性,提出了利用预测卫星轨道计算多普勒频移,并用于辅助载波环路跟踪的新方法。该方法有效地降低了低轨道卫星GPS信号跟踪中的动态,从而在跟踪过程中可以采取降低环路阶数、减小环路带宽、增加预检测积分时间这几种措施来提高环路跟踪弱信号的能力,有助于提高低轨道卫星的定位性能。     

一种大椭圆轨道卫星星历预报方法

针对大偏心率轨道长时间星历预报,稠密输出星历的低效率问题,提出了一种新的星历预报方法。该方法通过建立卫星摄动力模型,对卫星运动方程进行数值积分来获取卫星星历。该方法的轨道积分器以标准的8阶Adams-Cowell多步法为基础,针对大偏心率轨道的特性,在一个轨道周期的不同时段内采用不同的积分步长,同时引入了用于生成小间隔等间距卫星星历的插值公式。该方法降低了卫星运动方程右函数的计算次数,尤其适用于需要稠密输出卫星星历的情况。以STK(Satellite Tool Kit,卫星工具包)的HPOP(High Precision Orbit Propagator,高精度轨道预报)模型为验证基准,通过数学仿真校验了该方法的有效性和精度。算例表明,该方法在预报精度损失很小的情况下,计算时间远小于标准的多步法和HPOP模型。     

直接解算轨道根数的轨道约束自校准定轨方法

应用轨道约束自校准技术能够有效地修正系统误差和提高定轨精度。本文为了适应各种航天试验任务要求,将轨道约束自校准技术推广应用到直接解算轨道根数的定轨方法中,并导出了解算开普勒根数的轨道约束自校准公式。     

Autonomous navigation to quasi-periodic orbits near translunar Ubration points

Libration-point missions have been very useful and successful. Due to the unstable natures of most of these orbits, the long-time stationkeeping demands frequent maneuvers and precise orbit determinations. Earth-based tracking will have to undertake much more responsibilities with the increasing number of libration missions. An autonomous navigation system could offer a better way to decrease the need for Earth-based tracking. Nevertheless, when an autonomous navigation system is applied, there are three important factors affecting autonomous navigation accuracy, i.e., the accuracy of initial conditions, the accuracy of measurements, and the accuracy of onboard dynamics for propagation. This paper focuses on analyzing the influence from the third factor and finding an appropriate navigation dynamics, which can satisfy the requirement of estimation accuracy but not cause too much burden for onboard computation. When considering the restricted three-body model and the bicircular restricted four-body model as navigation dynamics, the astrin- gency is not shown during the simulations. Meanwhile, when considering the influences of the Sun＇s direct and indirect perturbations and the eccentricity of the Moon＇s orbit, a new navigation dynamic model with the standard ephemerides is proposed. The simulation shows the feasibility of the proposed model.     

A demonstration of sub meter GPS orbit determination and highprecision user positioning

High-accuracy orbits have been determined for satellites of the Global Positioning System (GPS), with submeter orbit accuracy demonstrated for two well-tracked satellites. Baselines of up to 2000 km in North America determined with the GPS orbits shows daily repeatability of 0.3-2 parts in 10⁸ and agree with very long baseline interferometry (VLBI) solutions at the level of 1.5 parts in 10 ⁸. Tests used to assess orbit accuracy include orbit repeatability from independent data sets, orbit prediction, ground baseline determination, and formal errors. One satellite tracked for eight hours each day shows RMS errors below 1 m even when predicted more than three days outside of a 1-week data arc. These results demonstrate the powerful relative positioning capability available from differential GPS tracking. Baselines have also been estimated between Florida and sites in the Caribbean region over 1000 km away, with daily repeatability of 1-4 parts in 10⁸. The best orbit estimation strategies included data arcs of 1-2 weeks, process noise models for tropospheric fluctuations, combined processing of GPS carrier phase and pseudorange data, and estimation of GPS solar pressure coefficients     

地月系共线平动点探测器的星上轨道预报问题

针对定点在地月系共线平动点附近运动的探测器，研究其轨道预报问题，并探讨了星上外推预报时的力模型简化问题。首先定量分析了共线平动点L1和L2附近探测器的受力情形；然后构造了真实力模型下这些点附近的目标轨道并研究了其误差传播规律，指出这类轨道相比一般卫星轨道预报的不同特征；最后结合星上有限的计算和存储资源限制探讨了力模型的简化问题。此项工作可为定点在平动点附近的探测器的星上预报提供参考。     

Phase Residual Estimations for PCVs of Spaceborne GPS Receiver Antenna and Their Impacts on Precise Orbit Determination of GRACE Satellites

In-flight phase center systematic errors of global positioning system(GPS) receiver antenna are the main restriction for improving the precision of precise orbit determination using dual-frequency GPS.Residual approach is one of the valid methods for in-flight calibration of GPS receiver antenna phase center variations(PCVs) from ground calibration.In this paper,followed by the correction model of spaceborne GPS receiver antenna phase center,ionosphere-free PCVs can be directly estimated by ionosphere-free carrier phase post-fit residuals of reduced dynamic orbit determination.By the data processing of gravity recovery and climate experiment(GRACE) satellites,the following conclusions are drawn.Firstly,the distributions of ionosphere-free carrier phase post-fit residuals from different periods have the similar systematic characteristics.Secondly,simulations show that the influence of phase residual estimations for ionosphere-free PCVs on orbit determination can reach the centimeter level.Finally,it is shown by in-flight data processing that phase residual estimations of current period could not only be used for the calibration for GPS receiver antenna phase center of foretime and current period,but also be used for the forecast of ionosphere-free PCVs in future period,and the accuracy of orbit determination can be well improved.     

一种有效提高超大偏心率轨道初轨确定精度的新方法

针对某型号航天器的运行轨道偏心率大、轨控结束后可用于初轨确定的测轨数据少的特点,提出了一种能有效提高超大偏心率短弧段初轨确定精度的新方法。该新方法将轨道改进的思想融入初轨计算方法中,使之既适用于各种偏心率轨道的初轨计算,也适用于各种偏心率轨道的长弧段、多圈、多站数据的轨道改进;解决了传统初轨确定方法超大偏心率轨道短弧段初轨确定误差偏大的问题。通过任务实测数据的检验,新方法适用于各种偏心率轨道,并且超大偏心率轨道的初轨确定精度明显优于传统方法。     

Orbit Determination Accuracies Using Satellite-to-Satellite Tracking

The results are reported of the ATS-6/GEOS-3 and the ATS-6 NIMBUS-6 satellite-to-satellite orbit determination experiments. NASA intends to use the tracking data relay satellite system for operational orbit determination of NASA satellites. Hence, in the near future, satellite-to-satellite tracking data will be routinely processed to obtain orbits. The satellite-to-satellite tracking system used in the ATS-6/NIMBUS-6 and ATS-6/GEOS-3 experiments performed with a resolution of 1 to 2 m in range and less than 1 mm/s in range rate for a 10-s averaging. A Bayesian least squares estimation technique utilizing independent ranging to the synchronous relay satellite was determined to be the most effective procedure for estimating orbits from satellite-to-satellite tracking data. The use of this technique yields estimates of user satellite orbits which are comparable in accuracy to what is usually obtained from ground based systems.     

一种低轨卫星轨道预报算法

在基于EMBET（Error Model Best Estimation of Trajectory，误差模型最佳弹道估计）的雷达自校准处理过程中，需要基于给定的低轨卫星初始状态完成轨道预报，得到与雷达测量序列对应的卫星位置序列，进而通过迭代收敛过程得到误差模型参数估计。针对低轨卫星轨道迭代预报的需要，提出了一种边积分边插值的轨道预报方法。即将低轨卫星轨道积分计算过程的加速度计算结果直接应用到三弯矩插值，省略了三弯矩插值中节点矩的计算过程，同时将积分步长以及插值区间步长设置为1 s，减少了积分及插值中乘法和除法的计算次数，进一步提高了计算效率。经仿真计算表明，该方法在保证轨道预报精度的情况下，计算效率比传统低轨卫星轨道预报方法提高了约20倍，有效提高了雷达自校准处理的时效性。     

星载双频GPS相位历元差缩减动力学定轨(英文)

研究了星载双频GPS相位历元差缩减动力学定轨方法,该方法既克服了相位历元差运动学方法在观测几何较差或数据不足情况下无法应用的缺点,又避免了相位非差动力学方法易受周跳和模糊度影响的缺点。历元差方法对相位周跳的影响不敏感,因此能够降低相位数据预处理中周跳探测的难度。在模型求解过程中,解决了高维矩阵的计算问题,将长弧段观测数据分成若干短弧段,相邻两个短弧段的连接处不做差分,仅在每个短弧段内部进行历元间差分处理。通过对GRACE卫星进行试算,并与GFZ事后科学轨道进行比较,结果表明相位历元差缩减动力学定轨精度在径向、沿迹方向和轨道法向分别可达1.92cm、3.83cm和3.80cm,三维位置精度可达5.76cm,该方法与相位非差缩减动力学定轨精度相当。     

Evaluation of Geometric Performance of Global Positioning System

The global positioning system (GPS) is a satellite-based radio navigation system to provide extremely accurate three-dimensional position fixes and system time to users anywhere on the Earth at any time regardless of weather conditions. The most significant performance parameter of the GPS is the degree of navigation accuracy which is strongly coupled to the choice of orbit configuration. The 3 X 8 orbit configuration has been considered as an operational GPS which consists of 24 satellites deployed in circular 63° inclined, subsynchronous 12-h orbits. In this paper, the geometric performance of several orbit configuration, including a 3 X 8 orbit configuration, is analyzed numerically by altering orbit period and elevation mask, respectively. It will be shown that 1) there are a few orbit configurations which are comparable to or better than the baseline 3 X 8 orbit configuration, and 2) for higher elevation mask, the geometric performance can be improved effectively by increasing orbit period to some extent.     

近地卫星磁测自主定轨及原型化

利用三轴磁强计的测量信息可实时地确定卫星轨道。采用扩展卡尔曼滤波作为处理磁测自主定轨问题的滤波算法．并以地磁场强度幅值作为测量值，建立了近地卫星磁测自主定轨的数学模型。在数学模型的基础上实现了基于PC机、dSPACE一体化系统的原型化(Prototyping)实验。该原型化实验对磁测自主定轨的方案、理论、算法及实时运行特性做了进一步的验证。     

低轨航天器长期轨道预报的初步研究

低轨航天器的长期管理和维护需要较高精度的长期轨道预报,影响长期预报精度最主要的因素来自低轨航天器所受的大气阻力摄动.借助平均大气密度模型,以340 km高度的低轨航天器为例,研究了低轨长期轨道预报问题.利用基于长弧段的逐天精密定轨,可以修正参考点的平均密度.根据目前积累的数据,通过引入太阳自转周期27 d和半年180 d这2个周期拟合平均密度序列,未来的平均密度可以预报到较高精度.目前的计算结果表明,在此基础上低轨航天器的长期轨道预报精度可以得到保证,在不同算例中表现基本稳定可靠.