The Orbital Evolution of Two Sounding Satellites and Analysis of the Accuracy of Orbit Determination

The satellites TC-1 and TC-2 are the two Chinese satellites with great elliptical orbits which are still in orbit around the earth at present. Since the launch the orbits of the two satellites have continuously evolved, which has a certain effect on the orbit determination and prediction precision. The regularities of the orbital evolution of the two sounding satellites are qualitatively and quantitatively analyzed. Under the current tracking mode the corresponding prediction precision of orbit determination is analyzed based on the different stages of the orbital evolution, thereby providing the basis for the adjustment of planning mode by the satellite application departments and the guarantee of normal satellite payload. Finally, the orbital lifetimes of the two satellites are predicted through the trend of the orbital evolution.     

土星卫星的精密定轨方案

由于星际探测事业的发展,对土星卫星的定位精度要求愈来愈高,经典的分析法定轨方法已难以适应,在当今计算技术条件高度发展的背景下,本文给出了土星卫星的数值法定轨方案,采用了土星卫星运动的高精度力学模型,并运用１８７４－１９８９这１００多年间的观测资料,引用现代最小二乘估计,对土星卫生进行精密定轨。该方案可以在引用同样的力学模型的前提下,对土星各颗卫星进行定轨,亦可同时进行多颗卫星的定轨。相应的软件比较     

环月飞行器精密定轨的模拟仿真

以中国正在实施的探月计划“嫦娥1号”工程为背景，分析了在中国联合S波段(USB)测控网和甚长基线射电干涉(VLBI)跟踪网的现有空间分布、观测精度水平下的环月飞行器精密定轨．采用的方法是模拟仿真计算，即首先模拟观测数据，然后在计入各误差源的影响后进行求解，并对解算结果进行比较．模拟仿真的工具是美国宇航局哥达德飞行中心的空间数据分析软件系统GEODYN．环月飞行的主要误差源是月球重力场，为此首先讨论了目前精度最高的月球重力场模型JGL165P1的(形式)误差．在模拟了测距、测速以及VLBI的时延、时延率数据后，计入月球重力场的误差进行精密轨道确定．定轨时采用了减缩动力学(reduced dynamic)方法，即选用合适的经验加速度参数吸收重力场误差对定轨的影响．结果表明对于一个不将月球重力场作为主要科学目标的探月计划(如“嫦娥1号”)，减缩动力学方法是一个简单、有效地提高环月飞行器定轨精度的方法．     

光压摄动计算中地影间断的处理

人卫精密定轨中受摄星历（或称精密星历,即状态转移）,可由分析解或数值解提供,相应的定轨方法亦有分析法定轨与数值法定轨之称。对于后者,在一般情况下,现有的常微分方程数值解法（或称积分器）已能满足精度要求,除长弧定轨外,有一定问题是值得注意的,即地影“间断”问题的处理,这关系到如何在保证星历精度的前提下提高计算效率的问题。本文针对这一问题,给出了相应的改进算法,并通过数值验证表明算法的有效性。     

The Effect of GPS Ephemeris on the Accuracy of Precise Orbit Determination of LEO Satellite-borne GPS

The satellite-borne GPS receivers dedicated to precise orbit determination are now being carried by more and more low earth orbit (LEO) satellites and the satellite-borne GPS has become one of the main means for the precise orbit determination of low earth orbit satellites. The accuracy of satellite-borne GPS precise orbit determination depends on the accuracies of the GPS ephemeris and the clock error. Based on the orbit determination function of SHORDEIII zero-difference dynamics and using the observational data obtained by the GRACE satellites for the week from 2005 August 1 to 7 as an example, three versions of GPS ephemerides (igs, igr and igu) are used to carry out orbit determination under the same conditions and to estimate the effect of the GPS ephemeris accuracy on the accuracy of orbit determination of low earth orbit satellites. Our calculated results show that the two ephemerides, igs and igr, are equivalent to each other in orbit determination accuracy (about 9.5 cm), while igu is slightly less accurate, at about 10.5 cm. The effect produced by the data of the high frequency GPS satellite clock error on the accuracy of orbit determination is 1–6 cm.     

从地面发射月球探测器的窗口选择

典型的月球探测器飞行轨道包括地球停泊轨道段、地月转移轨道段、月球卫星轨道段和着月轨道段。首先介绍了设计从地面发射月球探测器轨道典型的约束条件;然后,借助于二体假设,建立解析表达式,分析各种约束对窗口选择的影响,给出了各轨道段概略的飞行时间和粗窗口;最后,利用精确的探测器轨道动力学模型,计算精窗口,并给出了一则算例,所得结论可为月球探测器轨道发射、轨道设计提供依据。     

空间目标的圆轨道跟踪法

给出一种空间目标自动跟踪方法：圆轨道跟踪法．该方法在假设目标轨道为圆轨道的前提下计算目标轨道，而后在轨道平面中外推．和位置跟踪法比较表明：该方法不受空间目标视运动不均匀性的影响，有非常高的跟踪精度．即使采用低帧频CCD(1-2HZ)，使用本方法，也能实现对空间目标的高精度跟踪；并能给出目标的多点CCD坐标，实现对空间目标的多点分区采样，提高空间目标的定位精度．     

Design of lunar landing trajectory under constraints

The design of a lunar landing trajectory which satisfies certain constraints is considered and discussed. The constraints are of two kinds, kinetic constraints, which deal with the relative positions among the Sun, the Moon, the Earth, the spacecraft and tracking stations, and dynamic constraints, which deal with the orbital motion of the spacecraft. After a discussion of the characteristics of lunar flight trajectory, a method of designing standard flight trajectory is suggested that satisfies the constraints. This method is applied to the Chinese lunar landing flight and to the pre-design of the orbit of a lunar satellite.     

星载GPS自主定轨的长期稳定性

通过模拟长达100天的星载GPS伪距观测资料,进行卡尔曼滤波定轨仿真计算．重点研究：1)采用简化的动力学模型与简化状态转移矩阵,是否保证滤波的长期稳定性；2)模型误差矩阵Q的选取对滤波定轨精度的影响；3)与事后最小二乘批处理相比较,在简化模型下自主定轨的精度．同时给出了相应的结论．     

两行根数辅助的SLR单站定轨

单站测距资料定轨的困难限制了漫反射SLR(Satellite Laser Ranging)测距资料的应用.为此,提出利用两行根数模拟多站SLR测距资料作为辅助,实现单站SLR测距资料定轨的方法.该方法对卫星Ajisai单站SLR测距资料定轨并生成5 d预报轨道,误差小于40 m,实现利用单站测距资料的轨道改进,验证了方法的可行性.     

星载GPS低轨卫星运动学定轨及研究进展

重点论述了星载GPS低轨卫星运动学定轨的基本原理和方法,指出了各种运动学定轨法的优点和不足,分析了各种运动学定轨法解算的特点,并给出了相应的处理策略,同时着重介绍了星载GPS低轨卫星运动学定轨及相关研究的进展。     

同步卫星短弧定轨

同步卫星受到摄动力的影响,它的实际轨道有一点漂移．卫星需要不断的调轨调姿,以保证其正常运行．为了研究卫星在几小时,甚至更短的时间内的轨迹情况,采用短弧段定轨法．用动力学方法进行短弧定轨,分别研究1小时和15分钟定轨并进行比较,目的是为了在同步轨道卫星变轨后,能尽快地为卫星提供精密的预报轨道．此外,在系列短弧定轨后,得到精密轨道系列,为研究轨道变化的力学因素及研究短弧中卫星转发器时延变化规律等提供依据．     

多点高斯定轨方法

针对光学测角资料给出了一种多点高斯定轨方法,该方法公式简单,容易推广使用。经实测计算表明,观测资料分布较好,该方法对于较大的偏心率和小偏心率轨道计算是可靠和有效的。     

精密定轨用地球大气模型误差的补偿方法

本文提出了一种用于精密轨道确定的地球大气模型误差的补偿方法，这种方法采用改进 大气周日峰角的技术，有效地补偿了大气密度模型的误差，并具有较好的物理意义．与传统 的每圈改进一次加速度的方法比较，轨道确定达到了相当的径向精度，且避免了轨道改进参 数间的相关性，同时解算参数的数量也少了一半．     

The Data Depth-weight-kernel Estimation of the Model Error of Satellite Orbit Determination

It is an objective fact that there exists error in the satellite dynamic model and it will be transferred to satellite orbit determination algorithm, forming a part of the connotative model error. Mixed with the systematic error and random error of the measurements, they form the unitive model error and badly restrict the precision of the orbit determination. We deduce in detail the equations of orbit improvement for a system with dynamic model error, construct the parametric model for the explicit part of the model and nonparametric model for the error that can not be explicitly described. We also construct the partially linear orbit determination model, estimate and fit the model error using a two-stage estimation and a kernel function estimation, and finally make the corresponding compensation in the orbit determination. Beginning from the data depth theory, a data depth weight kernel estimator for model error is proposed for the sake of promoting the steadiness of model error estimation. Simulation experiments of SBSS are performed. The results show clearly that the model error is one of the most important effects that will influence the precision of the orbit determination. The kernel function method can effectively estimate the model error, with the window width as a major restrict parameter. A data depth-weight-kernel estimation, however, can improve largely the robustness of the kernel function and therefore improve the precision of orbit determination.     

星载GPS精密测轨研究及应用

星载ＧＰＳ定轨系统由于其全天侯、价格低、不受卫星高度的影响可达到米级、分米级乃至厘米级的测轨精度等特点已成为低轨道卫星精密定轨的要求,概述了星载ＧＰＳ系统的组成和定轨原理,给出了星载ＧＰＳ测轨的几种主要方法和数学模型,同时根据ＴＯＰＥＸ卫星星载ＧＰＳ实测数据分析了各种定轨方法的测轨精度以及影响定轨精度的各种因素。     

The basic parameters of static pointing model of telescope

In this paper, models of the static pointing errors and their correction of an altazimuth telescope are discussed, and a stable model with a small number of basic parameters is given. Compared with the common spherical harmonics model, the present model is not sensitive to the distribution of observing data and has a much higher correction accuracy. The residuals from this model follow the normal distribution in statistics. It can meet the need of precise orbit determination.     

High-eccentricity planets from the Anglo-Australian Planet Search

We report Doppler measurements of the stars HD 187085 and HD 20782 which indicate two high eccentricity low-mass companions to the stars. We find HD 187085 has a Jupiter-mass companion with a ∼1000-d orbit. Our formal 'best-fitting' solution suggests an eccentricity of 0.47, however, it does not sample the periastron passage of the companion and we find that orbital solutions with eccentricities between 0.1 and 0.8 give only slightly poorer fits (based on rms and  χ²_ν  ) and are thus plausible. Observations made during periastron passage in 2007 June should allow for the reliable determination of the orbital eccentricity for the companion to HD 187085. Our data set for HD 20782 does sample periastron and so the orbit for its companion can be more reliably determined. We find the companion to HD 20782 has   M sin   i = 1.77 ± 0.22  M _Jup  , an orbital period of 595.86 ± 0.03 d and an orbit with an eccentricity of 0.92 ± 0.03. The detection of such high-eccentricity (and relatively low-velocity amplitude) exoplanets appears to be facilitated by the long-term precision of the Anglo-Australian Planet Search. Looking at exoplanet detections as a whole, we find that those with higher eccentricity seem to have relatively higher velocity amplitudes indicating higher mass planets and/or an observational bias against the detection of high-eccentricity systems.     

Orbit error characteristic and distribution of TLE using CHAMP orbit data

Space object orbital covariance data is required for collision risk assessments, but publicly accessible two line element (TLE) data does not provide orbital error information. This paper compared historical TLE data and GPS precision ephemerides of CHAMP to assess TLE orbit accuracy from 2002 to 2008, inclusive. TLE error spatial variations with longitude and latitude were calculated to analyze error characteristics and distribution. The results indicate that TLE orbit data are systematically biased from the limited SGP4 model. The biases can reach the level of kilometers, and the sign and magnitude are correlate significantly with longitude.     

Numerical verification of analytic expressions for the perturbations due to an arbitrary zonal harmonic of the geopotential

Expressions are given for the first order node-to-node perturbations in the orbital elements of a satellite due to an arbitrary zonal harmonic of the geopotential. Accurate and efficient procedures for computing such perturbations are necessary for orbit determination methods which will fully utilize the highly accurate observations now available.Comparison with a double precision numerical integration is made for an intermediate altitude satellite, TELSTAR I. (Second order perturbations due to the second harmonic, derived elsewhere, are included, as are the first order perturbations due to the zonals through fourteenth order.) Discrepancies in semi-major axis after 1 period are of the order of 0.1 mm. Discrepancies in timing are of the order of 0.03 msec. A detailed discussion of computational efficiency is included.