单点弹道精度与轨道半长轴远地点高度计算精度的映射关系

在仅使用单点位置、速度信息计算轨道的奈件下,针对轨道半长轴、远地点高度的精度问题,在轨道面内,应用活力公式和二体运动学理论推导得出了轨道计算精度与弹道测量精度间映射关系的解析表达式,并采用数值分析方法给出了不同的位置、速度误差与半长轴、远地点高度最大误差之间的数值关系.仿真结果表明,对于位置误差和速度误差大小分别为100 m和1 m/s的算例,半长轴最大误差和远地点高度最大误差分别约为2 km和4 km.基于此方法,可以将弹道误差传递至轨道参数误差,进一步分析故障误判和漏判概率;也可根据轨道参数精度要求反算弹道测量精度要求,以作为地面测量系统建设的技术依据.     

基于地月三角平动点的卫星自主定轨

近年提出了利用地月系平动点建立深空导航星座的设想。在受太阳摄动的真实力模型下,地月系平动点是不稳定的,从而会导致导航星座必须通过控制才能定点在特定区域。针对此问题,引入一种特殊的平动点轨道,即动力学替代轨道。平动点轨道卫星星座可利用星间测距数据自主定轨,由于动力学替代轨道具有长期稳定性,整个自主定轨过程不需要来自地面的测控支持,且定轨精度可达到观测精度。研究结果表明,观测资料的长短、导航卫星垂直白道面的运动分量都将影响到导航星间的自主定轨精度。该研究成果可以应用在以后的地月系导航星座中。     

航天器多普勒测速平均误差的分析与修正

对航天器多普勒测速平均误差进行了分析,详细推导了圆轨道和椭圆轨道时该误差的计算公式,计算了不同采样周期和轨道高度时的误差大小。经过分析指出,该项误差对于高轨航天器影响较小,对于低轨航天器可以通过缩短采样周期或利用3个点或多个点的连续测量数据进行修正。     

相对测量在编队卫星自主定轨中的应用

针对编队卫星自主定轨问题进行了研究,设计了一种完全不依赖于地面站和GPS系统的自主导航方案。利用星间测量信息进行卫星编队相对轨道状态的自主确定;并在利用磁强计进行卫星绝对轨道自主确定的基础上,引入星间测量信息提高绝对定轨精度;设计扩展卡尔曼滤波器进行卫星编队轨道状态估计,数学仿真结果验证了这种导航方案和算法的有效性。     

Determination des orbites des satellites artificiels

Summary The problem of the determination of the orbit of a celestial body is an old astronomical problem, of which solutions can be found in many classical books on elementary celestial mechanics. However, the introduction of new (radioelectric) means of observations for the artificial satellites have brought up new solutions of this old problem.The author reminds the definitions of the six elliptic elements of an orbit. The problem of their determination is usually divided into two separate steps: a preliminary orbit determination and the improvement of the preliminary elements. Two principal types of preliminary orbit determination exist: the Gaussian type, purely geometrical in which the positions of the body at two different times are determined, and the Laplacian type, of a more dynamical character, in which both position and velocity vectors are found for a given time. The improvement of the preliminary elements is usually obtained by a numerical solution of equations of variations of the elements, minimizing the sum of the squares of the angular distances between the computed and the observed points. The elements on which these variations are applied can be quite various. The coefficients of the equations are usually obtained numerically, although their analytical expressions can also be derived.Most of the modification proposed to the classical methods of orbit determination are more technical improvements in connection with the computation on electronic machines. The most interesting modifications are inspired by the fact that time measurements are less precise than the position (Batrakov, Iszak), the effects of this difference in errors are discussed in this paper. In some cases, using Laplace's method, no preliminary orbit is computed, and all the observations can be used at once (Barlier, Kovalevsky).The determination of orbits from radar measurements is discussed. The proposed methods are quite different in principle from the classical ones. They are actually improvements of a circular orbit whose determination is made by a method of undetermined coefficients (Baker). Some of the elements determined by these methods are quite unstable, and it is always wiser to use other informations together with radar measurements.The determination of orbits from Doppler data alone has been worked out by many investigators. It is the inverse problem of the main problem of all navigational systems. The method proposed by Patton is summarized. The principles of others are quite analogous. The results are improved when more than one receiver are used. The different types of corrections: refraction, perturbations, etc., should be introduced in later stages of the determination, and the whole frequency curve is to be used if a good determination of all elements is desired.Finally, the author quotes a method (Baker) using both Doppler and radar data, and the solution of a new problem: the determination of the orbit of a satellite of another planet from Doppler data alone (Deutsch).     

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.     

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.     

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.     

导航星座自主导航技术--自主星历更新

自主星历更新是导航星座自主导航的关键技术之一,包括卫星轨道精密确定和轨道短时预报两个方面的内容。本文在系统地论述导航星座自主导航的信息处理流程的基础上,重点提出星座卫星轨道精密确定的自适应Kalman滤波算法。系统仿真结果表明：通过星间双向测量数据的滤波处理,能够获得高精度的卫星星历和较小的用户测距误差（URE）,满足高精度导航定位需求,初步证明导航星座自主导航信息处理流程及其星历更新算法的合理性和可行性。     

低轨卫星多普勒频移特性的快速计算

地面站利用低轨卫星进行通信时,地面接收站接收信号存在明显的多普勒频移现象。为描述多普勒频移特性,首先分析卫星轨道偏心率对多普勒特性曲线的影响,分析表明：轨道偏心率越大,地面站接收信号多普勒变化率越大。其次,推导了卫星多普勒频移的计算表达式,并讨论了低轨卫星多普勒频移特性曲线的快速计算。仿真计算结果表明,该算法可以很好地描述任意低轨道卫星多普勒频移特性,并明显缩短了精确算法的计算时间,对于10 000km轨道高度卫星,算法置信度可达99%以上。     

Improvement of Satellite Tracking Accuracy Using Optical Observations

A method to improve satellite tracking accuracy is presented and discussed theoretically and experimentally in terms of two parts: correction for errors of the tracking system and correction of satellite orbit predictions. In the first part, it is concluded that the pointing error of the tracking system can be determined accurately using data from stellar observations, so that correction is possible with an accuracy of about 0.001°. In the second part, it is shown that apparent errors of satellite orbital elements can be deduced from the optical observation of one orbit, and one can track the satellite after the correction with high accuracy for several subsequent orbits. The accuracy is 0.1-0.2 mrad or better for satellites at 1000 km altitude when given orbit prediction accuracy is approximately 1°.     

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.     

北斗空间信号误差统计特征及描述方法研究

通过对比北斗卫星导航系统(BeiDou Navigation Satellite System,BDS)广播星历与事后精密星历,提取了轨道和卫星时钟误差。基于北斗轨道误差及北斗卫星时钟误差统计特征分析,构建区别于全球定位系统(Global Positioning System,GPS)的BDS空间信号用户测距误差(Signal-In-Space User Range Error,SISRE)描述方法,对BDS广播星历中用户测距精度(User Range Accuracy,URA)进行了验证。6个月的北斗数据测试结果表明,北斗GEO、IGSO和MEO卫星的URA分别为3.0m、1.9m和1.6m。     

双线程滑动窗口多系统GNSS超快精密定轨实现及评估

全球导航卫星系统（GNSS）超快精密定轨为GNSS实时应用提供了高精度空间基准。基于天地协同定位、导航与授时（PNT）网络服务中心实现了四系统GNSS卫星超快精密定轨,并对定轨结果进行精度评价。介绍了天地协同PNT网络的概念内涵以及网络服务中心部署的超快精密定轨软件架构和详细功能,并针对实时应用需求提出了一种双线程滑动窗口超快精密定轨策略。最后利用重叠弧段比较、与外部轨道产品比较以及卫星激光测距（SLR）检核3种方式对定轨结果进行了精度评价。结果表明,与武汉大学分析中心的最终事后精密轨道产品相比,四系统GNSS MEO卫星预报6 h弧段的径向均方根（RMS）误差整体在2~5 cm水平,BDS2 IGSO卫星最小一维RMS误差在10~15 cm水平;GPS和Galileo卫星的SLR检核残差均值在1~3 cm水平,标准差在3~6 cm水平,能够满足后续厘米级实时应用对空间基准的精度需求。     

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     

Explanation of the “May Swarm” signature in the LDEF IDE impact data

The Interplanetary Dust Experiment (IDE) carried by the Long Duration Exposure Facility (LDEF) satellite detected a large number of small particle impacts. The dataset shows impact events recurring for a number of LDEF orbits. Such events show signatures of particle clouds that intersect the orbit of LDEF. In an effort to identify the impact of particles released during solid rocket motor burns, a new look at the IDE impact records was taken. The generation of dust particles due to solid rocket burns and a close encounter analysis of the released objects with LDEF's orbital path was simulated. An agreement of a specific IDE impact feature occurring in May 1984 with the firing of the apogee kick motors of the satellites WESTAR 6 and PALAPA B2 could be derived.     

Aiming at a 1-cm Orbit for Low Earth Orbiters: Reduced-Dynamic and Kinematic Precise Orbit Determination

The computation of high-accuracy orbits is a prerequisite for the success of Low Earth Orbiter (LEO) missions such as CHAMP, GRACE and GOCE. The mission objectives of these satellites cannot be reached without computing orbits with an accuracy at the few cm level. Such a level of accuracy might be achieved with the techniques of reduced-dynamic and kinematic precise orbit determination (POD) assuming continuous Satellite-to-Satellite Tracking (SST) by the Global Positioning System (GPS). Both techniques have reached a high level of maturity and have been successfully applied to missions in the past, for example to TOPEX/POSEIDON (T/P), leading to (sub-)decimeter orbit accuracy. New LEO gravity missions are (to be) equipped with advanced GPS receivers promising to provide very high quality SST observations thereby opening the possibility for computing cm-level accuracy orbits. The computation of orbits at this accuracy level does not only require high-quality GPS receivers, but also advanced and demanding observation preprocessing and correction algorithms. Moreover, sophisticated parameter estimation schemes need to be adapted and extended to allow the computation of such orbits. Finally, reliable methods need to be employed for assessing the orbit quality and providing feedback to the different processing steps in the orbit computation process. This revised version was published online in August 2006 with corrections to the Cover Date.     

Orbit Design for the THEMIS Mission

THEMIS, NASA’s fifth Medium Class Explorer (MIDEX) mission will monitor the onset and macro-scale evolution of magnetospheric substorms. It is a fleet of 5 small satellites (probes) measuring in situ the magnetospheric particles and fields while a network of 20 ground based observatories (GBOs) monitor auroral brightening over Northern America. Three inner probes (～1 day period, 10 R_E apogee) monitor current disruption and two outer probes (～2 day and ～4 day period, 20 R_E and 30 R_E apogees respectively) monitor lobe flux dissipation. In order to time and localize substorm onsets, THEMIS utilizes Sun–Earth aligned conjunctions between the probes when the ground-based observatories are on the nightside. To maintain high recurrence of conjunctions the outer orbits have to be actively adjusted during each observation season. Orbit maintenance is required to rearrange the inner probes for dayside observations and also inject the probes into their science orbits after near-simultaneous release from a common launch vehicle. We present an overview of the orbit strategy, which is primarily driven by the scientific goals of the mission but also represents a compromise between the probe thermal constraints and fuel capabilities. We outline the process of orbit design, describe the mission profile and explain how mission requirements are targeted and evaluated. Mission-specific tools, based on high-fidelity orbit prediction and common magnetospheric models, are also presented. The planning results have been verified by in-flight data from launch through the end of the first primary science seasons and have been used for mission adjustments subject to the early scientific results from the coast phase and first tail season.     

The observational data base on the motion and evolution of comets and asteroids

Current observational data base on the motion of comets and asteroids is reviewed. Particular attention is paid to the absolute and relative abundances of different dynamical types of objects, and to the time intervals between their first and last observations. The latter quantity, ranging from two days to two milliennia for individual objects, is the dominant measure of the accuracy of the orbit determination. Distribution of the tracking times of comets (distinguished by dynamical age: new, long-period, Halley type, Jupiter family) and asteroids (distinguished by stability: Apollos, Amors, main-belt asteroids, outer librators, outer unstable objects) are reconstructed. The peculiar shapes of individual distributions can be explained by the complex mechanisms of discoveries, rediscoveries, orbit computations, follow-up observations and backward identifications. A comparison is also made with the dynamical data base on meteoroids, as regards the accuracy of their orbits.The cumulative tracking times (170000 yr for all 7600 objects with known orbits taken together) are compared with the lifetimes and occurrence rates of different events of evolutionary significance. Only in the case of short-period comets the evolution is rapid enough to render observable a variety of important changes, ranging from drastic transformations of orbits to disruption or total outgassing. For asteroids, only minor cratering collisions which do not result in detectable changes of their orbits are covered by the whole observational history.Expected future improvements of observing and data-handling techniques are outlined. With these in view, the size and character of the data to become available by the end of this century are predicted. Dynamical types of objects, which are currently known in only one or a few examples, are pointed out. Apparently, other types of rare occurrence and short survival time still escape detection. A list of easiest targets of short-duration spacecraft missions is presented.The deficiencies of current statistics due to observational selection; the broad variety of regimes of motion occupied by widely differing proportional representations of the known objects; and demands for suitable targets of future spacecraft missions make it highly desirable to maintain the present rapid rate of augmentation of the data base for the years to come.Recent passages of two comets — 1983d IRAS-Araki-Alcock and 1983e Sugano-Saigusa-Fujikawa — near the Earth indicate that both the collision rate given in Table VIII and the contribution of long-period comets to it may have been slightly underestimated. The appropriate adjustment of the log-t values by less than — 0.10 has no effect of the general conclusions, however.The success of the orbiting observatory IRAS in detecting faint interplanetary objects lends better promises for the increase of the number of known objects (in particular comets) than anticipated in Section 6 and estimated in Table IX. Obviously, the outcome will largely depend on the implementation, time coverage and degree of exploitation of similar projects in the near future.