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.     

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.     

快速响应侦察的测控通信与地面站布设研究

快速响应侦察是空间快速响应技术的一个重要应用,而合理布设地面站以保障侦察卫星的发射测控和快速数据回收是侦察任务顺利完成的基础。通过分析近地快速覆盖轨道和近地重复覆盖轨道的对地覆盖特性,针对发射测控和快速数据回收提出了地面站的布设原则,结合我国领土特点给出了这2类轨道的地面站布设方案,并求解了该方案所能提供的发射测控弧段长度和侦察数据返回时间。分析表明,在我国境内布设地面站以保障快速响应侦察卫星的发射测控和快速数据回收是可行的,其数据返回时间小于1个轨道周期。     

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.     

Spaceborne GPS receiver antenna phase center offset and variation estimation for the Shiyan 3 satellite

In determining the orbits of low Earth orbit (LEO) satellites using spaceborne GPS, the errors caused by receiver antenna phase center offset (PCO) and phase center variations (PCVs) are gradually becoming a major limiting factor for continued improvements to accuracy. Shiyan 3, a small satellite mission for space technology experimentation and climate exploration, was developed by China and launched on November 5, 2008. The dual-frequency GPS receiver payload delivers 1 Hz data and provides the basis for precise orbit determination within the range of a few centime-ters. The antenna PCO and PCV error characteristics and the principles influencing orbit determi-nation are analyzed. The feasibility of PCO and PCV estimation and compensation in different directions is demonstrated through simulation and in-flight tests. The values of receiver antenna PCO and PCVs for Gravity Recovery and Climate Experiment (GRACE) and Shiyan 3 satellites are estimated from one month of data. A large and stable antenna PCO error, reaching up to 10.34 cm in the z-direction, is found with the Shiyan 3 satellite. The PCVs on the Shiyan 3 satellite are estimated and reach up to 3.0 cm, which is slightly larger than that of GRACE satellites. Orbit validation clearly improved with independent k-band ranging (KBR) and satellite laser ranging (SLR) measurements. For GRACE satellites, the average root mean square (RMS) of KBR resid-uals improved from 1.01 cm to 0.88 cm. For the Shiyan 3 satellite, the average RMS of SLR resid-uals improved from 4.95 cm to 4.06 cm.     

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     

星载GPS测量数据预处理方法研究

针对低地球轨道(LEO)卫星星载全球定位系统(GPS)接收机应用的特点,对星载GPS测量数据误差及其对周跳探测的影响进行了分析,提出TurboEdit数据预处理方法中周跳探测算法的改进算法。在原周跳判断算法的基础上,通过引入与测量数据观测高度角相关的加权系数,将周跳探测与测量误差紧密联系起来。根据观测高度角的变化对测量数据误差进行估计,并根据估计情况对加权系数取值,从而实现对周跳探测算法进行调节,达到降低周跳探测失误率的目的。增加参与定轨计算的观测数据量,提高了低轨卫星连续定轨的能力。通过GRACE编队卫星实测数据对改进算法进行了仿真验证。     

卫星轨道变化规律的综合分析

对于航天工程而言,无论是航天器的发射,卫星轨道设计,地面测控系统的跟踪、定轨和预报．还是卫星在轨运行过程中的轨道控制策略等,均需了解卫星轨道变化的规律。为此,本文对人造卫星(包括中心天体为快自转天体和慢自转天体两种引力源的绕飞轨道器)的轨道变化特征以及轨道寿命进行系统的综合分析。为各种应用提供简明信息。     

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.     

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。     

天/地基多平台空间目标光电观测时效性分析

针对如何部署光学探测设备才能更好实现对空间目标的高精度高频度监视问题,考虑光照条件、相对关系及探测性能,构建了天/地基空间目标探测与成像仿真模型;按照轨道特征选取了94颗LEO（Low Earth Orbit,低地球轨道）卫星、63颗GEO（Geosynchronous Earth Orbit,地球同步轨道）卫星和18颗大椭圆轨道卫星,选用春夏秋冬典型季节的特定时间长度,仿真分析了国内地基、南北极科考站、LEO卫星、准GEO卫星等多平台光电手段的位置探测和成像观测能力;比对分析地基平台纬度和季节、天基平台轨道高度和倾角对探测能力的影响得出：南北极科考站相比于国内站点可提高重点季节的探测时效性,98°倾角LEO平台对低轨目标成像时效性方面更具优势,等.在此基础上,提出了我国空间目标光电观测设备天地一体的布局构想.     

卫星定轨综述

对卫星定轨中的热点问题作一综述,内容包括短弧定轨和长弧精密定轨。对于短弧定轨(通常指初轨),不仅从原理上分析其关键之处,还介绍如何将适用于无摄运动的特殊定轨方法推广用于同时考虑各种摄动的受摄运动,并可同时适用于圆锥曲线的各种情况：变化的椭圆轨道、抛物线轨道和双曲线轨道,后者在深空探测器的运动过程中将会遇到。对于长弧精密定轨,阐述当今提高精密定轨精度的力模型补偿问题以及几何定轨的提法,天地基网联合定轨和星-星相对测量的自主定轨问题。     

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.     

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。     

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。     

Precise orbit determination for TH02-02 satellites based on BDS3 and GPS observations

The Tianhui-2 02 (TH02-02) satellite formation, as a supplement to the microwave mapping satellite system Tianhui-2 01 (TH02-01), is the first Interferometric Synthetic Aperture Radar (InSAR) satellite formation-flying system that supports the tracking of BeiDou global navigation Satellite system (BDS3) new B1C and B2a signals. Meanwhile, the twin TH02-02 satellites also support the tracking of Global Positioning System (GPS) L1&L2 and BDS B1I&B3I signals. As the spaceborne receiver employs two independent boards to track the Global Navigation Satellite System (GNSS) satellites, we design an orbit determination strategy by estimating independent receiver clock offsets epoch by epoch for each GNSS to realize the multi-GNSS data fusion from different boards. The performance of the spaceborne receiver is evaluated and the contribution of BDS3 to the kinematic and reduced-dynamic Precise Orbit Determination (POD) of TH02-02 satellites is investigated. The tracking data onboard shows that the average number of available BDS3 and GPS satellites are 8.7 and 9.1, respectively. The carrier-to-noise ratio and carrier phase noise of BDS3 B1C and B2a signals are comparable to those of GPS. However, strong azimuth-related systematic biases are recognized in the pseudorange multipath errors of B1C and B3I. The pseudorange noise of BDS3 signals is better than that of GPS after eliminating the multipath errors from specific signals. Taking the GPS-based reduced-dynamic orbit with single-receiver ambiguity fixing technique as a reference, the results of BDS3-only and BDS3 + GPS combined POD are assessed. The Root Mean Square (RMS) of orbit comparison of BDS3-based kinematic and reduced-dynamic POD with reference orbit are better than 7 cm and 3 cm in three-Dimensional direction (3D). The POD performance based on B1C&B2a data is comparable to that based on B1I&B3I. The precision of BDS3 + GPS combined kinematic orbit can reach up to 3 cm (3D RMS), which has a more than 25% improvement relative to the GPS-only solution. In addition, the consistency between the BDS3 + GPS combined reduced-dynamic orbit and the GPS-based ambiguity-fixed orbit is better than 1.5 cm (3D RMS).     

单频GPS接收机校频算法

基于工程实践介绍了单频单通道GPS接收机校频的基本算法、校频结果显著性的统计检验、数据采集和处理方法,并基于大量观测数据给出了校频不确定度。     

基于双星系统的卫星几何学精密定轨方法研究

双星导航系统的建立，为我国实现自主的卫星天基测控技术提供了可能。同时由于其全天候、全天时、相对定轨精度高等特点可望成为一种低、中轨卫星精密定轨的有效手段。但由于双星系统中静止卫星数目仅有两颗，要得到低、中轨卫星的三维定位信息，还需要额外的第三维观测量。本文根据双星系统的现状，结合国内对低、中轨卫星精密定轨的要求，提出了一种基于双星系统的卫星几何学精密定轨的方法，概述了其基本原理及其组成，给出了卫星定轨的方法和数学模型，同时根据数据仿真分析了该定轨系统的定轨精度，为下一步工程实现提供了理论基础。     

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.