Measuring atmospheric density using GPS–LEO tracking data

We present a method to estimate the total neutral atmospheric density from precise orbit determination of Low Earth Orbit (LEO) satellites. We derive the total atmospheric density by determining the drag force acting on the LEOs through centimeter-level reduced-dynamic precise orbit determination (POD) using onboard Global Positioning System (GPS) tracking data. The precision of the estimated drag accelerations is assessed using various metrics, including differences between estimated along-track accelerations from consecutive 30-h POD solutions which overlap by 6 h, comparison of the resulting accelerations with accelerometer measurements, and comparison against an existing atmospheric density model, DTM-2000. We apply the method to GPS tracking data from CHAMP, GRACE, SAC-C, Jason-2, TerraSAR-X and COSMIC satellites, spanning 12 years (2001–2012) and covering orbital heights from 400 km to 1300 km. Errors in the estimates, including those introduced by deficiencies in other modeled forces (such as solar radiation pressure and Earth radiation pressure), are evaluated and the signal and noise levels for each satellite are analyzed. The estimated density data from CHAMP, GRACE, SAC-C and TerraSAR-X are identified as having high signal and low noise levels. These data all have high correlations with anominal atmospheric density model and show common features in relative residuals with respect to the nominal model in related parameter space. On the contrary, the estimated density data from COSMIC and Jason-2 show errors larger than the actual signal at corresponding altitudes thus having little practical value for this study. The results demonstrate that this method is applicable to data from a variety of missions and can provide useful total neutral density measurements for atmospheric study up to altitude as high as 715 km, with precision and resolution between those derived from traditional special orbital perturbation analysis and those obtained from onboard accelerometers.     

基于UKF的雷达高度计自主定轨

探讨了利用推广卡尔曼滤波估计非线性系统状态时存在的问题,从而介绍了目前广泛使用的分步逼近的卡尔曼滤波(UKF,Unscented Kalman Filter).为了提高导航的可靠性和准确性,在星敏感器导航系统中引入雷达高度计作为一个新的测量设备,提出了一种基于星上雷达测高仪及星敏感器联合进行卫星自主定轨的算法.建立了比较复杂的地球海平面模型,并考虑了其中风生重力波的影响. 利用雷达测高仪的测量结果和地球形状模型,计算地心矢量在卫星本体中坐标系的方向.利用UKF滤波定轨算法,明显提高了自主定轨的精度.数值仿真结果表明,UKF定轨精度要远优于推广卡尔曼滤波.      

一种多步的基于切换星间测量的多星自主导航算法

针对基于星间测量的多星自主导航问题,从载荷优化和节约成本考虑,提出了一种单套敏感器切换测量的导航方案。建立了该导航方案下的系统状态空间模型,并基于扩展卡尔曼滤波方程给出了导航估计算法。基于多步卡尔曼滤波方法,将集中的滤波算法解耦为多个平行的子滤波器,使计算量降低到原算法的50%以下,并且在切换测量的导航方案下,部分解耦出的子滤波器可以只预测不更新,能够进一步地降低计算负担。给出了多步滤波算法的推导过程,证明了其与标准卡尔曼滤波的数学等价性,故算法的估计性能及计算结果与标准卡尔曼滤波一致,但计算速度有明显提升。最后,通过具体算例给出了算法的仿真验证。     

Orbit determination performances using single- and double-differenced methods: SAC-C and KOMPSAT-2

In this paper, Global Positioning System-based (GPS) Orbit Determination (OD) for the KOrea-Multi-Purpose-SATellite (KOMPSAT)-2 using single- and double-differenced methods is studied. The requirement of KOMPSAT-2 orbit accuracy is to allow 1 m positioning error to generate 1-m panchromatic images. KOMPSAT-2 OD is computed using real on-board GPS data. However, the local time of the KOMPSAT-2 GPS receiver is not synchronized with the zero fractional seconds of the GPS time internally, and it continuously drifts according to the pseudorange epochs. In order to resolve this problem, an OD based on single-differenced GPS data from the KOMPSAT-2 uses the tagged time of the GPS receiver, and the accuracy of the OD result is assessed using the overlapping orbit solution between two adjacent days. The clock error of the GPS satellites in the KOMPSAT-2 single-differenced method is corrected using International GNSS Service (IGS) clock information at 5-min intervals. KOMPSAT-2 OD using both double- and single-differenced methods satisfies the requirement of 1-m accuracy in overlapping three dimensional orbit solutions. The results of the SAC-C OD compared with JPL’s POE (Precise Orbit Ephemeris) are also illustrated to demonstrate the implementation of the single- and double-differenced methods using a satellite that has independent orbit information available for validation.     

近地卫星的GPS自主定轨算法研究

为了用GPS实现近地卫星的高精度自主定轨,提出了采用序贯UD协方差分解滤波算法作为定轨算法.完整地给出了序贯UD分解算法的计算公式,详细地推导了系统的状态方程和观测方程,建立了由9维状态向量和8维观测向量组成的导航系统模型.最后作了数字仿真试验,试验结果表明,文中的定轨算法既有较高的精度又便于星上计算机的实现.      

GPS-only gravity field recovery with GOCE,CHAMP, and GRACE

Gravity missions such as the Gravity field and steady-state Ocean Circulation Explorer (GOCE) are equipped with onboard Global Positioning System (GPS) receivers for precise orbit determination (POD), instrument time-tagging, and the extraction of the long wavelength part of the Earth’s gravity field. The very low orbital altitude of the GOCE satellite and the availability of dense 1 s GPS tracking data are ideal characteristics to exploit the contribution of GPS high-low Satellite-to-Satellite Tracking (hl-SST) to gravity field determination. We present gravity field solutions based on about 8 months of GOCE GPS hl-SST data from 2009 and compare the results with those obtained from the CHAllenging Minisatellite Payload (CHAMP) and Gravity Recovery And Climate Experiment (GRACE) missions. The very low orbital altitude of GOCE significantly improves gravity field recovery from GPS hl-SST data above degree 20, but not for the degrees below 20, where the quality of the spherical harmonic coefficients remains essentially unchanged. Despite the limited time span of GOCE data used, the gravity field of the Earth can be resolved up to about degree 115 using GPS data only. Empirically determined phase center variations (PCVs) of the GOCE onboard GPS helix antenna are, however, mandatory to achieve this performance.     

一种用于GPS/DR组合定位的非线性滤波算法

建立了适用于车辆导航系统的基于UKF(Unscented Kalman Filter)的GPS/DR(Global Positioning System/Dead Reckoning)组合定位滤波模型及算法.针对系统状态方程为线性、观测方程为非线性的特点,提出了一种将UKF和EKF(Extended Kalman Filter)相结合的非线性滤波算法.结合后的算法和原有UKF算法相比减少了在时间更新阶段的运算量,并且由于采用基于Unscented变换的思想来处理系统观测方程的非线性问题,避免了EKF引入的线性化误差,提高了滤波精度.仿真结果证明:算法在减少运算量的同时,仍具有较高的滤波精度,且明显优于EKF,因而能够满足车辆导航系统占用资源少、滤波精度高的要求.      

一种用于高动态GPS频率估计的滤波算法

针对常用高动态GPS(Global Positioning System)频率估计算法扩展卡尔曼滤波(EKF,Extended Kalman Filter)的缺陷,提出了一种新的称为简化无迹高斯粒子滤波(SUGPF,Simplified Unscented Gaussian Particle Filter)的算法.SUGPF将卡尔曼滤波(KF,Kalman Filter)、无迹卡尔曼滤波(UKF,Unscented Kalman Filter)与高斯粒子滤波(GPF, Gaussian Particle Filter)三者相结合.在时间更新阶段,用KF的方法更新预测分布;在测量更新阶段,用UKF的方法得到重要采样函数,并用GPF的方法更新后验分布.仿真结果表明:与EKF和UKF相比,SUGPF性能更优越,功能更全面,在高斯与非高斯观测噪声环境下均能取得与GPF类似的良好性能,并且其计算复杂度低于GPF.     

基于视线测量和轨道预报高轨非合作目标相对导航方法

对于非合作目标,由于中远距离星上相对测量手段有限,大多情况仅能获得视线角信息.仅视线测量相对导航方法在GEO轨道条件下滤波精度低、可观测性差.提出一种基于星间视线方位测量和轨道预报信息结合的非合作目标相对导航方法.建立基于星间相对运动模型的状态方程和基于星间视线测量和轨道预报信息的观测方程,分别选取了扩展卡尔曼滤波和无迹卡尔曼滤波两种方法,仿真分析了轨道预报信息精度和滤波方法对导航精度的影响.     

基于SSUKF的航天器自主导航算法

针对航天器自主导航系统对稳定性、精确性和实时性的要求,将超球面分布采 样点变换SSUT(Spherical Simplex Unscented Transformation)和Unscented卡尔曼滤波(UK F)相结合,研究了基于SSUT的UKF(SSUKF)导航滤波算法.由于SSUT减少了采样点个 数,在保证滤波精度和标准UKF相当的条件下减轻了计算负担.根据UKF和扩展卡尔曼滤波(E KF)计算过程相似的特点,设计了SSUKF和EKF相结合的混合卡尔曼滤波算法.算法通过能够 度量估计误差的模式切换函数,可以自适应地在SSUKF和EKF之间切换,避免了UKF计算效率低 以及EKF对滤波参数敏感、容易发散的缺点.数值仿真结果表明,混合卡尔曼滤波器提高了 计算效率,保证了估计精度,具有良好的鲁棒性,适合于航天器自主导航系统.      

基于GPS对地球同步轨道自动转移飞行器进行导航的可行性分析

研究利用GPS对地球同步轨道自动转移飞行器进行导航的方法,分析了飞行器在转移过程中可用的GPS卫星数目,在地心惯性坐标系下建立了惯导误差和GPS的伪距、伪距变率模型,采用渐消因子的自适应卡尔曼滤波对飞行器进行组合导航.仿真结果表明,可用GPS卫星的数目随着飞行器高度的增高而减少,因此无法利用单一历元观测信息直接对飞行器导航.但采用多历元观测信息和动力学模型相结合的滤波方法可对飞行器进行组合导航,当飞行器初始位置偏差为1 km,初始速度偏差为1 m/s,伪距及伪距变率观测均方差分别为10 m和0.05 m/s时,地球同步轨道自动转移飞行器的最终位置偏差小于50 m,速度偏差小于0.02 m/s.      

一种基于AUKF的航天器自主导航算法

 将非线性Sage-Husa噪声估计器与无迹滤波器(UKF)相结合,提出了一种新型的自适应无迹滤波器(AUKF).对基于AUKF的航天器自主导航系统进行了计算机仿真,仿真结果表明,对于存在测量偏差的自主导航系统,AUKF的导航滤波精度较传统的扩展卡尔曼滤波器(EKF)有显著的提高.进而,针对航天器自主导航系统测量偏差周期时变的特点,提出了提高偏差估计精度的改进算法.仿真结果表明,在适当增加计算量的条件下,利用偏差估计改进算法的AUKF能够进一步提高自主导航系统的导航精度.     

Generating precise and homogeneous orbits for Jason-1 and Jason-2

Driven by the GMES (Global Monitoring for Environment and Security) and GGOS (Global Geodetic Observing System) initiatives the user community has a strong demand for high-quality altimetry products. In order to derive such high-quality altimetry products, precise orbits for the altimetry satellites are a necessity. With the launch of the TOPEX/Poseidon mission in 1992 a still on-going time series of high-accuracy altimetry measurements of ocean topography started, continued by the altimetry missions Jason-1 in 2001 and Jason-2/OSTM in 2008. This paper contributes to the on-going orbit reprocessing carried out by several groups and presents the efforts of the Navigation Support Office at ESA/ESOC using its NAPEOS software for the generation of precise and homogeneous orbits referring to the same reference frame for the altimetry satellites Jason-1 and Jason-2. Data of all three tracking instruments on-board the satellites (beside the altimeter), i.e. GPS, DORIS, and SLR measurements, were used in a combined data analysis. About 7 years of Jason-1 data and more than 1 year of Jason-2 data were processed. Our processing strategy is close to the GDR-C standards. However, we estimated slightly different scaling factors for the solar radiation pressure model of 0.96 and 0.98 for Jason-1 and Jason-2, respectively. We used 30 s sampled GPS data and introduced 30 s satellite clocks stemming from ESOC’s reprocessing of the combined GPS/GLONASS IGS solution. We present the orbit determination results, focusing on the benefits of adding GPS data to the solution. The fully combined solution was found to give the best orbit results. We reach a post-fit RMS of the GPS phase observation residuals of 6 mm for Jason-1 and 7 mm for Jason-2. The DORIS post-fit residuals clearly benefit from using GPS data in addition, as the DORIS data editing improves. The DORIS observation RMS for the fully combined solution is with 3.5 mm and 3.4 mm, respectively, 0.3 mm better than for the DORIS-SLR solution. Our orbit solution agrees well with external solutions from other analysis centers, as CNES, LCA, and JPL. The orbit differences between our fully combined orbits and the CNES GDR-C orbits are of about 0.8 cm for Jason-1 and at 0.9 cm for Jason-2 in the radial direction. In the cross-track component we observe a clear improvement when adding GPS data to the POD process. The 3D-RMS of the orbit differences reveals a good orbit consistency at 2.7 cm and 2.9 cm for Jason-1 and Jason-2. Our resulting orbit series for both Jason satellites refer to the ITRF2005 reference frame and are provided in sp3 file format on our ftp server.     

超低轨道地球卫星脉冲星/星光折射/光谱组合导航

针对超低轨道地球卫星导航自主需求,提出了一种脉冲星/星光折射/光谱测速组合天文导航方法。首先根据地球超低轨道卫星运行轨道动力学方程建立导航系统状态模型;分别根据脉冲到达时间差和星光折射角与天体光谱频率建立导航系统量测模型;使用Unscented卡尔曼滤波方法,降低随机误差对导航精度的影响,使用基于UKF的信息融合方法,有效融合了三种天文导航方法结果数据。经计算机仿真分析,该组合导航方法位置导航误差均值为85.62m,速度误差均值0.190m/s,能够满足超低轨道地球卫星在轨运行导航需求。     

编队飞行卫星群相对轨道测量研究

编队飞行卫星群自主式相对轨道测量和确定是绕飞轨道的关键技术之一,考虑了利用星敏感器和雷达以及利用GPS(Global Positioning System)信号来进行相对定轨的传统方式,提出了基于伪卫星技术的定轨方案.伪卫星技术指在卫星上安装载波发生器和接收器,利用这些装置来进行卫星间的距离测量.在这些方案中,应用了差分GPS技术,采用优化方法求解多元非线性方程.这些测量方法分别适应于不同的情况.利用相对轨道要素的概念,在前面测量结果的基础上,通过卡尔曼滤波进一步提高了定轨精度.仿真计算表明这些方案可以满足不同尺度编队构型保持要求,并给出了部分结果.     

四种卡尔曼滤波器在仅视线测量相对导航中的性能比较

针对航天器交会时在仅有视线测量条件下的相对导航问题,比较了扩展卡尔曼滤波（extended Kalman filter,EKF）、无迹卡尔曼滤波（unscented Kalman filter,UKF）及平方根形式的卡尔曼滤波（square-root extended Kalman filter,SREKF以及square-root unscented Kalman filter,SRUKF）在这一导航问题中的性能.介绍了仅有视线测量条件下相对导航的特点以及上述4种卡尔曼滤波算法;建立了追踪航天器和目标航天器间相对动力学方程以及基于仅视线测量相对导航时的量测方程;结合3种典型的相对运动形式进行了数值仿真.仿真结果表明：在仅视线测量相对导航中,4种算法的精度处于同一量级;UKF估计相对距离的精度稍优于EKF;SREKF和SRUKF估计相对距离的精度稍优于EKF和UKF.     

基于SINS/CNS组合导航系统的多模型自适应估计算法

针对单一模型滤波器在未知或不确定的系统参数下适应性较差的问题,提出了一种新的基于多模型自适应估计(multiple model adaptive estimation,MMAE)的滤波方法。该方法利用改进的卡尔曼滤波代替传统的卡尔曼滤波,比如扩展卡尔曼滤波(extended Kalman filter,EKF)和无迹卡尔曼滤波(unscented Kalman filter,UKF)。EKF和UKF被用来作为多模型自适应估计的子滤波器,从而实现对非线性系统的状态估计。同时,还将该方法应用于基于弹道导弹模型的组合导航中实现了系统仿真。仿真结果表明,与传统的EKF和UKF算法比较,改进的滤波方法可以解决传统模型滤波器适应性差的问题,并提高系统的导航精度。     

粗差拟准检定法在星载GPS低轨卫星定轨中的应用

利用自适应卡尔曼滤波进行星载GPS低轨卫星定轨时,必须解决量测方程中经常存在的粗差问题．在分析以往方法的优缺点后,用拟准检定法来探测和修正量测方程中存在的粗差．该法的优点是辨识粗差准确率高,能同时定位多个粗差．另外,为了克服星载GPS低轨卫星定轨的滤波器可能出现的数值不稳定性及发散现象,还采用了UD分解算法及Sage自适应滤波器．最后用一个CHAMP卫星的模拟算例验证本方法的可行性和有效性．     

Guidepost-based autonomous orbit determination method for GEO satellite

Guidepost-based navigation system is a novel autonomous orbit determination method for the GEO satellite. The system is achieved by using the camera imaging function to obtain the guidepost images and the GNSS signal receiver to obtain the pseudoranges between the GEO and the navigation satellites. Due to the high altitude of GEO satellite and the time-varying sunlight condition in the space environment, it may be difficult to obtain object image points and the distance measurements of GNSS because of the weak visibility of the guideposts. To deal with the problem, a novel integrated orbit determination system is presented. The Earth landmarks, the in-orbit spacecraft and GNSS navigation satellites whose line-of-sights and the distance can be easily obtained are used at the same time as information for the GEO satellite navigation based on the observability conditions analysis. The observability of the GEO satellite navigation system is analyzed through the physical observability, the mathematical observability and the engineering observability through the observing geometry, the rank of observability matrix and the Cramer-Rao lower bound (CRLB) respectively. Besides, the maximum correntropy unscented Kalman filter (MCUKF) algorithm is applied to improve the estimation stability of the system in the presence of non-Gaussian noises. The simulation indicates the feasibility of the proposed scheme.     

脉冲星非实时平差的火星探测自主导航模型

针对基于X射线脉冲星观测的火星探测器自主导航,研究了几种不同的实时自适应方法,包括:扩展卡尔曼滤波(EKF),自适应扩展卡尔曼滤波(AEKF)和鲁棒自适应扩展滤波(RAEKF)。首先根据脉冲星导航原理,模拟了观测值:脉冲到达时刻;接着,分别利用扩展卡尔曼滤波,自适应扩展卡尔曼滤波和鲁棒自适应扩展滤波方法估算出探测器的位置和速度;最后,上述几种滤波轨道与STK模拟的标称轨道较差,然后比较它们的滤波精度发现:AEKF和RAEKF的精度相对较高,AEKF的三个轴向滤波位置精度达到:X轴优于100m、Y和Z轴优于30m,优于VLBI技术的km量级,和Doppler技术的精度相当。