低轨导航增强卫星的轨道状态型星历参数设计

导航增强卫星从高轨拓展到低轨,需要设计可靠的低轨道LEO广播星历参数。GLONASS广播星历模型能够利用9个状态参数高精度描述30min内中高轨卫星的摄动运动,但不能直接用于低轨卫星。为了适应LEO的摄动力的短期快变化,设计了基于轨道状态型的21参数广播星历模型。分析了低轨卫星主要摄动力的短期变化规律,选取了二次多项式和基于轨道半周期的三角函数来补偿大气阻力等主要摄动在3个方向上的累计。基于星历拟合试验讨论了拟合参数个数、拟合时段和数据间隔对500~1200km轨道高度的LEO圆轨道的拟合精度影响。试验表明,当拟合时段为20min(约1/5个轨道周期)时,轨道高度大于700km的近圆轨道,拟合用户距离误差(FURE)精度优于0.05m;高度为1000km时,FURE平均精度达到0.03m。     

LEO广播星历参数设计的无奇点根数法

针对LEO卫星的广播星历参数设计,在分析低地球轨道(LEO)卫星轨道根数变化特征的基础上,从第二类无奇点根数出发,对标准GPS广播星历的轨道及其摄动表征进行改造,提出一套专用于LEO卫星的23参数星历表示法,并推导了相应的用户卫星位置计算公式。拟合试验表明,20 min星历拟合的用户距离误差(URE)的均方根优于0.05 m。     

广播星历参数拟合算法研究

导航卫星一般采用近圆轨道,当卫星轨道偏心率或者轨道倾角接近于0时,利用GPS卫星开普勒轨道根数拟合卫星广播星历会出现一些问题。当高轨卫星轨道偏心率接近0时,广播星历拟合精度下降甚至拟合失败,为此本文提出了减少拟合参数个数、固定轨道根数M0或者延长星历参数拟合弧段长度的方法;针对GEO卫星在小倾角情况下,广播星历可能拟合失败的情况,本文提出了改变坐标系参考轨道面,在新的坐标系下拟合广播星历的方法。结果表明,改进后的拟合方法能适用于各种类型的导航卫星轨道,拟合精度在cm级或者mm级。     

基于第一类无奇点根数的LEO历书参数设计

GNSS技术蓬勃发展,在国防建设和国民经济发展中发挥了重要作用。但也因其无法快速解算整周模糊度、复杂环境下适应性差、完好性差等缺点,限制了其作用的最大发挥。基于LEO通信卫星星座的系统增强可以很好地克服这些缺点。要实现该增强系统,基础之一就是如何生成LEO卫星的历书星历。为解决这个问题,从第一类无奇点出发对GPS标准历书进行改造,提出了一套专用于LEO卫星的10参数历书集,并推导了历书计算公式。对600~1 500 km轨道高度的2~7 d的LEO卫星轨道进行了拟合实验。结果表明,高度600 km时长2 d,高度700 km时长4 d,高度800 km时长7 d历书拟合的用户距离误差(URE)的均方根误差(RMS)分别优于936.021,944.087和956.183 m。     

GEO广播星历参数设计的无奇点根数法

北斗导航星座的GEO广播星历格式与MEO和IGSO的格式一致,但是GEO星历参数拟合和用户GEO卫星位置计算均需要引进人为设置的5°倾角旋转。从第二类无奇点根数出发,对标准广播星历的轨道及其摄动表征进行改造,提出一套专用于GEO卫星的16参数星历表示法,并推导了相应的用户卫星位置计算公式。拟合试验表明,在非地影期间,2h和3h星历拟合的用户距离误差(URE)的均方根分别优于0.05m和0.1m。     

工程化广播星历参数拟合算法与接口设计

对导航卫星广播星历参数拟合算法和接口设计问题进行了研究。通过条件数、参数相关性分析,指出小倾角问题是造成GPS开普勒轨道根数广播星历拟合算法不能适用于GEO卫星的最主要原因;通过分析定轨理论和拟合实例证明,GEO卫星星历参数Crc、Crs超限的主要原因是由于其轨道特性决定的;针对GEO卫星星历参数拟合法方程严重病态的问题,提出了动态加权的带参数约束条件平差算法。该方法能有效稳定星历拟合结果,解决Δn等星历参数超限的问题。     

GPS卫星定轨研究及STK仿真分析

首先对GPS卫星的轨道定轨的原理进行了简单描述,以卫星的广播星历数据为基础,计算出卫星的16个轨道参数,进而得到该卫星任一时刻的瞬时坐标。以2017年4月7日的GPS07号卫星的广播星历数据为例,计算该GPS卫星当天的轨道坐标,并将结果与当天IGS提供的精密星历所提供的卫星轨道坐标进行比较,计算结果显示广播星历误差可达5 m。最后使用STK软件调用MATLAB软件读取数据进行仿真分析,模拟出卫星的轨道,并计算出卫星的坐标,数值结果可为轨道设计提供技术参考。     

傅里叶级数拟合LEO轨道误差下的BDS/GPS/LEO精密单点定位

针对目前多数低轨道地球卫星(LEO)设计处于初步论证阶段,LEO轨道无法精确获取,轨道误差难以准确表述的问题,提出了一种傅里叶级数拟合LEO轨道误差下的BDS/GPS/LEO精密单点定位(PPP)分析方法.该方法根据LEO精密定轨后的轨道误差呈现准周期正弦特性,利用傅里叶级数拟合LEO轨道误差,并仿真生成LEO观测数据...     

面向精密位置服务的低轨卫星轨道预报精度分析EI北大核心CSCD

LEO卫星精密轨道预报是LEO导航增强系统中重要的技术环节之一,本文使用多种算法来实现不同任务需求下的轨道预报。对于在地面处理系统实现的LEO轨道预报,算法1采用定轨预报同时处理的策略,算法2将离散轨道点进行动力学拟合再进行积分外推。GRACE-C卫星预报5、10、15 min的URE平均精度分别为5.25、5.67、6.25 cm;HY2A卫星为7.83、8.69、9.66 cm;SWARM-A卫星为8.88、9.22、9.63 cm;SWARM-B卫星为8.49、8.98、9.63 cm。对于计算条件受限的LEO星上轨道预报,本文利用单个轨道点及简单动力学模型进行轨道积分外推的算法。该算法主要考虑地球中心引力及非球形引力摄动,因此地球重力场阶次对轨道预报精度产生较大影响。平均高度为500 km的LEO卫星选取60阶重力场,高度为1000 km的LEO卫星选取30阶重力场,可实现预报10 min轨道优于10 cm的预报精度。     

一种地球静止轨道卫星的快速恢复定轨方法

地球静止轨道(GEO)卫星频繁的轨道机动对高精度、实时不间断的导航服务需求提出新的更高要求,如何在短弧跟踪条件下提高GEO卫星轨道快速恢复能力,是提升导航系统服务精度的关键因素。针对该问题,提出基于9参数星历拟合的GEO卫星短弧运动学定轨方法,详细推导定轨的数学模型与偏导模型,针对GEO卫星星历参数拟合中的奇异问题,提出相应的解决方法和措施。利用COMPASS GEO卫星实测自发自收数据进行短弧定轨试验与分析,结果表明:①10 min短弧运动学定轨的位置精度优于19 m,速度精度为4 mm/s,速度精度明显优于MEO卫星;②预报5 min的位置精度为17.760 m,预报10 min的位置精度为18.168 m;③解决GEO卫星频繁轨控所带来的轨道快速恢复问题,满足短弧跟踪条件下RDSS的服务需求。     

Design and validation of broadcast ephemeris for low Earth orbit satellites

Low Earth orbit (LEO) constellations have potentialities to augment global navigation satellite systems for better service performance. The prerequisite is to provide the broadcast ephemerides that meet the accuracy requirement for navigation and positioning. In this study, the Kepler ephemeris model is chosen as the basis of LEO broadcast ephemeris design for backward compatibility and simplicity. To eliminate the singularity caused by the smaller eccentricity of LEO satellites compared to MEO satellites, non-singular elements are introduced for curve fitting of parameters and then transformed to Kepler elements to assure the algorithm of ephemeris computation remains unchanged for the user. We analyze the variation characteristics of LEO orbital elements and establish suitable broadcast ephemeris models considering fit accuracy, number of parameters, fit interval, and orbital altitude. The results of the fit accuracy for different fit intervals and orbital altitudes suggest that the optimal parameter selections are \((Crs3,Crc3)\), \((Crs3,Crc3, \, \dot{a},\dot{n})\) and \(\left( {Crs3,Crc3, \, \dot{a},\dot{n}, \, \ddot{i},\ddot{a}} \right)\), i.e., adding two, four or six parameters to the GPS 16-parameter ephemeris. When adding four parameters, the fit accuracy can be improved by about one order of magnitude compared to the GPS 16-parameter ephemeris model, and fit errors of less than 10 cm can be achieved with 20-min fit interval for a 400–1400 km orbital altitude. In addition, the effects of the number of parameters, fit interval, and orbit altitude on fit accuracy are discussed in detail. The validation with four LEO satellites in orbit also confirms the effectiveness of proposed models.     

GPS卫星广播星历轨道误差突变性分析

针对GPS卫星播发的广播星历存在误差突变的问题进行了有关研究。利用切比雪夫多项式,分别以不同的拟合时段计算卫星轨道坐标,然后分别与对应历元的IGS精密星历所提供的GPS卫星的坐标进行比较,发现了某些GPS卫星广播星历轨道误差变化的规律。这对如何削弱广播星历的轨道误差,提高导航与定位精度是十分有益的。     

无旋转倾角的NAV/CNAV型GEO广播星历拟合

目前北斗GEO的星历拟合算法和用户卫星位置算法均引进了人为设置的5°倾角旋转,此外,少数星历参数还有超限现象。取消GEO的旋转倾角和抑制参数超限能够统一北斗混合星座的用户算法。基于第一类无奇点根数,分析了无旋转倾角的GEO两步法星历参数拟合算法。讨论了GEO的参数超限原因,提出采用固定1至2个超限参数取值的缩减参数拟合法。北斗GEO卫星在非地影期和地影期的拟合试验表明,拟合成功率和拟合精度能够保证,拟合用户距离误差(URE)的平均值优于3mm;缩减参数拟合法能够抑制特定时段下的参数超限问题,但是拟合URE放大到2cm。     

低轨卫星增强北斗三号导航星座性能分析

针对低轨卫星星座有待合理化设计的问题,深入研究了低轨卫星星座增强北斗三号系统定位性能。分析轨道高度、轨道倾角、星座构型对星座覆盖性能的影响,仿真北斗三号、GPS和3种不同类型的低轨星座,研究各低轨星座与北斗三号、GPS的组合系统在所选7个测站以及全球范围内的可见卫星数和PDOP值分布。结果表明低轨卫星对北斗三号的增强效果主要与低轨卫星数目有关,且不同轨道倾角的组合低轨星座有利于均衡系统在全球范围内的可见卫星数与PDOP值分布。低轨卫星有望通过改善卫星观测几何构型提高北斗三号系统的定位性能,且增强效果与低轨星座构型密切相关。     

Precision real-time navigation of LEO satellites using global positioning system measurements

Continued advancements in remote sensing technology along with a trend towards highly autonomous spacecraft provide a strong motivation for accurate real-time navigation of satellites in low Earth orbit (LEO). Global Navigation Satellite System (GNSS) sensors nowadays enable a continuous tracking and provide low-noise radiometric measurements onboard a user spacecraft. Following the deactivation of Selective Availability a representative real-time positioning accuracy of 10 m is presently achieved by spaceborne global positioning system (GPS) receivers on LEO satellites. This accuracy can notably be improved by use of dynamic orbit determination techniques. Besides a filtering of measurement noise and other short-term errors, these techniques enable the processing of ambiguous measurements such as carrier phase or code-carrier combinations. In this paper a reference algorithm for real-time onboard orbit determination is described and tested with GPS measurements from various ongoing space missions covering an altitude range of 400–800 km. A trade-off between modeling effort and achievable accuracy is performed, which takes into account the limitations of available onboard processors and the restricted upload capabilities. Furthermore, the benefits of different measurements types and the available real-time ephemeris products are assessed. Using GPS broadcast ephemerides a real-time position accuracy of about 0.5 m (3D rms) is feasible with dual-frequency carrier phase measurements. Slightly inferior results (0.6–1 m) are achieved with single-frequency code-carrier combinations or dual-frequency code. For further performance improvements the use of more accurate real-time GPS ephemeris products is mandatory. By way of example, it is shown that the TDRSS Augmentation Service for Satellites (TASS) offers the potential for 0.1–0.2 m real-time navigation accuracies onboard LEO satellites.     

联合地面和星载数据精密确定GPS卫星轨道

给出了联合定轨的数学模型,从6个试验的结果说明低轨卫星的星载GPS观测值对GPS卫星精密定轨的贡献。单天解的结果表明,相对于仅使用43个地面跟踪站的定轨结果,增加3颗低轨卫星的观测数据可以使GPS卫星的轨道准确度平均提高40%,即使仅用21个地面站和3颗低轨卫星也可以使GPS卫星的轨道与IGS最终轨道之差的RMS在5cm左右。     

高精度星载GPS实时定轨卡尔曼滤波模型

在动力学模型补偿算法的基础上,推导了星载GPS实时定轨的卡尔曼滤波模型。以此为理论基础,自主研制了星载GPS实时定轨软件SATODS。使用CHAMP卫星上的星载GPS实测伪距数据以及GPS卫星广播星历来模拟实时定轨数据处理,并将实时定轨结果与JPL精密轨道进行比较分析。结果表明,在滤波收敛后,实时定轨的轨道精度和速度精度的3dRMS分别可达到1.0m和1.2mm/s,受观测数据的GPS卫星数、PDOP值、粗差数据和数据中断等因素的影响较小。     

Pseudo-Stochastic Orbit Modeling Techniques for Low-Earth Orbiters

The Earth’s non-spherical mass distribution and atmospheric drag cause the strongest perturbations on very low-Earth orbiting satellites (LEOs). Models of gravitational and non-gravitational accelerations are utilized in dynamic precise orbit determination (POD) with GPS data, but it is also possible to derive LEO positions based on GPS precise point positioning without dynamical information. We use the reduced-dynamic technique for LEO POD, which combines the geometric strength of the GPS observations with the force models, and investigate the performance of different pseudo-stochastic orbit parametrizations, such as instantaneous velocity changes (pulses), piecewise constant accelerations, and continuous piecewise linear accelerations. The estimation of such empirical orbit parameters in a standard least-squares adjustment process of GPS observations, together with other relevant parameters, strives for the highest precision in the computation of LEO trajectories. We used the procedures for the CHAMP satellite and found that the orbits may be validated by means of independent SLR measurements at the level of 3.2 cm RMS. Validations with independent accelerometer data revealed correlations at the level of 95% in the along-track direction. As expected, the empirical parameters compensate to a certain extent for deficiencies in the dynamic models. We analyzed the capability of pseudo-stochastic parameters for deriving information about the mismodeled part of the force field and found evidence that the resulting orbits may be used to recover force field parameters, if the number of pseudo-stochastic parameters is large enough. Results based on simulations showed a significantly better performance of acceleration-based orbits for gravity field recovery than for pulse-based orbits, with a quality comparable to a direct estimation if unconstrained accelerations are set up every 30 s.