Swarm低轨卫星星座的GPS接收机差分码偏差估计

差分码偏差(differential code bias,DCB)是指由全球导航卫星系统(global navigation satellite system, GNSS)信号接收和发射硬件导致的频率相关的偏差项,对电离层估计有显著的影响,在利用GNSS观测数据提取电离层总电子含量时需要被精确修正,研究利用低轨卫星的星载GNSS观测数据估计DCB尤为重要。使用Swarm星座3颗卫星GPS接收机2016年1月的双频观测值,设计了独立估计和联合估计两种估计方案,采用附加限制条件的间接平差方法对GPS卫星以及星载接收机的DCB进行估计。以中国科学院和德国宇航中心的DCB产品作为参考,分析了两种估计方案的精度和稳定性,相较于独立估计方案,联合估计方案得到的GPS卫星DCB的稳定性较独立估计方案提高了16.6%,且与参考DCB具有更好的一致性。     

基于GPS矢量观测信息的姿态确定算法

用于GPS姿态确定的矢量化算法可等价于两级最优问题。第一级把GPS载波相位观测量转换为矢量观测量。第二级是Wahba问题,即从矢量观测量获得最佳姿态解。Wahba问题可用四元数法求解,如QUEST方法。本文采用基于小角度的迭代法求解Wahba问题。在均衡星座或均衡基线务件下,两级最优解亦是全局最优解。实验结果表明迭代解的精度与QUEST解相同。实验中也应用了改进的TRIAD算法以比较两级最优解。     

偏航姿态对GPS和GLONASS精密轨道和钟差的影响

利用全球约110个国际GNSS服务（International GNSS Service,IGS）测站2013年全年观测数据,分析和研究了GPS和全球卫星导航系统（global navigation satellite system,GLONASS）卫星偏航姿态对其精密轨道和钟差的影响。结果表明,偏航姿态对不同型号GPS卫星轨道和钟差的影响程度不同,当采用偏航姿态改正后地影期的BLOCK ⅡA型卫星轨道改善可达17 mm,BLOCK ⅡF为近5 mm,而BLOCK ⅡR几乎不受影响。由于偏航姿态对GLONASS-M卫星定轨精度影响较大,因此,当改正偏航姿态后所有GLONASS卫星相对于IGS最终轨道平均一维差异提高10 mm,相对于德国地学中心（German Research Center for Geosciences,GFZ）最终钟差平均标准差提升0.034 ns。     

Combination of GNSS and SLR observations using satellite co-locations

Satellite Laser Ranging (SLR) observations to Global Navigation Satellite System (GNSS) satellites may be used for several purposes. On one hand, the range measurement may be used as an independent validation for satellite orbits derived solely from GNSS microwave observations. On the other hand, both observation types may be analyzed together to generate a combined orbit. The latter procedure implies that one common set of orbit parameters is estimated from GNSS and SLR data. We performed such a combined processing of GNSS and SLR using the data of the year 2008. During this period, two GPS and four GLONASS satellites could be used as satellite co-locations. We focus on the general procedure for this type of combined processing and the impact on the terrestrial reference frame (including scale and geocenter), the GNSS satellite antenna offsets (SAO) and the SLR range biases. We show that the combination using only satellite co-locations as connection between GNSS and SLR is possible and allows the estimation of SLR station coordinates at the level of 1–2 cm. The SLR observations to GNSS satellites provide the scale allowing the estimation of GNSS SAO without relying on the scale of any a priori terrestrial reference frame. We show that the necessity to estimate SLR range biases does not prohibit the estimation of GNSS SAO. A good distribution of SLR observations allows a common estimation of the two parameter types. The estimated corrections for the GNSS SAO are 119 mm and −13 mm on average for the GPS and GLONASS satellites, respectively. The resulting SLR range biases suggest that it might be sufficient to estimate one parameter per station representing a range bias common to all GNSS satellites. The estimated biases are in the range of a few centimeters up to 5 cm. Scale differences of 0.9 ppb are seen between GNSS and SLR.     

Hybrid derivative-free extended Kalman filter for unknown lever arm estimation in tightly coupled DGPS/INS integration

Differential carrier phase observations from GPS (Global Positioning System) integrated with high-rate sensor measurements, such as those from an inertial navigation system (INS) or an inertial measurement unit (IMU), in a tightly coupled approach can guarantee continuous and precise geo-location information by bridging short outages in GPS and providing a solution even when less than four satellites are visible. However, to be efficient, the integration requires precise knowledge of the lever arm, i.e. the position vector of the GPS antenna relative to the IMU. A previously determined lever arm by direct measurement is not always available in real applications; therefore, an efficient automatic estimation method can be very useful. We propose a new hybrid derivative-free extended Kalman filter for the estimation of the unknown lever arm in tightly coupled GPS/INS integration. The new approach takes advantage of both the linear time propagation of the Kalman filter and the nonlinear measurement propagation of the derivative-free extended Kalman filter. Compared to the unscented Kalman filter, which in recent years is typically used as a superior alternative to the extended Kalman filter for nonlinear estimation, the virtue of the new Kalman filter is equal estimation accuracy at a significantly reduced computational burden. The performance of the new lever arm estimation method is assessed with simulated and real data. Simulations show that the proposed technique can estimate the unknown lever arm correctly provided that maneuvers with attitude changes are performed during initialization. Field test results confirm the effectiveness of the new method.     

导航卫星自主定轨的算法研究及模拟结果

讨论了利用卫星-卫星间的距离观测值建立导航卫星系统自主定轨的数学方法，并用GPS星座模拟星间观测值，采用滤波算法计算卫星的状态参数。模拟结果表明，在空间测距精度一定的情况下，自主定轨精度能高于GPS广播星历，因而能较精确地维持卫星系统的坐标框架。     

针对北斗系统的降维快速高精度定向算法

通过分析北斗系统的星座特点及GEO卫星特征,提出了一种针对北斗系统的快速高精度定向方法。该方法利用北斗GEO卫星东西向几何构型好的优势,首先由GEO卫星的观测值结合降维解算理论解算基线向量候选值;然后通过模糊度函数法对候选值进行判决,得到最优基线向量,解出宽巷模糊度;最后在此基础上解算B1模糊度,进行高精度定向。该方法不但可以改善利用北斗定向解算所产生的病态性,而且可以减小模糊度搜索范围,实现单历元整周模糊度快速解算。利用实测北斗星历对算法进行了仿真验证,结果表明在实时动态条件下,该方法解算B1的整周模糊度成功率为99.31%,确定的俯仰角标准差为0.07°,航向角标准差为0.13°,是一种高效快速的定向算法。     

GIM和不同约束条件相结合的BDS差分码偏差估计

现阶段BDS卫星和地面跟踪站数量较少,用BDS单系统获取的DCB精度有限,针对此问题,本文基于CODE GIM,采用两种不同的"零均值"基准约束方案(分别称为约束1和约束2),选取2015年(DOY002-090)MGEX的BDS数据,求解BDS的DCB,并对其进行精度评估。结果表明,两种约束方案下,卫星DCB差值整体趋势一致,DCBC2I-C7I、DCBC2I-C6I的系统性偏差分别约为-3.3ns和1.2ns,接收机DCB的系统性偏差与卫星DCB大小相同,符号相反。相对于约束1,施加约束2后,IGSO和MEO卫星DCB估值更加稳定(DCBC2I-C7ISTD最大改善21%,DCBC2I-C6ISTD最大改善13%),IGSO和MEO卫星的稳定性(分别在0.1ns和0.2ns左右)优于GEO卫星(0.150.32ns)。约束2的DCB估值效果不仅与CAS/DLR产品有较好的一致性(Bias:-0.40.2ns),而且顾及了BDS卫星DCB间的稳定性差异。两种约束方案下,BDS接收机DCB的STD无明显变化,说明约束的选择对BDS接收机DCB的稳定性无明显影响。BDS接收机DCB稳定性整体上优于1ns,中高纬度区域较好(STD 0.4ns左右),低纬度区域稍差(STD 0.81ns)。     

基于双差伪距/伪距率的GPS/SINS紧组合导航

GPS/SINS组合导航系统的观测模型直接关系着导航系统的精度。提出了一种基于双差伪距/伪距率的GPS/SINS紧组合观测模型。分析了采用双差伪距和采用双差伪距/伪距率两种观测模型对组合导航输出参数精度的影响。实测数据结果表明,采用双差伪距和采用双差伪距/伪距率作为观测值均能实现组合导航系统的收敛。引入双差伪距率观测值明显改善了系统的可观测性,不仅提高了组合导航中速度和姿态角的估计精度,也加快了速度误差和姿态角误差估计的收敛速度。     

A new model for GPS yaw attitude

modeling of the GPS satellite yaw attitude is a key element in high-precision geophysical applications. This fact is illustrated here as a new model for the GPS satellite yaw attitude is introduced. The model constitutes a significant improvement over the previously available model in terms of efficiency, flexibility and portability. The model is described in detail and implementation issues, including the proper estimation strategy, are addressed. The performance of the new model is analyzed and an error budget is presented. Finally, the implementation of the yaw bias on the GPS satellites is reviewed from its inception until it reached a steady state in November, 1995.     

多星融合的土壤湿度滚动式估算模型

全球定位系统干涉反射测量(GPS-IR)是一种新的遥感技术,可用于估算近地表土壤水分含量。考虑到多卫星融合的优势和土壤湿度的时空尺度性,提出一种基于多星融合的土壤湿度最小二乘支持向量机(LS-SVM)滚动式估算模型。首先通过低阶多项式拟合分离GPS卫星直射和反射信号,进而建立反射信号正弦拟合模型,获取相对延迟相位。最后,通过线性回归模型有效分析和选取多卫星相对延迟相位,并建立基于多星融合的最小二乘支持向量机模型进行滚动式估算土壤湿度。以美国板块边界观测计划PBO提供的监测数据为例,对比分析利用单颗、多颗GPS卫星进行土壤湿度滚动式估算的可行性和有效性。经理论分析和两个测站实验表明:该模型充分发挥了LS-SVM的优势,有效综合了各卫星的性能,改善了采用单颗卫星进行土壤湿度估算时,其结果极易出现异常跳变的现象;模型只需较少的建模数据,采用滚动式能实现较长时间的估算,估算误差较为稳定;模型所估算的结果与土壤湿度实测值之间的相关系数R2以及均方根误差分别为0.942和0.962、0.072和0.032,相对于部分单一卫星至少提高了18.18%。因此,土壤湿度问题可作为非线性事件处理,采用多卫星融合估算是可行和有效的。     

VLBI observations of GNSS-satellites: from scheduling to analysis

The possibility of observing satellites with the very long baseline interferometry (VLBI) technique has been discussed for several years in the geodetic community, with observations of either existing satellites of the global navigation satellite systems or of satellites dedicated to realise a space tie. Such observations were carried out using the Australian telescopes in Hobart and Ceduna which, for the first time, integrated all the necessary steps: planning the observations (automated scheduling), correlation of the data and the generation of a series of time delay observables suitable for a subsequent geodetic analysis. We report on the development of new and the adaptation of existing routines for observing and data processing, focusing on technology development. The aim was to use methods that are routinely used in geodetic VLBI. A series of test experiments of up to six hours duration was performed, allowing to improve the observations from session to session and revealing new problems still to be solved. The newly developed procedures and programs now enable more observations. Further development assumed, this bears the prospect of being directly applied to the observation of dedicated space-tie satellites.     

多模GNSS精密卫星钟差估计与分析

对基于历元间差分相位和非差伪距观测值的混合差分卫星钟差估计方法进行了改进,实现了多模全球导航卫星系统（Global Navigation Satellite System,GNSS）卫星钟差联合快速估计。选择了全球分布的50个跟踪站进行实验,对卫星钟差精度进行了分析和精密单点定位（Precise Point Positioning,PPP）验证。结果表明:多模卫星钟差与武汉大学提供的最终精密卫星钟差互差优于0.2 ns,精密单点定位结果与武汉大学发布的最终精密卫星轨道和钟差产品的定位精度相当。     

实时估计不同类型北斗卫星观测值的随机模型

为分析北斗卫星观测值随机特性,估计了地球静止轨道、倾斜地球同步卫星轨道、中地球轨道卫星载波相位观测值的方差分量。发现不同接收机和不同类型卫星观测值方差分量的大小和时变特性具有明显差异。为构建更切实际的方差结构随机模型,提出利用迭代最小二乘和最小范数二次无偏估计相结合的方法,实时估计不同类型北斗卫星观测值方差分量。为评估实时估计随机模型的性能,对243 m、645 m、10 137 m三条不同长度基线进行精密相对定位测试,结果表明:实时估计随机模型能有效改善北斗卫星精密单历元动态相对定位性能,尤其当站间距离较长时改善更显著。10 137m基线测试结果表明,1h数据单历元解在北、东、高方向,平均定位精度分别提高了41.3%、54.5%、51.6%,稳定性分别提高了38.4%、17.7%、39.7%。     

Precise orbit determination of BeiDou constellation: method comparison

Chinese BeiDou navigation satellite system is in official service as a regional constellation with five geostationary earth orbit (GEO) satellites, five inclined geosynchronous satellite orbit (IGSO) satellites and four medium earth orbit (MEO) satellites. There are mainly two methods for precise orbit determination of the BeiDou constellation found in the current literatures. One is the independent single-system method, where only BeiDou observations are used without help from other GNSS systems. The other is the two-step GPS-assisted method where in the first step, GPS data are used to resolve some common parameters, such as station coordinates, receiver clocks and zenith tropospheric delay parameters, which are then introduced as known quantities in BeiDou processing in the second step. We conduct a thorough performance comparison between the two methods. Observations from the BeiDou experimental tracking stations and the IGS Multi-GNSS Experiment network from January 1 to March 31, 2013, are processed with the Positioning and Navigation Data Analyst (PANDA) software. The results show that for BeiDou IGSO and MEO satellites, the two-step GPS-assisted method outperforms the independent single-system method in both internal orbit overlap precision and external satellite laser ranging validation. For BeiDou GEO satellites, the two methods show close performances. Zenith tropospheric delays estimated from the first method are very close to those estimated from GPS precise point positioning in the second method, with differences of several millimeters. Satellite clock estimates from the two methods show similar performances when assessing the stability of the BeiDou on board clocks.     

Performance analysis of triple-frequency ambiguity resolution with BeiDou observations

We investigate triple-frequency ambiguity resolution performance using real BeiDou data. We test four ambiguity resolution (AR) methods which are applicable to triple-frequency observations. These are least squares ambiguity decorrelation adjustment (LAMBDA), GF-TCAR (geometry-free three-carrier ambiguity resolution), GB-TCAR (geometry-based three-carrier ambiguity resolution) and GIF-TCAR (three-carrier ambiguity resolution based on the geometry-free and ionospheric-free combination). A comparison between LAMBDA, GF-TCAR and GB-TCAR was conducted over three short baselines and two medium baselines. The results indicated that LAMBDA is optimal in both short baseline and medium baseline cases. However, the performances of GB-TCAR and LAMBDA differ slightly for short baselines. Compared with GF-TCAR, which uses the geometry-free model, the GB-TCAR using the geometry-based model improves the AR performance significantly. Compared with dual-frequency observations, the LAMBDA AR results show a significant improvement when using triple-frequency observations over short baselines. The performance of GIF-TCAR is evaluated using multi-epoch observations. The results indicated that multi-path errors on carrier phases will have a significant influence on GIF-TCAR AR results, which leads to different GIF-TCAR AR performance for different type of satellites. For GEO (Geostationary Orbit) satellites, the ambiguities can barely be correctly fixed because the multi-path errors on carrier phases are very systematic. For IGSO (Inclined Geosynchronous Orbit) and MEO (Medium Earth Orbit) satellites, when the elevation cutoff angle is set as 30°, several tens to several hundreds of epochs are needed for correctly fixing the narrow lane ambiguities. The comparison of positioning performance between dual-frequency observations and triple-frequency observations was also conducted. The results indicated that a minor improvement can be achieved by using triple-frequency observations compared with using dual-frequency observations.     

"北斗"系统低纬度区域定位精度增强方案探讨

针对我国“北斗”双星定位系统(BDS BeiDou System)在低纬度地区定位精度差的弱点，探讨了几种增强方案，并从精度因子(GDOP Geography Dilution of Precision)的角度比较各方案的优劣，研究表明，基于伪卫星增强双星的方案可改善卫星几何布局，从而有效提高该区域用户的定位精度。仿真说明改方案可提供百米级的定位结果，优于常规的单点定位精度。     

INS辅助的实时动态GNSS单频周跳探测

采用全球卫星导航系统（Global Navigation Satellite System,GNSS）模糊度固定解可提高GNSS/惯性导航系统（inertial navigation system,INS）组合导航定位精度,而在复杂环境下,单频GNSS难以实现完善的实时动态周跳探测,影响GNSS模糊度保持。研究了星间单差与站星双差的INS辅助GNSS单频周跳探测检验量,重点分析检验量的误差特性。分析得出检验量误差主要与INS增量误差有关,受接收机至待检星与参考星之间星地矢量夹角的影响。提出了选取两颗参考星并优选探测检验量的方法,降低方位角因素的影响,提高周跳探测性能。周跳探测的阈值在滑动窗口内估计,对INS误差被GNSS误差淹没的部分进行抑制,充分反映INS误差影响,阈值估计具有较强的自适应性。     

Low-low satellite-to-satellite tracking: a comparison between analytical linear orbit perturbation theory and numerical integration

Low-low satellite-to-satellite tracking (ll-SST) range-rate observations have been predicted by two methods: one based on a linear perturbation theory in combination with the Hill equations, and one based on solving the equations of motion of two low-flying satellites by numerical integration. The two methods produce almost equivalent Fourier spectra of the range-rate observations after properly taking into account a few resonant terms. For a typical GRACE-type configuration, where the two satellites trail each other at a distance of 300 km at an altitude of 460 km, and in the presence of the EGM96 gravity field model, complete to spherical harmonic degree and order 70, the agreement between the Fourier spectra is about 1 mm/s compared to a root-mean-square (RMS) value of more than 220 mm/s for the range-rate signal. The discrepancy of 1 mm/s can be reduced significantly when not taking into account perturbations caused by the J₂ term. Excluding the J₂ term, the agreement between the two methods improves to 0.4 mm/s compared to a RMS value of 6 mm/s for the range-rate signal. These values are 0.01 and 2.3 mm/s when ignoring the spectrum for frequencies below two cycles per orbital revolution, reducing the discrepancy even further to about 0.5% of the signal. The selected linear perturbation theory is thus capable of modeling gravity field induced range-rate observations with very high precision for a large part of the spectrum.     

一种历元间差分单站单频周跳探测与修复方法

提出了一种基于历元间单差观测值的单站单频周跳探测与修复方法。通过假定前一历元为基准站,当前历元为流动站,采用相对定位处理模式获取当前历元观测值的验后单位权中误差,并基于抗差最小二乘获取每颗卫星的观测值残差,对单站单频数据进行周跳探测与修复。通过对实测数据的验证分析表明,按照本文方法可以100%探测周跳发生的历元。并且,当至少4颗卫星未发生周跳时,如发生异常卫星数小于可视卫星数的30%,则在95%以上的情况下可以有效确定异常卫星;当异常卫星过多时,本文方法确定异常卫星的成功率会有所下降。但是,对于探测出发生周跳的异常卫星,本文方法均可100%对其周跳进行修复。