Kinematic absolute and relative orbit determination of Swarm satellites with heterogeneous orbits
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摘要:
精密位置信息是低轨卫星在轨任务成功实施的关键。载波相位模糊度的固定对GPS精密定位、定轨至关重要。利用观测值偏差产品对卫星端硬件偏差进行改正，采用星间单差消除接收机端偏差，实现单接收机模糊度固定。利用Swarm星载实测数据开展运动学绝对和相对精密定轨，分别固定单星模糊度和双差模糊度，研究模糊度固定对运动学定轨精度的影响。结果表明：固定模糊度可明显提升定轨精度。作为参考的简化动力学单星模糊度固定(SD-AR)解轨道卫星激光测距(SLR)残差标准差优于10 mm，相对于浮点解提升了20%。对于运动学绝对定轨，双差模糊度固定(DD-AR)解定轨精度相对浮点解提升26%，SD-AR解定轨精度提升46%。运动学相对定轨中，Swarm-AC编队SD-AR和DD-AR解基线精度相对浮点解提升40%；对于Swarm-AB和Swarm-BC异构轨道编队卫星，选取特定时段观测数据开展相对定轨，相对于浮点解结果，SD-AR解基线精度提升48%，DD-AR解基线精度提升54%。低轨卫星运动学定轨中固定载波相位模糊度可显著提升绝对和相对定轨的精度。
Abstract:Precise position information is the key to guaranteeing the successful implementation of low-earth-orbit satellite missions. The fixing of carrier phase ambiguities is important for the precise positioning and precise orbit determination of the GPS. The satellite-end hardware bias was corrected by using the observation specific bias product, and the receiver-end bias was eliminated by using the inter-satellite single difference to fix the single receiver ambiguity. Swarm satellite-borne measured data was used to carry out kinematic absolute and relative orbit determination, and the single-satellite ambiguity and double-difference ambiguity were fixed respectively to research the influence of fixing ambiguities on kinematic orbit determination accuracy. The results show that fixing ambiguities can significantly improve orbit determination accuracy. The standard deviation of the satellite laser ranging (SLR) residuals for the reduced dynamic single difference ambiguity resolution (SD-AR) orbit as a reference is better than 10 mm, which is improved by 20% compared with that of the floating solution. For kinematic absolute orbit determination, the orbit determination accuracy of the double difference ambiguity resolution (DD-AR) is improved by 26% compared with that of the floating solution, and the accuracy of the SD-AR is improved by 46%. For kinematic relative orbit determination, the baseline accuracy of the SD-AR and DD-AR of the Swarm-AC formation is improved by 40% compared with that of the floating solution. For the Swarm-AB and Swarm-BC formation satellites on heterogeneous orbits, observation data of specific periods are selected for relative orbit determination. Compared with the floating solution results, the baseline accuracy of the SD-AR is improved by 48%, and the accuracy of the DD-AR is improved by 54%. Fixing the carrier phase ambiguity in the kinematic orbit determination of low-earth-orbit satellites can significantly improve the accuracy of absolute and relative orbit determination.
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图 1 Swarm卫星运动学绝对和相对定轨流程
Figure 1. Kinematic absolute and relative orbit determination workflow of Swarm satellites
图 2 Swarm星座简化动力学SD-AR解轨道SLR残差
Figure 2. SLR residuals of reduced dynamic SD-AR orbit of Swarm constellation
图 3 Swarm-A卫星2016年第185天运动学轨道与参考轨道的差异
Figure 3. Difference between kinematic orbit and reference orbit of Swarm-A satellite for day 185 in 2016
图 5 Swarm星座运动学SD-AR解轨道与参考轨道的差异
Figure 5. Difference between kinematic SD-AR orbits and reference orbit of Swarm constellation
图 6 Swarm星座运动学轨道与参考轨道三维差异的RMS值
Figure 6. RMS of three dimensional difference between kinematic orbits and reference orbit of Swarm constellation
图 7 简化动力学SD-AR解和DD-AR解基线差异
Figure 7. Baseline difference between reduced dynamic SD-AR solution and DD-AR solution
图 8 2016年第202天Swarm-AC、Swarm-AB和Swarm-BC基线长度
Figure 8. Baseline length of Swarm-AC, Swarm-AB,and Swarm-BC for day 202 in 2016
图 9 Swarm卫星编队平均基线长度及固定的双差模糊度数量
Figure 9. Average baseline length and number of fixed double-difference ambiguity of Swarm satellite formations
图 11 Swarm-AC运动学基线与参考基线的差异
Figure 11. Differences between kinematic baseline and reference baseline of Swarm-AC
图 12 Swarm-AB运动学基线与参考基线的差异
Figure 12. Difference between kinematic baseline and reference baseline of Swarm-AB
图 13 Swarm-BC运动学基线与参考基线的差异
Figure 13. Difference between kinematic baseline and reference baseline of Swarm-BC
表 1 Swarm星载GPS天线、SLR反射器和质心坐标[29]
Table 1. Coordinate of Swarm satellite-borne GPS antennas, SLR retroreflectors, and center of mass[29]
卫星 设备 x/mm y/mm z/mm Swarm-A GPS天线 − 1650.26 0.96 −805.86 SLR反射器 − 2419.56 520.75 −31.05 卫星质心 − 1956.00 1.00 −334.00 Swarm-B GPS天线 − 1651.00 1.76 −805.68 SLR反射器 − 2419.56 521.73 −31.29 卫星质心 − 1956.00 1.00 −334.00 Swarm-C GPS天线 − 1650.18 1.03 −805.55 SLR反射器 − 2420.10 521.12 −31.66 卫星质心 − 1954.00 1.00 −334.00 
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表 2 Swarm卫星简化动力学定轨策略
Table 2. Reduced dynamic orbit determination strategy for Swarm satellites
类型 参数 描述 力模型 地球重力场 EIGEN-6C（130×130)[31] 地球固体潮和极潮 IERS 2010[32] 海潮 FES2004（30×30)[33] 海洋极潮 Desai（30×30)[34] N体摄动 JPL’s DE405 相对论效应 IERS 2010[32] 太阳光压 宏模型[3] 大气阻力 宏模型[3]，DTM-2013[35] 数据和产品 定轨弧长/h 24 GPS观测量 无电离层组合，采样间隔10 s 截止高度角/（°） 0 GPS轨道 CODE GPS最终轨道 GPS钟差/相位偏差 CODE GPS钟差和OSB产品 GPS天线改正 igs14.atx 接收天线改正 PCO改正[29] 相位缠绕 改正[25] 引力弯曲和相对论改正 IERS 2010[32] 估计参数 初始状态量 卫星初始位置和速度 大气阻力系数 每轨道周期估计一个 太阳辐射压因子 每定轨弧段估计一个 经验加速度 切向和法向加速度，每轨道周期估计一组 接收机钟差 每历元估计 载波模糊度 每跟踪弧段估计一个
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