Celestial Navigation for Mars Probe Considering Relativistic Effect
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摘要:广义相对论效应使恒星发出的星光在经过大质量天体时发生一定程度的偏折，狭义相对论使高速运行的航天器能够观测到恒星光行差，这两者会造成航天器实际采集到的量测量与星历中对应的信息不符，进而影响导航精度问题，提出一种考虑相对论效应的天文测角导航方法。通过对星光角距量测模型进行相对论效应修正，使其符合实际观测结果，以提高导航精度。仿真结果表明，在火星环绕轨道上，提出的方法可有效修正相对论效应对航天器测角导航造成的影响。当星敏感器量测误差为3″，火星敏感器量测误差为0.05°时，修正后的平均位置误差和平均速度误差相比于未修正的情况分别减少了13.97%和13.89%。Abstract:Celestial navigation based on star angle is a classical autonomous navigation method for spacecraft. By measuring the angular relationship between spacecraft, near celestial bodies and background stars, the current position and velocity information of spacecraft can be deduced. However, the effect of general relativity causes the starlight from a star to be somewhat deflected as it passes through a massive object, and special relativity allows high-speed spacecraft to observe stellar aberration. These two factors will cause the difference between the actual measurement of spacecraft and the corresponding information in the ephemeris, and then affect the navigation accuracy. To solve this problem, a celestial navigation method considering relativistic effect is proposed in this paper. The star angle measurement model is correct by relativistic effect to conform to the actual observation result, so as to improve the navigation accuracy. The simulation result shows that the proposed method can effectively correct the influence of relativistic effect on spacecraft star angle navigation in Mars surrounding orbit. When the star sensor measurement error is 3″ and the Mars sensor measurement error is 0.05°, the corrected average position error and average velocity error are reduced by 13.97% and 13.89% respectively, compared with the uncorrected case.
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Key words:
- Mars exploration/
- automation navigation/
- star angle/
- relativity/
- stellar aberration
Highlights● Celestial navigation is based on the star angle. ● Both of general relativity and special relativity are considered in error correction. ● Compared with the uncorrected case，the corrected average position error and average velocity error are reduced by 13.97% and 13.89% respectively when the star sensor measurement error is 3″ and the Mars sensor measurement error is 0.05°. -
图 2广义相对论效应造成的光线偏转的示意图
Fig. 2Diagram of the deflection of light caused by general relativistic effects
图 4相对论修正前航天器在火星环绕轨道上的位置误差
Fig. 4Position error of spacecraft in orbit around Mars before relativity correction
图 5相对论修正前航天器在火星环绕轨道上的速度误差
Fig. 5Velocity error of spacecraft in orbit around Mars before relativity correction
图 6广义相对论对星光角距量测数值的影响
Fig. 6Influence of general relativity on measurements of star angle
图 7狭义相对论对星光角距量测数值的影响
Fig. 7Influence of special relativity on measurements of star angle
图 8相对论修正前后位置误差对比
Fig. 8Comparison of the position errors before and after the relativity correction
图 9相对论修正前后速度误差对比
Fig. 9Comparison of the velocity errors before and after the relativity correction
图 10相对论修正后不同量测误差情况下的位置误差对比
Fig. 10Comparison of position errors under different measurement errors after relativistic correction
图 11相对论修正后不同量测误差情况下的速度误差对比
Fig. 11Comparison of velocity errors under different measurement errors after relativistic correction
表 1火星环绕轨道仿真参数设置
Table 1Mars surrounding orbit simulation parameters setting
项目 数据设置 初始距离误差 ${\left[ 1\;000\;{\rm{m} },1\;000\;{\rm{m} },{1\;000\;{\rm{m} },0.1\;\rm m/s,0.1\;m/s,0.1\;m/s} \right]^{\rm{T}}}$ 初始估计误差协方差P $\rm diag[ { {(1\;000\;m)}^2},{ {(1\;000\;m)}^2},{ {(1\;000\;m)}^2},{ {(0.1\;m/s)}^2}, { {(0.1\;m/s)}^2},{ {(0.1\;m/s)}^2} ]$ 过程噪声协方差矩阵Q $\rm diag[ { { {1{0^{ - 3} }\;m} }^2},{ { {1{0^{ - 3} }\;m} }^2},{ { {1{0^{ - 3} }\;m} }^2},{ { 1{0^{ - 7} }\left(m/s \right)}^2}, { { 1{0^{ - 7} }\left(m/s \right)}^2},{ { 1{0^{ - 7} }\left(m/s \right)}^2} ]$ 滤波周期/s 60 
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表 2相对论修正前后平均距离误差与平均速度误差对比
Table 2Comparison of mean distance errors and mean velocity errors before and after relativity correction
分类 平均位置误差/m 平均速度误差/（m·s-1） 未修正相对论效应 580.99 0.36 修正相对论效应 499.82 0.31 下载:
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表 3相对论效应修正后不同量测误差下的平均位置误差和平均速度误差对比
Table 3Comparison of mean distance errors and mean velocity errors under different measurement errors after relativistic correction
星敏感器量测误差大小/（″） 平均位置误差/m 平均速度误差/（m•/s-1） 1 498.763 2 0.313 8 3 499.822 4 0.314 3 10 503.921 1 0.316 5 下载:
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