Onboard Real-time Estimation of Mean Orbital Elements with Atmospheric Drag
-
摘要: 为了满足卫星长期自主运行的任务需求, 本文同时考虑了大气阻力摄动和非球形摄动带谐项两种摄动对卫星平均轨道根数的影响, 提出了采用滤波算法在轨实时估计平均轨道根数的方法. 基于指数大气密度模型推导了大气阻力摄动下平均轨道根数的变化率, 分析了非球形带谐项摄动势函数对平均轨道根数的影响并推导了该影响下平均轨道根数变化率的通用计算方法, 由此建立了滤波状态方程以及以瞬时轨道根数为观测量的量测方程并分析了测量噪声特性; 为减小计算量以便于在轨实现,提出采用基于球形单边Sigma采样的平方根UKF (Unscented Kalman filter)滤波来估计平均轨道根数. 数值仿真结果表明, 该算法有效、精度较高且鲁棒性好, 能够满足卫星长期自主在轨实时计算平均轨道根数的要求.Abstract: To solve the problem of mean orbital elements calculation for long-term autonomous missions, a filter estimation method is used to estimate the mean orbital elements with the effects of atmospheric drag and the gravitational potential of zonal harmonics. The effects of atmospheric drag are analyzed by virtue of analytical orbital mechanics with the spherical exponential model of atmospheric density. The general formulas are derived for the rates of change of mean orbital elements perturbed by gravitational potential zonal harmonics. The state equations and measurement equations are established to treat the mean orbital elements as state variables and the osculating orbital elements as measurements. The distribution of the measurement noise is analyzed. In this estimator, the spherical simplex sigma-point selection and the square root form of unscented Kalman filter (UKF) are fused for less computational cost and better numerical stability on-board. Numerical simulations are performed to demonstrate the viability of the proposed method. Comparison with another approach shows that the proposed one can estimate mean orbital elements on-board for a real-time and long-term mission and can offer a higher accuracy.
-
Key words:
- Mean orbital elements /
- atmospheric drag /
- zonal harmonics /
- unscented Kalman filter (UKF) /
- Monte Carlo
-
[1] Lin Xiao-Hui, Zhang Jin-Xiu, Cao Xi-Bin. Orbit modulation method based on mean orbit elements. Journal of Jilin University (Engineering and Technology Edition), 2005, 35(5): 556-561(林晓辉, 张锦绣, 曹喜滨. 基于平均轨道要素的轨道修正方法. 吉林大学学报(工学版), 2005, 35(5): 556-561) [2] Wang Gong-Bo, Zheng Wei, Tang Guo-Jian. Application of UKF in spacecraft relative navigation based on quasi-mean element differences. Journal of Astronautics, 2011, 32(5): 1047-1053(王功波, 郑伟, 汤国建. 基于拟平均根数之差的航天器相对导航UKF滤波算法. 宇航学报, 2011, 32(5): 1047-1053) [3] Gurfil P, Herscovitz J, Pariente M. The SAMSON project—cluster flight and geolocation with three autonomous nano-satellites. In: Proceedings of the 26th AIAA/USU Conference on Small Satellites. Salt Lake City, UT, USA, 2012. 1-8 [4] Mazal L, Mingotti G, Gurfil P. Continuous-thrust cooperative guidance law for disaggregated satellite. In: Proceedings of the 2002 AIAA/AAS Astrodynamics Specialist Conference. Minneapolis, MN, USA, 2012 [5] Mazal L, Gurfil P. Cluster-keeping algorithms for the SAMON project. In: 63rd International Astronautical Congress, Naples, Italy, 2012. 5384-5393 [6] Liu Lin. Orbit Theory of Spacecraft. Beijing: National Defence Industry Press, 2000(刘林. 航天器轨道理论. 北京: 国防工业出版社, 2000) [7] Schaub H, Junkins J. Analytical Mechanics of Space Systems. Reston, VA: AIAA, 2003 [8] Li Ji-Shen. Orbit Determination of Spacecraft. Beijing: National Defence Industry Press, 2003(李济生. 航天器轨道确定. 北京: 国防工业出版社, 2003) [9] Gurfil P. Modern astrodynamics. Elsevier Astrodynamics Series. Oxford: Butterworth-Heinemann, 2006 [10] Julier S J, Uhlmann J K, Durrant-Whyte H F. A new approach for filtering nonlinear systems. In: Proceedings of the 1995 American Control Conference. Seattle, WA: IEEE, 1995. 1628-1632 [11] Julier S, Uhlmann J, Durrant-Whyte H F. A new method for the nonlinear transformation of means and covariances in filters and estimators. IEEE Transactions on Automatic Control, 2000, 45(3): 477-482 [12] Julier S J. The spherical simplex unscented transformation. In: Proceedings of the 2003 American Control Conference. Denver, CO, USA: IEEE, 2003. 2430-2434 [13] Van Der Merwe R, Wan E A. The square-root unscented Kalman filter for state and parameter-estimation. In: Proceedings of the 2006 IEEE International Conference on Acoustics, Speech, and Signal Processing. Salt Lake City, UT: IEEE, 2001. 3461-3464 [14] Liu Lin, Hu Song-Jie, Wang Xin. Introduction Astrodynamics. Nanjing: Nanjing University Press, 2006(刘林, 胡松杰, 王歆. 航天动力学引论. 南京: 南京大学出版社, 2006) [15] Liu L. The Motion Theory of Artificial Earth Satellite. Beijing: Science Press, 1974(刘林. 人造地球卫星运动理论. 科学出版社, 1974) [16] Zong Z W, Rao L, Dan M. A UKF tracking method based on Runge-Kutta Integration. Radar Science and Technology, 2010, 8(4): 352-356(宗志伟, 饶彬, 丹梅. 一种基于Runge-Kutta积分的UKF跟踪算法. 雷达科学与技术. 2010, 8(4): 352-356)
点击查看大图
计量
- 文章访问数: 1644
- HTML全文浏览量: 84
- PDF下载量: 961
- 被引次数: 0