董一超 , 代洪华 , 王昌涛 , 杨文传 , 石琳 . 基于多项式代理的空间碎片群高效轨道预报[J]. 航空学报, 0 : 1 -0 . DOI: 10.7527/S1000-6893.2026.33492

[1] ESA's Space Debris Office. Space debris by the numbers[EB/OL]. (2026-01-16) [2026-02-06]. https:// www.esa.int/Space_Safety/Space_Debris/Space_debris_by_the_numbers [2] ESA's Space Debris Office. ESA's annual space environment report 2025[EB/OL]. (2025-10-21) [2026-02-06]. https://www.sdo.esoc.esa.int/environment_repor t/Space_Environment_Report_latest.pdf [3] 金紫涵, 温昶煊, 乔栋. 基于可达域的解体碎片云中期演化建模方法[J]. 航空学报, 2024, 45(21): 272-282. JIN Z H, WEN C X, QIAO D. Modeling medium-term debris cloud of breakups based on reachable domain[J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(21): 272-282 (in Chinese). [4] ANZ-MEADOR P, OPIELA J, LIOU J C. History of on-orbit satellite fragmentations, 16th Edition[R]. Huston, USA: NASA Johnson Space Center, 2023. [5] PARDINI C, ANSELMO L. Review of past on-orbit collisions among cataloged objects and examination of the catastrophic fragmentation concept[J]. Acta Astro-nautica, 2014, 100: 30-39. [6] KELSO T S. Analysis of the Iridium 33-Cosmos 2251 collision[J]. Advances in the Astronautical Sciences, 2009, 135(2): 1099-1112. [7] 金紫涵, 温昶煊, 乔栋. 卫星解体碎片云对低轨星座的碰撞影响分析[J]. 航空学报, 2024, 45(S1): 211-220. JIN Z H, WEN C X, QIAO D. Impact analysis of satellite debris cloud on low-orbit constellation[J]. Acta Aero-nautica et Astronautica Sinica, 2024, 45(S-1): 211-220 (in Chinese). [8] PALMER C. Russian anti-satellite test spotlights space debris danger[J]. Engineering, 2022, 12(5): 3-5. [9] KESSLER D J, COUR-PALAIS B G. Collision fre-quency of artificial satellites: The creation of a debris belt[J]. Journal of Geophysical Research: Space Physics, 1978, 83(A6): 2637-2646. [10] 李宗凌, 龙腾, 赵保军, 等. 面向预警场景的大规模星座协同调度标准建模与求解方法[J]. 航空学报, 2024, 45(22): 208-224. LI Z L, LONG T, ZHAO B J，et al. Standard modeling and solving methods for large-scale constellation co-llaborative scheduling for early warning scenarios[J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(22): 208-224 (in Chinese). [11] 卢哲俊, 胡卫东. 基于随机有限集的空间碎片群运动状态估计[J]. 航空学报, 2017, 38(11): 254-264. LU Z J, HU W D. State estimation of space debris group based on random finite set[J]. Acta Aeronautica et Astronautica Sinica, 2017, 38(11): 254-264(in Chinese). [12] GIUDICI L, GONZALO J L, COLOMBO C. Density-based in-orbit collision risk model valid for any impact geometry[J]. Acta Astronautica, 2024, 219: 785-803. [13] LETIZIA F, COLOMBO C, LEWIS H G. Collision probability due to space debris clouds through a continuum approach[J]. Journal of Guidance, Control, and Dynamics, 2016, 39(10): 2240-2249. [14] BERZ M. Modern map methods in particle beam physics[M]. New York: Academic Press, 1999. [15] LIZIA P D, ARMELLIN R, LAVAGNA M. Application of high order expansions of two-point boundary value problems to astrodynamics[J]. Celestial Mechanics and Dynamical Astronomy, 2008, 102(4): 355-375. [16] ALESSI E M, FARRES A, VIEIRO A, et al. Jet transport and applications to NEOs[C]// The 1st IAA Planet-ary Defense Conference, Granada, Spain, April 27-30, 2009. [17] CHEN J L, MASDEMONT J J, GóMEZ G, et al. Analysis of jet transport-based geostationary trajectory uncertainty propagation[J]. Journal of Guidance, Control, and Dynamics, 2020, 43(6): 1210-1219. [18] Wang C T, Dai H H, Chen J L, et al. High-efficiency semi-analytical method for initial value problem under dense initial conditions[J]. International Journal for Numerical Methods in Engineering, 2025, 126(24): e70222. [19] RICCARDI A, TARDIOLI C, VASILE M. An intrusive approach to uncertainty propagation in orbital mechanics based on Tchebycheff polynomial algebra[J]. Advances in Astronautical Sciences, 2015, 156(1): 707-722. [20] VASILE M, ABSIL C O, RICCARDI A. Set propagation in dynamical systems with generalised polynomial algebra and its computational complexity[J]. Com-munications in Nonlinear Science and Numerical Simulation, 2019, 75: 22-49. [21] MAKINO K, BERZ M. Taylor models and other validated functional inclusion methods[J]. International Journal of Pure and Applied Mathematics, 2003, 6: 239-316. [22] GIORGI P. On polynomial multiplication in Chebyshev basis[J]. IEEE Transactions on Computers, 2011, 61(6): 780-789. [23] BRISEBARRE N, JOLDE? M. Chebyshev interpolation polynomial-based tools for rigorous computing[C]// The 2010 International Symposium on Symbolic and Alge-braic Computation, Munich, Germany, July 25-28, 2010. [24] HARO A. Automatic differentiation tools in computa-tional dynamical systems[D]. Spain: University of Barcelona, 2008. [25] PALAU D P. Dynamical transport mechanisms in celestial mechanics and astrodynamics problems[D]. Spain: University of Barcelona, 2016. [26] HAIRER E, NORSETT S P, WANNER G. Solving ordinary differential equations I: Nonstiff problems[J]. SIAM Review, 1990, 32(3): 485-486. [27] BERRY M M, HEALY L M. Implementation of Gauss Jackson integration for orbit propagation[J]. The Journal of the Astronautical Sciences, 2004, 52(3): 331-357. [28] GEORGIOS D T, MARIA C G. Production of the reduction formula of seventh order Runge-Kutta method with step size control of an ordinary differential equation[J]. Applied Mathematics, 2022, 13(4): 325-337. [29] WANG X C, Yue X K, DAI H H, et al. Feedback-accelerated Picard iteration for orbit propagation and lambert’s problem[J]. Journal of Guidance, Control, and Dynamics, 2017, 40(10): 2442-2451. [30] WANG C T, DAI H H, YANG W C, et al. High-efficiency unscented Kalman filter for multi-target trajectory estimation[J]. Aerospace Science and Tech-nology, 2025, 159: 109962. [31] YAN Z P, DAI H H, WANG Q S, et al. Harmonic balance methods: A review and recent development[J]. CMES-Computer Modeling in Engineering and Sciences, 2023, 137(2): 1419-1459. [32] JOHNSON N L, KRISKO P H, LIOU J C, et al. NASA’s new breakup model of EVOLVE4.0[J]. Advances in Space Research, 2001, 25(9): 1377-1384. [33] 兰胜威, 柳森, 李毅, 等. 航天器解体模型研究的新进展[J]. 实验流体力学, 2014, 28(2): 73-79, 104. LAN S W, LIU S, LI Y, et al. Recent progress on spacecraft breakup model[J]. Journal of Experiments in Fluid Mechanics, 2014, 28(2): 73-79, 104 (in Chinese). [34] KRISKO P H, HORSTMAN M, FUDGE M L. SOCIT4 collisional-breakup test data analysis: With shape and materials characterization[J]. Advances in Space Re-search, 2008, 41(7): 1138-1146. [35] KLINKRAD H, SDUNNUS H, BENDISCH J. Develop-ment status of the ESA space debris reference model[J]. Advances in Space Research, 1995, 16(11): 93-102. [36] 方群, 李新国, 朱战霞, 等. 航天飞行动力学[M]. 西安: 西北工业大学出版社, 2015: 365-369. FANG Q, LI X G, ZHU Z X, et al. Aerospace flight[M]. Xi'an: Northwestern Polytechnical University Press, 2015: 365-369 (in Chinese). [37] 欧阳洁, 聂玉峰, 车刚明, 等. 数值分析[M]. 北京: 高等教育出版社, 2009: 106-128. OUYANG J, NIE Y F, CHE G M, et al. Numerical Analysis[M]. Beijing: Higher Education Press, 2009: 106-128 (in Chinese). [38] MSIS 2.1 Atmosphere Model. [2026-01-12]. https:// ccmc.gsfc.nasa.gov/models/NRLMSIS~2.1 [39] 靳旭红, 黄飞, 程晓丽, 等. 超低地球轨道卫星大气阻力预测与影响因素分析[J]. 清华大学学报(自然科学版), 2020, 60(3): 219-226. JIN X H, HUANG F, CHENG X L, et al. Atmospheric drag on satellites flying in lower low earth orbit[J]. Journal of Tsinghua University (Science and Technology), 2020, 60(3): 219-226 (in Chinese).