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A review of space-object collision probability computation methods

Abstract

The collision probability computation of space objects plays an important role in space situational awareness, particularly for conjunction assessment and collision avoidance. Early works mainly relied on Monte Carlo simulations to predict collision probabilities. Although such simulations are accurate when a large number of samples are used, these methods are perceived as computationally intensive, which limits their application in practice. To overcome this limitation, many approximation methods have been developed over the past three decades. This paper presents a comprehensive review of existing space-object collision probability computation methods. The advantages and limitations of different methods are analyzed and a systematic comparison is presented. Advice regarding how to select a suitable method for different short-term encounter scenarios is then provided. Additionally, potential future research avenues are discussed.

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References

  1. Luo, Y. Z., Yang, Z. A review of uncertainty propagation in orbital mechanics. Progress in Aerospace Sciences, 2017, 89: 23–39.

    Article  Google Scholar 

  2. Liou, J. C. Collision activities in the future orbital debris environment. Advances in Space Research, 2006, 38(9): 2102–2106.

    Article  Google Scholar 

  3. Flohrer, T., Krag, H., Klinkrad, H. Assessment and categorization of TLE orbit errors for the US SSN catalogue. In: Proceedings of the Advanced Maui Optical and Space Surveillance Technologies Conference, 2008.

  4. Hoots, F., Starchville, T. Debris risk assessment process. In: Proceedings of the AIAA/AAS Astrodynamics Specialist Conference and Exhibit, 2008: AIAA 2008–6269.

  5. Liou, J. C., Anilkumar, A. K., Bastida, B., Hanada, T., Sharma, R. K. Stability of the future LEO environment. In: Proceedings of the European Conference on Space Debris, 2013.

  6. Letizia, F., Colombo, C., Lewis, H. G. Collision probability due to space debris clouds through a continuum approach. Journal of Guidance, Control, and Dynamics, 2015, 39(10): 2240–2249.

    Article  Google Scholar 

  7. Kessler, D. J., Cour-Palais, B. G. Collision frequency of artificial satellites: The creation of a debris belt. Journal of Geophysical Research Space Physics, 1978, 83(A6): 2637–2646.

    Article  Google Scholar 

  8. Levin, G. M., Hauck, F. H., Shawcross, P. J., Christiansen, E. L. Protecting the space shuttle from meteoroids and orbital debris. Space Debris, 2000: 231–237.

  9. Bérend, N. Estimation of the probability of collision between two catalogued orbiting objects. Advances in Space Research, 1999, 23(1): 243–247.

    Article  Google Scholar 

  10. Jenkin, A. B. Effect of orbit data quality on the feasibility of collision risk management. Journal of Spacecraft and Rockets, 2004, 41(4): 677–683.

    Article  Google Scholar 

  11. Hechler, M., van der Ha, J. C. Probability of collisions in the geostationary ring. Journal of Spacecraft and Rockets, 1981, 18(4): 361–366.

    Article  Google Scholar 

  12. Takahashi, K. Collision between satellites in stationary orbits. IEEE Transactions on Aerospace and Electronic Systems, 1981, AES-17(4): 591–596.

    Article  Google Scholar 

  13. Chobotov, V. A. Classification of orbits with regard to collision hazard in space. Journal of Spacecraft and Rockets, 1983, 20(5): 484–490.

    Article  Google Scholar 

  14. Kessler, D. J. Orbital debris issues. Advances in Space Research, 1985, 5(2): 3–10.

    Article  Google Scholar 

  15. McKnight, D. S., Anz-Meador, P. D. Historical growth of quantities affecting on-orbit collision hazard. Journal of Spacecraft and Rockets, 1993, 30(1): 120–124.

    Article  Google Scholar 

  16. Khutorovsky, Z., Boikov, V., Kamensky, S. Direct method for the analysis of collision probability of artificial space objects in LEO: Techniques, methods and applications. In: Proceedings of the European Conference on Space Debris European Space Agency, 1993: 491–499.

  17. Uriot, T., Izzo, D., Simões, L. F., Abay, R., Einecke, N., Rebhan, S., Martinez-Heras, J., Letizia, F., Siminski, J., Merz, K. Spacecraft collision avoidance challenge: Design and results of a machine learning competition. Astrodynamics, 2021, https://doi.org/10.1007/s42064-021-0101-5.

  18. Akella, M. R., Alfriend, K. T. Probability of collision between space objects. Journal of Guidance, Control, and Dynamics, 2000, 23(5): 769–772.

    Article  Google Scholar 

  19. Patera, R. P. General method for calculating satellite collision probability. Journal of Guidance, Control, and Dynamics, 2001, 24(4): 716–722.

    Article  Google Scholar 

  20. Alfano, S. A numerical implementation of spherical object collision probability. The Journal of the Astronautical Sciences, 2005, 53(1): 103–109.

    Article  Google Scholar 

  21. Chan, K. F. Spacecraft Collision Probability. El Segundo, USA: The Aerospace Press, 2008.

    Book  Google Scholar 

  22. Coppola, V. T. Including velocity uncertainty in the probability of collision between space objects. In: Proceedings of the AIAA/AAS Astrodynamics Specialist Conference and Exhibit, 2012.

  23. Dolado, J. C., Legendre, P., Garmier, R., Revelin, B., Pena, X. Satellite collision probability computation for long term encounters. In: Proceedings of the AAS/AIAA Astrodynamics Specialist Conference, 2011.

  24. Yang, C. H., Zhang, H. Formation flight design for a LISA-like gravitational wave observatory via Cascade optimization. Astrodynamics, 2019, 3(2): 155–171.

    Article  Google Scholar 

  25. Chan, K. F. Short-term vs. long-term spacecraft encounters. In: Proceedings of the AIAA/AAS Astrodynamics Specialist Conference and Exhibit, 2004: AIAA 2004–5460.

  26. Alfriend, K. T., Akella, M. R., Frisbee, J., Foster, J. L., Lee, D. J., Wilkins, M. Probability of collision error analysis. Space Debris, 1999, 1(1): 21–35.

    Article  Google Scholar 

  27. Alfano, S. Review of conjunction probability methods for short-term encounters. Advances in the Astronautical Sciences, 2007, 127: 719–746.

    Google Scholar 

  28. Patera, R. P. Space vehicle conflict probability for ellipsoidal conflict volumes. Journal of Guidance, Control, and Dynamics, 2007, 30(6): 1819–1822.

    Article  Google Scholar 

  29. Patera, R. P. Satellite collision probability for nonlinear relative motion. Journal of Guidance, Control, and Dynamics, 2003, 26(5): 728–733.

    Article  Google Scholar 

  30. Dolado-Perez, J. C., Pardini, C., Anselmo, L. Review of uncertainty sources affecting the long-term predictions of space debris evolutionary models. Acta Astronautica, 2015, 113: 51–65.

    Article  Google Scholar 

  31. Yang, Z., Luo, Y. Z., Zhang, J. Nonlinear semi-analytical uncertainty propagation of trajectory under impulsive maneuvers. Astrodynamics, 2019, 3(1): 61–77.

    Article  Google Scholar 

  32. Carpenter, J. R., Markley, F. L., Alfriend, K. T., Wright, C., Arcido, J. Sequential probability ratio test for collision avoidance maneuver decisions based on a bank of norm-inequality-constrained epoch-state filters. In: Proceedings of the AIAA/AAS Astrodynamics Specialist Conference and Exhibit, 2011: AAS 11–437.

  33. Chan, K. F. International space station collision probability. In: Proceedings of the AIAA/AAS Astrodynamics Specialist Conference and Exhibit, 2008.

  34. Alfano, S. Satellite conjunction Monte Carlo analysis. Advances in the Astronautical Sciences, 2009, 134: 2007–2024.

    Google Scholar 

  35. De Vries, W. H., Phillion, D. W. Monte Carlo method for collision probability using 3D satellite models. In: Proceedings of the Advanced Maui Optical and Space Surveillance Technologies Conference, 2010.

  36. Sabol, C., Binz, C., Segerman, A., Roe, K., Schumacher, P. W. Probability of collision with special perturbations dynamics using the Monte Carlo method. Advances in the Astronautical Sciences, 2012, 142: 1081–1093.

    Google Scholar 

  37. Grande-Olalla, I., Sanchez-Ortiz, N., Pulido, J. A., Merz, K. Collision risk assessment and avoidance maneuvers: New tools CORAM for ESA. In: Proceedings of the 6th European Conference on Space Debris, 2013.

  38. Yang, C., Kumar, M. An adaptive Monte Carlo method for uncertainty forecasting in perturbed two-body dynamics. Acta Astronautica, 2019, 155: 369–378.

    Article  Google Scholar 

  39. Binder, K., Heermann, D., Roelofs, L., Mallinckrodt, A. J., McKay, S. Monte Carlo simulation in statistical physics. Computers in Physics, 1993, 7(2): 156–157.

    Article  Google Scholar 

  40. Dagum, P., Karp, R., Luby, M., Ross, S. An optimal algorithm for Monte Carlo estimation. SIAM Journal on Computing, 2000, 29(5): 1484–1496.

    MathSciNet  MATH  Article  Google Scholar 

  41. Dolado, J. C., Legendre, P., Garmier, R., Revelin, B., Pena, X. Satellite collision probability computation for long term encounters. In: Proceedings of the AAS/AIAA Astrodynamics Specialist Conference, 2012: 275–294.

  42. Pastel, R. Estimating satellite versus debris collision probability via the adaptive splitting technique. In: Proceedings of the 3rd International Conference on Computer Modeling and Simulation, 2011.

  43. Jones, B. A., Doostan, A. Satellite collision probability estimation using polynomial chaos expansions. Advances in Space Research, 2013, 52(11): 1860–1875.

    Article  Google Scholar 

  44. Jones, B. A., Doostan, A., Born, G. Conjunction assessment using polynomial chaos expansions. In: Proceedings of the 23rd International Symposium and Space Flight Dynamics: JPL, 2012.

  45. Ghrist, R., Plakalovic, D. Impact of non-Gaussian error volumes on conjunction assessment risk analysis. In: Proceedings of the AIAA/AAS Astrodynamics Specialist Conference, 2012: AIAA 2012–4965.

  46. Armellin, R., Morselli, A., di Lizia, P., Lavagna, M. Rigorous computation of orbital conjunctions. Advances in Space Research, 2012, 50(5): 527–538.

    Article  Google Scholar 

  47. Morselli, A., Armellin, R., di Lizia, P., Bernelli Zazzera, F. A high order method for orbital conjunctions analysis: Monte Carlo collision probability computation. Advances in Space Research, 2015, 55(1): 311–333.

    Article  Google Scholar 

  48. Morselli, A., Armellin, R., di Lizia, P., Bernelli Zazzera, F. A high order method for orbital conjunctions analysis: Sensitivity to initial uncertainties. Advances in Space Research, 2014, 53(3): 490–508.

    MATH  Article  Google Scholar 

  49. Vittaldev, V., Russell, R. P. Space object collision probability via Monte Carlo on the graphics processing unit. The Journal of the Astronautical Sciences, 2017, 64(3): 285–309.

    Article  Google Scholar 

  50. Jones, B. A., Parrish, N., Doostan, A. Postmaneuver collision probability estimation using sparse polynomial chaos expansions. Journal of Guidance, Control, and Dynamics, 2015, 38(8): 1425–1437.

    Article  Google Scholar 

  51. Adurthi, N., Singla, P. Conjugate unscented transformation-based approach for accurate conjunction analysis. Journal of Guidance, Control, and Dynamics, 2015, 38(9): 1642–1658.

    Article  Google Scholar 

  52. Zhang, S., Fu, T., Chen, D. F., Cao, H. W. Satellite instantaneous collision probability computation using equivalent volume cuboids. Journal of Guidance, Control, and Dynamics, 2020, 43(9): 1757–1763.

    Article  Google Scholar 

  53. Foster, J. L., Estes, H. S. A parametric analysis of orbital debris collision probability and maneuver rate for space vehicles. NASA/JSC-25898, 1992.

  54. Patera, R. P. Method for calculating collision probability between a satellite and a space tether. Journal of Guidance, Control, and Dynamics, 2002, 25(5): 940–945.

    Article  Google Scholar 

  55. Patera, R. P. Calculating collision probability for arbitrary space vehicle shapes via numerical quadrature. Journal of Guidance, Control, and Dynamics, 2005, 28(6): 1326–1328.

    Article  Google Scholar 

  56. Bai, X. Z., Chen, L. Research on calculational method of collision probability between space objects. Journal of Astronautics, 2008, 29(4): 1435–1442, 1456. (in Chinese)

    Google Scholar 

  57. Bai, X. Z., Chen, L. A rapid algorithm of space debris collision probability based on space compression and infinite series. Acta Mathematicae Applicatae Sinica, 2009, 32(2): 336–353.

    MathSciNet  MATH  Google Scholar 

  58. Bai, X. Z., Chen, L. Explicit expression and influencing factor analysis of collision probability between space objects. Chinese Journal of Space Science, 2009, 29(4): 422–431. (in Chinese)

    Google Scholar 

  59. Xu, X. L., Xiong, Y. Q. A research on collision probability calculation of space debris for nonlinear relative motion. Acta Astronautica Sinica, 2011, 52(1): 73–85. (in Chinese)

    Google Scholar 

  60. Xu, X. L., Xiong, Y. Q. Analysis of the applicability of collision probability algorithms for nonlinear relative motion. Science China Physics, Mechanics and Astronomy, 2013, 56(5): 1041–1046.

    Article  Google Scholar 

  61. Xu, X. L., Xiong, Y. Q. A method for calculating probability of collision between space objects. Research in Astronomy and Astrophysics, 2014, 14(5): 601–609.

    Article  Google Scholar 

  62. Serra, R., Arzelier, D., Joldes, M., Lasserre, J. B., Rondepierre, A., Salvy, B. Fast and accurate computation of orbital collision probability for short-term encounters. Journal of Guidance, Control, and Dynamics, 2016, 39(5): 1009–1021.

    Article  Google Scholar 

  63. García-Pelayo, R., Hernando-Ayuso, J. Series for collision probability in short-encounter model. Journal of Guidance, Control, and Dynamics, 2016, 39(8): 1904–1912.

    Article  Google Scholar 

  64. Maron, M. J. Numerical Analysis: A Practical Approach. New York: Macmillan Publishing Company, 1982.

    MATH  Google Scholar 

  65. Patera, R. P. Collision probability for larger bodies having nonlinear relative motion. Journal of Guidance, Control, and Dynamics, 2006, 29(6): 1468–1472.

    Article  Google Scholar 

  66. Coppola, V. T., Woodburn, J., Hujsak, R. Effects of cross correlated covariance on space-craft collision probability. In: Proceedings of the AAS/AIAA Spaceflight Mechanics Meeting, 2004: AAS 04-181.

  67. Coppola V. T. Evaluating the short encounter assumption of the probability of collision formula. In: Proceedings of the 22nd AAS/AIAA Space Flight Mechanics Meeting, 2012.

  68. Schaeffer, V., Laurens, S., Seimandi, P., Delmas, F. Collision probability through time integration implementation and operational results. In: Proceedings of the 15th International Conference on Space Operations, 2018: AIAA 2018-2720.

  69. Alfano, S. Eliminating assumptions regarding satellite conjunction analysis. The Journal of the Astronautical Sciences, 2012, 59(4): 676–705.

    Article  Google Scholar 

  70. Alfano, S. Addressing nonlinear relative motion for spacecraft collision probability. In: Proceedings of the AIAA/AAS Astrodynamics Specialist Conference and Exhibit, 2006: AIAA 2006-6760.

  71. McKinley, D. Development of a nonlinear probability collision tool for the earth observing system. In: Proceedings of the 15th AIAA/AAS Astrodynamics Specialist Conference and Exhibit, 2006: AIAA 2006–6295.

  72. DeMars, K. J., Cheng, Y., Jah, M. K. Collision probability with Gaussian mixture orbit uncertainty. Journal of Guidance, Control, and Dynamics, 2014, 37(3): 979–985.

    Article  Google Scholar 

  73. Vittaldev, V., Russell, R. P. Space object collision probability using multidirectional Gaussian mixture models. Journal of Guidance, Control, and Dynamics, 2016, 39(9): 2163–2169.

    Article  Google Scholar 

  74. Shelton, C. T., Junkins, J. L. Probability of collision between space objects including model uncertainty. Acta Astronautica, 2019, 155: 462–471.

    Article  Google Scholar 

  75. Chan, K. F. Spacecraft collision probability for long-term encounters. In: Proceedings of the AIAA/AAS Astrodynamics Specialist Conference, 2003: AAS 21–604.

  76. Luo, Y. Z., Liang, L. B., Wang, H., Tang, G. J. Quantitative performance for spacecraft rendezvous trajectory safety. Journal of Guidance, Control, and Dynamics, 2011, 34(4): 1264–1269.

    Article  Google Scholar 

  77. Foster, J. The analytic basis for debris avoidance operations for the International Space Station. In: Proceedings of the 3rd European Conference on Space Debris, 2001.

  78. Pulido, J. A., Sánchez, N., Poniente, R. D., Str, R.B., Gran De, I., Merz, K. ESA’s collision risk assessment and avoidance maneuvers tool. ESA, 2013.

  79. Information on https://physicstoday.scitation.org/do/10.1063/PT.5.026998/full/ (cited 30 Mar 2021).

  80. Gavin, R. T. NASA’s orbital debris conjunction assessment and collision avoidance strategy. In: Proceedings of the 33rd Annual AAS Rocky Mountain Guidance and Control Conference, 2010.

  81. Phillips, M. R. Spacecraft collision probability estimation for rendezvous and proximity operations. M.S. Dissertation. Utah, Logan, USA: Aerospace Department, Utah State University, 2012.

  82. Acciarini, G., Pinto, F., Metz, S., Boufelja, S., Baydin, A. G. Spacecraft collision risk assessment with probabilistic programming. In: Proceedings of the 3rd Workshop on Machine Learning and the Physical Sciences, 2020.

  83. Browns, A. C. Human spaceflight recent conjunctions of interest. In: Proceedings of the USSTRATCOM Conjunction Summary Message Workshop, 2010.

  84. Luo, Y. Z., Liang, L. B., Niu, Z. Y., Tang, G. J. Safety-optimal linearized impulsive rendezvous with trajectory uncertainties. Journal of Aerospace Engineering, 2014, 27(6): 04014038.

    Article  Google Scholar 

  85. Sun, Z. J., Luo, Y. Z., Niu, Z. Y. Spacecraft rendezvous trajectory safety quantitative performance index eliminating probability dilution. Science China Technological Sciences, 2014, 57(6): 1219–1228.

    Article  Google Scholar 

  86. Sun, Z. J., Luo, Y. Z., Li, H. Y. Uncertainty-dependent warning threshold for spacecraft rendezvous collision probability. IEEE Transactions on Aerospace and Electronic Systems, 2019, 55(1): 2–16.

    Article  Google Scholar 

  87. Richards, A., Schouwenaars, T., How, J. P., Feron, E. Spacecraft trajectory planning with avoidance constraints using mixed-integer linear programming. Journal of Guidance, Control, and Dynamics, 2002, 25(4): 755–764.

    Article  Google Scholar 

  88. Wu, B. L., Wang, D. W., Poh, E. K., Xu, G. Y. Nonlinear optimization of low-thrust trajectory for satellite formation: Legendre pseudospectral approach. Journal of Guidance, Control, and Dynamics, 2009, 32(4): 1371–1381.

    Article  Google Scholar 

  89. Di Cairano, S., Park, H., Kolmanovsky, I. Model predictive control approach for guidance of spacecraft rendezvous and proximity maneuvering. International Journal of Robust and Nonlinear Control, 2012, 22(12): 1398–1427.

    MathSciNet  MATH  Article  Google Scholar 

  90. Morgan, D., Chung, S. J., Hadaegh, F. Y. Model predictive control of swarms of spacecraft using sequential convex programming. Journal of Guidance, Control, and Dynamics, 2014, 37(6): 1725–1740.

    Article  Google Scholar 

  91. Park, H., Zappulla, R., Zagaris, C., Virgili-Llop, J., Romano, M. Nonlinear model predictive control for spacecraft rendezvous and docking with a rotating target. In: Proceedings of the 27th AAS/AIAA Space Flight Mechanics Meeting, 2017: AAS 17-496.

  92. Bombardelli, C. Analytical formulation of impulsive collision avoidance dynamics. Celestial Mechanics and Dynamical Astronomy, 2014, 118(2): 99–114.

    MathSciNet  Article  Google Scholar 

  93. Bombardelli, C., Hernando-Ayuso, J. Optimal impulsive collision avoidance in low earth orbit. Journal of Guidance, Control, and Dynamics, 2015, 38(2): 217–225.

    Article  Google Scholar 

  94. Greco, C., Sanchez, L., Manzi, M., Vasile, M. A robust Bayesian agent for optimal collision avoidance maneuver planning. In: Proceedings of the 8th European Conference on Space Debris, 2021.

  95. Mason, J., Stupl, J., Marshall, W., Levit, C. Orbital debris-debris collision avoidance. Advances in Space Research, 2011, 48(10): 1643–1655.

    Article  Google Scholar 

  96. Bonnal, C., McKnight, D., Phipps, C., Dupont, C., Missonnier, S., Lequette, L., Merle, M., Rommelaere, S. Just in time collision avoidance—A review. Acta Astronautica, 2020, 170: 637–651.

    Article  Google Scholar 

  97. Gonzalo, J. L., Colombo, C., di Lizia, P. Analytical framework for space debris collision avoidance maneuver design. Journal of Guidance, Control, and Dynamics, 2020, 44(3): 469–487.

    Article  Google Scholar 

  98. Wang, Y., Bai, Y. Z., Ran, D. C., Zhao, Y., Zhang, X., Chen, X. Q. The equal-collision-probability-surface method for spacecraft collision avoidance. Advances in the Astronautical Sciences, 2017, 161: 761–776.

    Google Scholar 

  99. Wang, Y., Bai, Y. Z., Xing, J. J., Radice, G., Ni, Q., Chen, X. Q. Equal-collision-probability-curve method for safe spacecraft close-range proximity maneuvers. Advances in Space Research, 2018, 62(9): 2599–2619.

    Article  Google Scholar 

  100. Wang, Y., Chen, X. Q., Ran, D. C., Ou, Y. W., Ni, Q., Bai, Y. Z. Multi-equal-collision-probability-cure method for convex polygon-shape spacecraft safe proximity manoeuvres. Journal of Navigation, 2019, 72(2): 405–429.

    Article  Google Scholar 

  101. Wang, Y., Bai, Y. Z., Ran, D. C., Chen, Q., Ni, Q., Chen, X. Q. Dual-equal-collision-probability-curve method for spacecraft safe proximity maneuvers in presence of complex shape. Acta Astronautica, 2019, 159: 65–76.

    Article  Google Scholar 

  102. Hua, B., Huang, Y., Wu, Y. H., Chen, Z. M., Nicholas, D. Spacecraft formation reconfiguration trajectory planning with avoidance constraints using adaptive pigeon-inspired optimization. Science China-Information Sciences, 2019, 62(7): 70209.

    MathSciNet  Article  Google Scholar 

  103. Hua, B., Sun, S. G., Wu, Y. H., Chen, Z. M. Path planning method for spacecraft formation reconfiguration based on CGAPIO. Journal of Beijing University of Aeronautics and Astronautics, 2021, 47(2): 223–230. (in Chinese)

    Google Scholar 

  104. Xie, Y. C., Chan, K., Zhang, J. R. Collision probability of composite cubesats hovering in leader-follower configuration. Acta Astronautica, 2020, 168: 211–219.

    Article  Google Scholar 

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Acknowledgements

The authors acknowledge financial support from the National Natural Science Foundation of China (Nos. 11902347 and 11972044).

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Correspondence to Zhen Yang.

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Jia-Sheng Li received his B.S. degree in aerospace engineering from National University of Defense Technology, China, in 2019. He is currently a Ph.D. candidate in the Department of Aerospace, National University of Defense Technology, China. His current research interests include astrodynamics, collision probability, and collision avoidance.

Zhen Yang received his B.S., M.S., and Ph.D. degrees in aerospace engineering from National University of Defense Technology, China, in 2011, 2013, and 2018, respectively. He was a visiting scholar of Cranfield University, UK, in 2016. Since December 2020, he has been an associate professor in National University of Defense Technology. His current research interests include astrodynamics, uncertainty quantification, and space trajectory optimization.

Ya-Zhong Luo received his B.S., M.S., and Ph.D. degrees in aerospace engineering from National University of Defense Technology, China, in 2001, 2003, and 2007, respectively. Since December 2013, he has been a professor in National University of Defense Technology. His current research interests include astrodynamics, spaceflight mission planning, and space trajectory optimization.

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Li, JS., Yang, Z. & Luo, YZ. A review of space-object collision probability computation methods. Astrodyn 6, 95–120 (2022). https://doi.org/10.1007/s42064-021-0125-x

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Keywords

  • collision probability
  • space situational awareness
  • collision avoidance
  • astrodynamics