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No AccessEngineering Note

Collision Probability with Gaussian Mixture Orbit Uncertainty

Published Online:25 Apr 2014https://doi.org/10.2514/1.62308
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References

  • [1] Kessler D. J., Johnson N. L., Liou J.-C. and Matney M., “Kessler Syndrome: Implications to Future Space Operations,” Proceedings of the 33rd Annual AAS Rocky Mountain Guidance and Control Conference, Vol. 137, Advances in the Astronautical Sciences, Univelt, San Diego, CA, 2010, pp. 47–62. Google Scholar

  • [2] Coppola V. and Woodburn J., “Determination of Close Approaches Based on Ellipsoidal Threat Volumes,” Proceedings of the AAS/AIAA Spaceflight Mechanics Meeting, Vol. 102, Advances in the Astronautical Sciences, Univelt, San Diego, CA, 1999, pp. 1013–1024. Google Scholar

  • [3] Alfano S., “Determining Satellite Close Approaches, Part II,” Journal of the Astronautical Sciences, Vol. 42, No. 2, 1994, pp. 143–152. JALSA6 0021-9142 Google Scholar

  • [4] Carpenter J. R. and Markley F. L., “Sequential Probability Ratio Test for Collision Avoidance Maneuver Decisions,” Proceedings of the AAS Kyle T. Alfriend Astrodynamics Symposium, Vol. 139, Advances in the Astronautical Sciences, Univelt, San Diego, CA, 2010, pp. 267–280. Google Scholar

  • [5] Carpenter J. R., Markley F. L., Alfriend K. T., Wright C. and Arcido J., “Sequential Probability Ratio Test for Collision Avoidance Maneuver Decisions Based on a Bank of Norm-Inequality-Constrained Epoch-State Filters,” Proceedings of the AAS/AIAA Astrodynamics Specialist Conference, Vol. 142, Advances in the Astronautical Sciences, Univelt, San Diego, CA, 2011, pp. 1105–1124. Google Scholar

  • [6] Carpenter J. R. and Markley F. L., “Current-State Constrained Filter Bank for Wald Testing of Spacecraft Conjunctions,” Proceedings of the 23rd International Symposium on Space Flight Dynamics, Paper  CR-SD-1-2, 2012. Google Scholar

  • [7] Patera R. P., “Space Vehicle Conflict-Avoidance Analysis,” Journal of Guidance, Control, and Dynamics, Vol. 30, No. 2, 2007, pp. 492–498.doi:https://doi.org/10.2514/1.24067 JGCDDT 0162-3192 LinkGoogle Scholar

  • [8] Foster J. L. and Estes H. S., “Parametric Analysis of Orbital Debris Collision Probability and Maneuver Rate for Space Vehicles,” NASA TR-JSC-25898, Aug. 1992. Google Scholar

  • [9] Alfriend K. T., Akella M. R., Frisbee J., Foster J. L., Lee D.-J. and Wilkins M., “Probability of Collision Error Analysis,” Space Debris, Vol. 1, No. 1, 1999, pp. 21–35. 1572-9664 CrossrefGoogle Scholar

  • [10] Kessler D. J., “Collision Probability at Low Altitudes Resulting from Elliptical Orbits,” Advances in Space Research, Vol. 10, Nos. 3–4, 1990, pp. 393–396.doi:https://doi.org/10.1016/0273-1177(90)90376-B ASRSDW 0273-1177 CrossrefGoogle Scholar

  • [11] Khutorovsky Z. N., Boikov V. F. and Kamensky S. Y., “Direct Method for the Analysis of Collision Probability of Artificial Space Objects in LEO: Techniques, Results, and Applications,” Proceedings of the First European Conference on Space Debris, European Space Agency, Paris, France, April 1993, pp. 491–508. Google Scholar

  • [12] Lee D.-J. and Alfriend K. T., “Effect of Atmospheric Density Uncertainty on Collision Probability,” Proceedings of the AAS/AIAA Spaceflight Mechanics Meeting, Vol. 105, Advances in the Astronautical Sciences, Univelt, San Diego, CA, 2000, pp. 1255–1274. Google Scholar

  • [13] Vedder J. D. and Tabor J. L., “New Method for Estimating Low-Earth-Orbit Collision Probabilities,” Journal of Spacecraft and Rockets, Vol. 28, No. 2, 1991, pp. 210–215.doi:https://doi.org/10.2514/3.26232 JSCRAG 0022-4650 LinkGoogle Scholar

  • [14] Chan K. F., “Spacecraft Collision Probability for Long-Term Encounters,” Proceedings of the AAS/AIAA Astrodynamics Conference, Vol. 116, Advances in the Astronautical Sciences, Univelt, San Diego, CA, 2003, pp. 767–784. Google Scholar

  • [15] Flury W., “Collision Probability and Spacecraft Disposition in the Geostationary Orbit,” Advances in Space Research, Vol. 11, No. 12, 1991, pp. 67–79.doi:https://doi.org/10.1016/0273-1177(91)90544-T ASRSDW 0273-1177 CrossrefGoogle Scholar

  • [16] Carpenter J. R., “Conservative Analytical Collision Probability for Design of Orbital Formations,” Second International Symposium on Formation Flying, NASA GSFC, Washington, D.C., 2004. Google Scholar

  • [17] Carpenter J. R., “Non-Parametric Collision Probability for Low-Velocity Encounters,” Proceedings of the AAS/AIAA Spaceflight Mechanics Meeting, Vol. 127, Advances in the Astronautical Sciences, Univelt, San Diego, CA, 2007, pp. 227–242. Google Scholar

  • [18] Kessler D. J., “Derivation of the Collision Probability Between Orbiting Objects: The Lifetimes of Jupiter’s Outer Moons,” Icarus, Vol. 48, No. 1, 1981, pp. 39–48.doi:https://doi.org/10.1016/0019-1035(81)90151-2 ICRSA5 0019-1035 CrossrefGoogle Scholar

  • [19] Jenkin A. B., “Probability of Collision During the Early Evolution of Debris Clouds,” Acta Astronautica, Vol. 38, Nos. 4–8, 1996, pp. 525–538.doi:https://doi.org/10.1016/0094-5765(96)00059-8 AASTCF 0094-5765 CrossrefGoogle Scholar

  • [20] Alfano S., “Numerical Implementation of Spherical Object Collision Probability,” The Journal of the Astronautical Sciences, Vol. 53, No. 1, 2005, pp. 103–109. JALSA6 0021-9142 CrossrefGoogle Scholar

  • [21] Alfano S., “Addressing Nonlinear Relative Motion For Spacecraft Collision Probability,” AIAA/AAS Astrodynamics Specialist Conference and Exhibit, AIAA Paper  2006-6760, 2006. LinkGoogle Scholar

  • [22] Chan K., “Analytical Expressions for Computing Spacecraft Collision Probabilities,” Proceedings of the AAS/AIAA Spaceflight Mechanics Meeting, Vol. 108, Advances in the Astronautical Sciences, Univelt, San Diego, CA, 2001, pp. 305–320. Google Scholar

  • [23] McKinley D. P., “Development of a Nonlinear Probability of Collision Tool for the Earth Observing System,” AIAA/AAS Astrodynamics Specialist Conference and Exhibit, AIAA Paper  2006-6295, 2006. LinkGoogle Scholar

  • [24] Bérend N., “Estimation of the Probability of Collision Between Two Catalogued Orbiting Objects,” Advances in Space Research, Vol. 23, No. 1, 1999, pp. 243–247.doi:https://doi.org/10.1016/S0273-1177(99)00009-5 ASRSDW 0273-1177 CrossrefGoogle Scholar

  • [25] Coppola V. T., “Evaluating the Short Encounter Assumption of the Probability of Collision Formula,” Proceedings of the 22nd AAS/AIAA Space Flight Mechanics Meeting, Vol. 143, Advances in the Astronautical Sciences, Univelt, San Diego, CA, 2012, pp. 2179–2190. Google Scholar

  • [26] Patera R. P., “General Method for Calculating Satellite Collision Probability,” Journal of Guidance, Control, and Dynamics, Vol. 24, No. 4, 2001, pp. 716–722.doi:https://doi.org/10.2514/2.4771 JGCDDT 0162-3192 LinkGoogle Scholar

  • [27] Chan K., “Improved Analytical Expressions for Computing Spacecraft Collision Probabilities,” Proceedings of the AAS/AIAA Spaceflight Mechanics Meeting, Vol. 114, Advances in the Astronautical Sciences, Univelt, San Diego, CA, 2003, pp. 1197–1216. Google Scholar

  • [28] Coppola V. T., “Including Velocity Uncertainty in the Probability of Collision Between Space Objects,” Proceedings of the 22nd AAS/AIAA Space Flight Mechanics Meeting, Vol. 143, Advances in the Astronautical Sciences, Univelt, San Diego, CA, 2012, pp. 2159–2178. Google Scholar

  • [29] Patera R. P., “Method for Calculating Collision Probability Between a Satellite and a Space Tether,” Journal of Guidance, Control, and Dynamics, Vol. 25, No. 5, 2002, pp. 940–945.doi:https://doi.org/10.2514/2.4967 JGCDDT 0162-3192 LinkGoogle Scholar

  • [30] de Vries W. H. and Phillion D. W., “Monte Carlo Method for Collision Probability Calculations Using 3D Satellite Models,” Proceedings of the Advanced Maui Optical and Space Surveillance Technologies Conference, Curran Associates, Inc., Red Hook, NY, 2010, pp. 124–133. Google Scholar

  • [31] Akella M. R. and Alfriend K. T., “Probability of Collision Between Space Objects,” Journal of Guidance, Control, and Dynamics, Vol. 23, No. 5, 2000, pp. 769–772.doi:https://doi.org/10.2514/2.4611 JGCDDT 0162-3192 LinkGoogle Scholar

  • [32] Alfano S., “Review of Conjunction Probability Methods for Short-Term Encounters,” Proceedings of the AAS/AIAA Space Flight Mechanics Meeting, Vol. 127, Advances in the Astronautical Sciences, Univelt, San Diego, CA, 2007, pp. 719–746. Google Scholar

  • [33] Alfano S., “Satellite Collision Probability Enhancements,” Journal of Guidance, Control, and Dynamics, Vol. 29, No. 3, 2006, pp. 588–592.doi:https://doi.org/10.2514/1.15523 JGCDDT 0162-3192 LinkGoogle Scholar

  • [34] Patera R. P., “Satellite Collision Probability for Nonlinear Relative Motion,” Journal of Guidance, Control, and Dynamics, Vol. 26, No. 5, 2003, pp. 728–733.doi:https://doi.org/10.2514/2.5127 JGCDDT 0162-3192 LinkGoogle Scholar

  • [35] Alfano S., “Satellite Conjunction Monte Carlo Analysis,” Proceedings of the 19th AAS/AIAA Space Flight Mechanics Meeting, Vol. 134, Advances in the Astronautical Sciences, Univelt, San Diego, CA, 2007–2024. Google Scholar

  • [36] Chan K. F., Spacecraft Collision Probability, Aerospace Corp., El Segundo, CA, 2008, pp. 1–12, 77–97, 153–171. LinkGoogle Scholar

  • [37] DeMars K. J., Nonlinear Orbit Uncertainty Prediction and Rectification for Space Situational Awareness, Ph.D. Thesis, Univ. of Texas, Austin, TX, 2010. Google Scholar

  • [38] Horwood J. T., Aragon N. D. and Poore A. B., “Gaussian Sum Filters for Space Surveillance: Theory and Simulations,” Journal of Guidance, Control, and Dynamics, Vol. 34, No. 6, 2011, pp. 1839–1851.doi:https://doi.org/10.2514/1.53793 JGCDDT 0162-3192 LinkGoogle Scholar

  • [39] Fujimoto K. and Scheeres D. J., “Non-Linear Propagation of Uncertainty with Non-Conservative Effects,” Proceedings of the 22nd AAS/AIAA Space Flight Mechanics Meeting, Vol. 143, Advances in the Astronautical Sciences, Univelt, San Diego, CA, 2012, pp. 2409–2427. Google Scholar

  • [40] DeMars K. J., Bishop R. H. and Jah M. K., “Entropy-Based Approach for Uncertainty Propagation of Nonlinear Dynamical Systems,” Journal of Guidance, Control, and Dynamics, Vol. 36, No. 4, 2013, pp. 1047–1057. doi:https://doi.org/10.2514/1.58987 JGCDDT 0162-3192 LinkGoogle Scholar

  • [41] Maruskin J. M., Scheeres D. J. and Alfriend K. T., “Correlation of Optical Observations of Objects in Earth Orbit,” Journal of Guidance, Control, and Dynamics, Vol. 32, No. 1, 2009, pp. 194–209.doi:https://doi.org/10.2514/1.36398 JGCDDT 0162-3192 LinkGoogle Scholar

  • [42] DeMars K. J. and Jah M. K., “Probabilistic Initial Orbit Determination Using Gaussian Mixture Models,” Journal of Guidance, Control, and Dynamics, Vol. 36, No. 5, 2013, pp. 1324–1335. doi:https://doi.org/10.2514/1.59844 JGCDDT 0162-3192 LinkGoogle Scholar

  • [43] Vittaldev V. and Russell R. P., “Collision Probability for Space Objects Using Gaussian Mixture Models,” Proceedings of the 23rd AAS/AIAA Space Flight Mechanics Meeting, Vol. 148, Advances in the Astronautical Sciences, Univelt, San Diego, CA, 2013. Google Scholar

  • [44] DeMars K. J., Bishop R. H. and Jah M. K., “Splitting Gaussian Mixture Method for the Propagation of Uncertainty in Orbital Mechanics,” Proceedings of the 21st AAS/AIAA Space Flight Mechanics Meeting, Vol. 140, Advances in the Astronautical Sciences, Univelt, San Diego, CA, 2011, pp. 1419–1438. Google Scholar

  • [45] Lebedev V. and Laikov D., “Quadrature Formula for the Sphere of the 131st Algebraic Order of Accuracy,” Doklady Mathematics, Vol. 59, No. 3, 1999, pp. 477–481. 1064-5624 Google Scholar

  • [46] Press W. H., Teukolsky S. A., Vetterling W. T. and Flannery B. P., Numerical Recipes: The Art of Scientific Computing, 3rd ed., Cambridge Univ. Press, New York, 2007, pp. 156–162. Google Scholar

  • [47] Julier S. J. and Uhlmann J. K., “Unscented Filtering and Nonlinear Estimation,” Proceedings of the IEEE, Vol. 92, No. 3, 2004, pp. 401–422. doi:https://doi.org/10.1109/JPROC.2003.823141 IEEPAD 0018-9219 CrossrefGoogle Scholar

  • [48] van der Merwe R., Sigma-Point Kalman Filters for Probabilistic Inference in Dynamic State-Space Models, Ph.D. Thesis, Oregon Health and Science Univ., Portland, OR, 2004. Google Scholar

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