Skip to main content
SpringerLink
Log in

Space Object Collision Probability via Monte Carlo on the Graphics Processing Unit

  • Published:
The Journal of the Astronautical Sciences Aims and scope Submit manuscript

Abstract

Fast and accurate collision probability computations are essential for protecting space assets. Monte Carlo (MC) simulation is the most accurate but computationally intensive method. A Graphics Processing Unit (GPU) is used to parallelize the computation and reduce the overall runtime. Using MC techniques to compute the collision probability is common in literature as the benchmark. An optimized implementation on the GPU, however, is a challenging problem and is the main focus of the current work. The MC simulation takes samples from the uncertainty distributions of the Resident Space Objects (RSOs) at any time during a time window of interest and outputs the separations at closest approach. Therefore, any uncertainty propagation method may be used and the collision probability is automatically computed as a function of RSO collision radii. Integration using a fixed time step and a quartic interpolation after every Runge Kutta step ensures that no close approaches are missed. Two orders of magnitude speedups over a serial CPU implementation are shown, and speedups improve moderately with higher fidelity dynamics. The tool makes the MC approach tractable on a single workstation, and can be used as a final product, or for verifying surrogate and analytical collision probability methods.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18

Similar content being viewed by others

References

  1. Adurthi, N., Singla, P.: Conjugate unscented transformation-based approach for accurate conjunction analysis. J. Guid. Control. Dyn. 38(9), 1642–1658 (2015). doi:10.2514/1.G001027

    Article  Google Scholar 

  2. Alfano, S.: Determining satellite close approaches, part II. J. Astronaut. Sci. 42(2), 143–152 (1994)

    Google Scholar 

  3. Alfano, S.: Review of conjunction probability methods for short-term encounters. In: AAS/AIAA Space Flight Mechanics Meeting, Sedona, Arizona, AAS 07-148 (2007)

  4. Alfano, S.: Satellite conjunction Monte Carlo analysis. In: AIAA Space Flight Mechanics Meeting, AAS 09-233 (2009)

  5. Arora, N., Russell, R.P.: A GPU accelerated multiple revolution Lambert Solber for fast mission design. In: AAS/AIAA Space Flight Mechanics Meeting, San Diego, CA, AAS 10-198 (2010)

  6. Arora, N., Russell, R.P.: Efficient interpolation of high-fidelity geopotential. J. Guid. Control. Dyn. (2015). doi:10.2514/1.G001291

    Google Scholar 

  7. Arora, N., Vittaldev, V., Russell, R.P.: Parallel computation of trajectories using graphics processing units and interpolated gravity models. J. Guid. Control. Dyn. 38(8), 1345–1355 (2015). doi:10.2514/1.G000571

    Article  Google Scholar 

  8. Brown, A., Tichy, J., Demoret, M., Rand, D.: GPU accelerated conjunction assessment with applications to formation flight and space debris, paper AAS 13-902 (2013)

    Google Scholar 

  9. Cheng, J.: Sampling algorithms for estimating the mean of bounded random variables. Comput. Stat. 16 (1), 1–23 (2001). doi:10.1007/s001800100049

    Article  MathSciNet  MATH  Google Scholar 

  10. Coppola, V.: Including velocity uncertainty in the probability of collision between space objects. In: AAS/AIAA Spaceflight Mechanics Meeting, Charleston, SC, AAS 12-247 (2012)

  11. Dagum, P., Karp, R., Luby, M., Ross, S.: An optimal algorithm for monte carlo estimation. SIAM J. Comput. 29(5), 1484–1496 (2000). doi:10.1137/S0097539797315306

    Article  MathSciNet  MATH  Google Scholar 

  12. DeMars, K.J., Jah, M.K.: Collision probability with gaussian mixture orbit uncertainty. J. Guid. Control. Dyn. 37 (3), 979–985 (2014). doi:10.2514/1.62308

  13. Fujimoto, K., Scheeres, D.J.: Tractable expressions for nononlinear propagated uncertainties. J. Guid. Control. Dyn. 38(6), 1146–1151 (2015). doi:10.2514/1.G000795

    Article  Google Scholar 

  14. Gajek, L., Niemiro, W., Pokarowski, P.: Optimal monte carlo integration with fixed relative precision. J. Complex. 29 (1), 4–26 (2013). doi:10.1016/j.jco.2012.09.001 [http://www.sciencedirect.com/science/ article/pii/S0885064X12000805]

    Article  MathSciNet  MATH  Google Scholar 

  15. Hobson, T., Clarkson, V.: GPU-based space situational awareness simulation utilising parallelism for enhanced multi-sensor management. In: Advance Maui Optical and Space Surveillance Technologies Conference, Wailea, Maui, Hawaii (2012)

  16. Jones, B.A., Doostan, A.: Satellite collision probability estimation using polynomial chaos. Adv. Space Res. 52(11), 1860–1875 (2013). doi:10.1016/j.asr.2013.08.027

    Article  Google Scholar 

  17. Jones, B.A., Parrish, N., Doostan, A.: Postmaneuver collision probability estimation using sparse polynomial chaos expansions. J. Guid. Control Dyn. 38(8), 1425–1437 (2015). doi:10.2514/1.G000595

    Article  Google Scholar 

  18. Kaplinger, B., Wie, B.: Optimized GPU simulation of a disrupted near-earth object including self gravity. In: 21st AAS/AIAA Space Flight Mechanics Meeting, New Orleans, LA (2011)

  19. Kessler, D.J., Johnson, N.L., Liou, J.C., Matney, M.: The kessler syndrome: implications to future space operations. In: 33rd Annual AAS Guidance and Control Conference (2010)

  20. Lyzhoft, J., Hawkings, M., Kaplinger, B., Wie, B.: GPU-based optical navigation and terminal guidance simulation of a hypervelocity asteroid intercept vehicle. In: AIAA Guidance, Navigation, and Control (GNC) Conference, pp 2013–4966. AIAA, Boston, MA (2013)

  21. Nakhjiri, N., Villac, B.F.: An algorithm for trajectory propagation and uncertainty mapping on GPU, Paper AAS 13-376. In: 23Rd AAS/AIAA Space Flight Mechanics Meeting, Kauai, HI (2013)

  22. Nayak, M.: Impact of national space policy on orbital debris mitigation and US Air Force end of life satellite operations. In: SpaceOps Conference, Stockholm, Sweden. doi:10.2514/6.2012-1284611 (2012)

  23. Parrish, N.: Accelerating Lambert’s Problem on the GPU in MATLAB. Senior project report, California Polytechnic State University - San Luis Obispo (2012)

  24. Russell, R.P., Arora, N.: Global point mascon models for simple, accurate and parallel geopotential computation. J. Guid. Control. Dyn. 35(5), 1568–1581 (2012). doi:10.2514/1.54533

    Article  Google Scholar 

  25. Sabol, C., Binz, C., Segerman, A., Roe, K., Schumacher, PW: Probabiliy of collision with special perturbations dynamics using the Monte Carlo method. In: AAS/AIAA Astrodynamics Specialist Conference, Girdwood, Alaska, AAS 11-435 (2011)

  26. Shen, H., Vittaldev, V., Karlgaard, C.D., Russell, R.P., Pellegrini, E.: Parallelized sigma point and particle filters for navigation problems, paper AAS 13-034. In: 36th Annual AAS Guidance and Control Conference, Feb 1–6, Breckenridge, CO (2013)

  27. Ueng, S.Z., Lathara, M., Baghsorkhi, S.S., Hwu, W.M.W.: Languages and Compilers for Parallel Computing. In: CUDA-Lite: Reducing GPU Programming Complexity. doi:10.1007/978-3-540-89740-8_1, pp 1–15. Springer, Berlin (2008)

  28. Vallado, D.A.: Fundamental of Astrodynamics and Applications, 3rd edn. Microcosm Press/Springer (2007)

  29. Vittaldev, V., Russell, R.: Collision probability for space objects using gaussian mixture models. In: Proceedings of the 23Rd AAS/AIAA Space Flight Mechanics Meeting, vol. 148 (2013a)

  30. Vittaldev, V., Russell, R.P.: Collision probability for resident space objects using gaussian mixture models, AAS 13-351 (2013b)

  31. Vivek, Vittaldev, Russell Ryan, P.: Space object collision probability using multidirectional gaussian mixture models. J. Guid. Control. Dyn. 39(9), 2163–2169 (2016). doi:10.2514/1.G001610

    Article  Google Scholar 

  32. Wagner, S., Wie, B., Kaplinger, B.: Cocomputation solutions to Lambert’s problem on modern graphics processing units. J. Guid. Control. Dyn. 38 (7), 1305–1310 (2015). doi:10.2514/1.G000840

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Aerospace Engineering and Engineering Mechanics, The University of Texas at Austin, W. R. Woolrich Laboratories, C0600, 210 E 24th Street, Austin, TX, 78712-1221, USA

    Vivek Vittaldev & Ryan P. Russell

Authors
  1. Vivek Vittaldev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ryan P. Russell
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Vivek Vittaldev.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Vittaldev, V., Russell, R.P. Space Object Collision Probability via Monte Carlo on the Graphics Processing Unit. J of Astronaut Sci 64, 285–309 (2017). https://doi.org/10.1007/s40295-017-0113-9

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40295-017-0113-9

Keywords

Search

Navigation