Papers
Topics
Authors
Recent
Search
2000 character limit reached

Treatment of Epistemic Uncertainty in Conjunction Analysis with Dempster-Shafer Theory

Published 28 Jan 2024 in cs.AI, cs.IT, math.IT, and math.PR | (2402.00060v2)

Abstract: The paper presents an approach to the modelling of epistemic uncertainty in Conjunction Data Messages (CDM) and the classification of conjunction events according to the confidence in the probability of collision. The approach proposed in this paper is based on the Dempster-Shafer Theory (DSt) of evidence and starts from the assumption that the observed CDMs are drawn from a family of unknown distributions. The Dvoretzky-Kiefer-Wolfowitz (DKW) inequality is used to construct robust bounds on such a family of unknown distributions starting from a time series of CDMs. A DSt structure is then derived from the probability boxes constructed with DKW inequality. The DSt structure encapsulates the uncertainty in the CDMs at every point along the time series and allows the computation of the belief and plausibility in the realisation of a given probability of collision. The methodology proposed in this paper is tested on a number of real events and compared against existing practices in the European and French Space Agencies. We will show that the classification system proposed in this paper is more conservative than the approach taken by the European Space Agency but provides an added quantification of uncertainty in the probability of collision.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (31)
  1. Merz, K., Braun, V., Benjamin Bastida, V., Flohrer, T., Funke, Q., Krag, H., and Lemmens, S., “Current collision avoidance service by ESA’s Space Debris Office,” 7thth{}^{\text{th}}start_FLOATSUPERSCRIPT th end_FLOATSUPERSCRIPT European Conference on Space Debris, ESA/ESOC, Darmstadt, Germany, 18-21 April 2017.
  2. Newman, L., Mashiku, A., Hejduk, M., Johnson, M., and Rosa, J., “NASA Conjunction Assessment Risk Analysis (CARA) updated requirements architecture,” AAS/AIAA Astrodynamics Specialist Conference, Portland, Maine, US, 2019.
  3. Recommended Standard: CCSDS 508.0-B-1, “Recommendation for space data system standards. Conjunction data message,” Tech. rep., CCSDS, Washington, DC, USA, Jun. 2013. https://public.ccsds.org/Pubs/508x0b1e2s.pdf.
  4. Aristoff, J. M., Horwood, J. T., Singh, N., and Poore, A., “Nonlinear uncertainty propagation in orbital elements and transformation to Cartesian space without loss of realism,” AAS/AIAA Astrodynamics Specialist Conference, San Diego, CA, US, 2014.
  5. Cano, A., Pastor, A., Escobar, D., Míguez, J., and Sanjurjo-Rivo, M., “Covariance determination for improving uncertainty realism in orbit determination and propagation,” Advances in Space Research. Space Environment Management and Space Sustainability, Vol. 72, No. 7, 2023, pp. 2759–2777. DOI: https://doi.org/10.1016/j.asr.2022.08.001.
  6. Pinto, F., Acciarini, G., Metz, S., Boufelja, S., Kaczmarek, S., Merz, K., Martínez-Heras, J., Letizia, F., Bridges, C., and Baydin, A., “Towards automated satellite conjunction management with bayesian deep learning,” AI for Earth Sciences Workshop at NeurIPS, 2020. URL https://nips.cc/virtual/2020/public/workshop_16105.html.
  7. Acciarini, G., Pinto, F., Letizia, F., Martínez-Heras, J., Merz, K., Bridges, C., and Güneş Baydin, A., “Kessler: a machine learning library for spacecraft collision avoidance,” 8thth{}^{\text{th}}start_FLOATSUPERSCRIPT th end_FLOATSUPERSCRIPT European Conference on Space Debris, ESA/ESOC, Darmstadt, Germany, 2021.
  8. Uriot, T., Izzo, D., Simões, L., Abay, R., Einecke, N., Rebhan, S., Martinez-Heras, J., Letizia, F., Siminski, J., and Merz, K., “Spacecraft collision avoidance challenge: design and results of a machine learning competition,” Astrodynamics, Vol. 6, No. 2, 2022, pp. 121–140. DOI: https://doi.org/10.1007/s42064-021-0101-5.
  9. Caldas, F., Soares, C., Nunes, C., and Guimarães, M., “Conjunction Data Messages for space collision behave as a Poisson process,” 31stst{}^{\text{st}}start_FLOATSUPERSCRIPT st end_FLOATSUPERSCRIPT European Signal Processing Conference (EUSIPCO), Hesinki, Finland, 2023.
  10. Laporte, F., “JAC Software, dedicated to the analysis of conjunction messages,” SpaceOps 2014 Conference, Pasadena, CA, US, 5-9 May 2014. DOI: https://doi.org/10.2514/6.2014-1774.
  11. Laporte, F., “JAC Software, solving conjunction assessment issues,” Proceedings of the Advanced Maui Optical and Space Surveillance Technologies Conference (AMOS), Maui, Hawaii, US, 9-12 September 2014.
  12. Tardioli, C., and Vasile, M., “Collision and re-entry analysis under aleatory and epistemic uncertainty,” Advances in Astronautical Sciences, Vol. 156, 2015, pp. 4205 – 4220.
  13. Delande, E., Houssineau, J., and Jah, M., “A New Representation of uncertainty for data fusion in SSA Detection and Tracking Problems,” 2018 21st International Conference on Information Fusion (FUSION), Cambridge, United Kingdom, 2018. DOI: https://doi.org/10.23919/ICIF.2018.8455540.
  14. Balch, M., Martin, R., and Ferson, S., “Satellite conjunction analysis and the false confidence theorem,” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 475, No. 20180565, 2019. DOI: https://doi.org/10.1098/rspa.2018.0565.
  15. Greco, C., Sánchez, L., and Vasile, M., “A robust Bayesian agent for optimal collision avoidance manoeuvre planning,” 8thth{}^{\text{th}}start_FLOATSUPERSCRIPT th end_FLOATSUPERSCRIPT European Conference on Space Debris, ESA/ESOC, Darmstadt, Germany, 12-14 April 2021.
  16. Sánchez, L., and Vasile, M., “On the use of machine learning and evidence theory to improve collision risk management,” Acta Astronautica, Vol. 181, 2021, pp. 694–706. DOI: https://doi.org/10.1016/j.actaastro.2020.08.004.
  17. Sánchez, L., and Vasile, M., “Intelligent agent for decision-making support and collision avoidance manoeuvre design on space traffic management,” Advances in Space Research. In press, 2022. DOI: https://doi.org/10.1016/j.asr.2022.09.023.
  18. Sánchez, L., Stevenson, E., Vasile, M., Rodríguez-Fernández, V., and Camacho, D., “An intelligent system for robust decision-making in the all-vs-all conjunction screening problem,” 3rdrd{}^{\text{rd}}start_FLOATSUPERSCRIPT rd end_FLOATSUPERSCRIPT IAA Conference on Space Situational Awareness (ICSSA), Tres Cantos, Madrid, Spain, 4-6 April 2022.
  19. Helton, J. C., Oberkampf, W., and Johnson, J., “Competing failure risk analysis using evidence theory,” Risk Analysis, Vol. 25, No. 4, 2005, pp. 973–995. DOI: https://doi.org/10.1111/j.1539-6924.2005.00644.x.
  20. Dvoretzky, A., Kiefer, J., and Wolfowitz, J., “Asymptotic minimax character of the sample distribution function and of the classical multinomial estimator,” Annals of Mathematical Statistics, Vol. 27, No. 3, 1956, pp. 642–669. DOI: https://doi.org/10.1214/aoms/1177728174.
  21. ISBN: 9780691100425.
  22. Serra, R., Arzelier, D., Joldes, M., Lasserre, J., Rondepierre, A., and Salvy, B., “Fast and accurate computation of orbital collision probability for short-term encounters,” Journal of Guidance, Control, and Dynamics, Vol. 39, 2016, pp. 1–13. DOI: https://doi.org/10.2514/1.G001353.
  23. Greco, C., and Vasile, M., “Robust Bayesian particle filter for space object tracking under severe uncertainty,” Journal of Guidance, Control, and Dynamics, Vol. 45, No. 3, 2021, pp. 481–498. DOI: https://doi.org/10.2514/1.G006157.
  24. Ferson, S. and Kreinovich, V. and Ginzburg, L. and Sentz, K. and Myers, D.S., “Constructing probability boxes and Dempster-Shafer structures,” Tech. rep., Sandia National Lab., Albuquerque, NM, United States, 2023. DOI: https://doi.org/10.2172/809606.
  25. DOI: https://doi.org/10.2172/910198.
  26. He, Y., Mirzargar, M., and Kirby, R., “An efficient reliability analysis approach for structure based on probability and probability box models,” Structural and Multidisciplinary Optimization, Vol. 56, 2017, pp. 167–181. DOI: https://doi.org/10.1007/s00158-017-1659-7.
  27. European Space Agency, “Kelvins collision avoidance challenge,” https://kelvins.esa.int/collision-avoidance-challenge/home/, 2019.
  28. He, Y., Mirzargar, M., and Kirby, R., “Mixed aleatory and epistemic uncertainty quantification using fuzzy set theory,” International Journal of Approximate Reasoning, Vol. 66, 2015, pp. 1–15. DOI: https://doi.org/10.1016/j.ijar.2015.07.002.
  29. Chojnacki, E., Baccou, J., and Destercke, D., “Numerical sensitivity and efficiency in the treatment of epistemic and aleatory uncertainty,” 5t⁢h𝑡ℎ{}^{th}start_FLOATSUPERSCRIPT italic_t italic_h end_FLOATSUPERSCRIPT International Conference on Sensitivity Analysis of Model Output, Budapest, Hungary, 18-22 June 2007. DOI: https://doi.org/10.1016/j.ijar.2015.07.002.
  30. Ferson, S., Nelsen, R., Hajagos, J., Berleant, D., Zhang, J., Tucker, W. T., Ginzburg, L. R., and Oberkampf4, W., “Dependence in probabilistic modeling, Dempster-Shafer theory, and probability bounds analysis,” Tech. rep., Sandia National Lab., United States, Oct. 2004. DOI: https://doi.org/10.2172/919189.
  31. Stroe, I., Stanculescu, A., Ilioaica, P., Blaj, C., Nita, M., Butu, A., Escobar, D., Tirado, J., Bija, B., and Saez, D., “AUTOCA autonomous collision avoidance system,” 8thth{}^{\text{th}}start_FLOATSUPERSCRIPT th end_FLOATSUPERSCRIPT European Conference on Space Debris, ESA/ESOC, Darmstadt, Germany, 20-23 April 2021.
Citations (1)
View on Semantic Scholar

Summary

No one has generated a summary of this paper yet.

Sign Up to Summarize

Paper to Video (Beta)

No one has generated a video about this paper yet.

Sign Up to Generate All Videos Subscribe on YouTube

Whiteboard

No one has generated a whiteboard explanation for this paper yet.

Sign Up to Generate

Open Problems

We haven't generated a list of open problems mentioned in this paper yet.

Generate Now

Continue Learning

We haven't generated follow-up questions for this paper yet.

Generate Now

Collections

Sign up for free to add this paper to one or more collections.

Sign Up

Tweets

Sign up for free to view the 2 tweets with 10 likes about this paper.

Sign Up for Free