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Probability of Collision of satellites and space debris for short-term encounters: Rederivation and fast-to-compute upper and lower bounds

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[In the Journal]


The accelerated increase in space debris in the low earth orbit (LEO) is a growing concern. Given the high speeds that these millions of fragments can reach, even the fragments that are a few millimetres in size, can cause fractures in a satellite’s hull or put a serious crack in the window of a space shuttle. The conventional method proposed by Akella and Alfriend in 2000 remains widely used to estimate the probability of collision in short-term encounters. This study introduces a novel derivation based on first principles that naturally allow for tight and fast upper and lower bounds for the probability of collision.

Read the paper to know how we:

  • Derive from first principles the expression for the probability of collision
  • Introduce accurate and fast-to-compute upper and lower bounds of the probability of collision
  • Study the computational complexity of our method when compared with the naive one
  • Validate our approach on a real dataset of Conjunction Data Messages (CDM)

Download the paper