Utkarsh Ranjan Mishra, Texas A&M University; Weston Faber, L3Harris; Suman Chakravorty, Texas A&M University; Islam Hussein, Thornton Tomasetti
Keywords: MCMC, Subset Simulation, Conjunction Assessment, Probability of Collision, Space Situational Awareness, Parallel Computing, Orbital Debris
Abstract:
Calculating the probability of collision is an important part of conjunction assessment risk analysis. Reliable probability of collision calculation is imperative to assess the need for conducting collision avoidance manoeuvres. Analytically, the cumulative collision probability, P, can be found by integrating the relative position density over the volume of the collision tube that is swept out by the combined hardbody of the two space objects over a specified time interval. Unlike analytical methods, the Markov Chain Monte Carlo (MCMC) sampling techniques enable the calculation of the probability of collision without worrying about the integration volume of the volume tube and with no assumptions on the constancy or the direction of the relative velocity over the encounter’s time span for both long-term and short-term encounters. Brute force MCMC sampling can be computationally expensive but Subset Simulation can dramatically reduce the number of samples and consequently the computation time required.
Subset Simulation is an MCMC sampling-based method used to compute probabilities of rare failure events. The technique expresses failure probability as a product of larger conditional failure probabilities and uses MCMC sampling to effectively compute these conditional probabilities of intermediate failure events. Let failure be F and three intermediate failure events F4, F3, F2, F1 … where, F= F1, F2 belongs to F1, F3 belongs to F2, F4 belongs to F3 and so on. Now P(F)=P(F1) can be written as P(F1) = P(F1|F2)*P(F2|F3)*P(F3|F4)*P(F4) where although P(F1) might have been small, the conditional probabilities, P(Fi|Fj), are large enough to be sampled from via MCMC.
The paper will have details on the theory and implementation of the Subset Sampling algorithm for the probability of collision of space objects. Also included will be a comparison of the suggested Subset Simulation-based probability of collision scheme with analytical and other MCMC sampling-based schemes for short and long term encounters in multiple different orbital regimes. The concluding remarks will be on the advantages and disadvantages of the probability of collision calculation methods and their appropriateness for different types of orbital conjunction events and operational constraints.
Date of Conference: September 14-17, 2021
Track: Conjunction/RPO