Sample-based computation of the joint-time probability of collision motivates developing the Mahalanobis Shell Sampling (MSS) algorithm, which samples nondegenerate normal random variables, enabling rare event simulation without unduly penalizing sample size. The MSS method has unbiased estimators in sample mean and covariance, and it may achieve arbitrary precision when approximating probability measures. For Clohessy–Wiltshire relative orbital dynamics, computational MSS exponential rates of error convergence (in the mean-square-error sense) are shown to improve by one order of magnitude (for sample mean and covariance) over Monte Carlo; when reproducing the instantaneous probability of collision, MSS has a comparable mean-square-error convergence rate performance to Monte Carlo.
Stochastic Convergence of Sobol-Based Mahalanobis Shell Sampling Collision Probability Computation
Journal of Guidance, Control, and Dynamics ; 46 , 5 ; 796-814
2023-05-01
Conference paper , Article (Journal)
Electronic Resource
English
Space Vehicle Collision Avoidance , Rendezvous Proximity Operations and Capture , Quasi Monte Carlo Method , Collision Risk Modeling Tool , Standard Gravitational Parameter , Spacecraft Formation Flying , quasi-random sampling , Spacecraft Autonomous Operations , rare event simulation , Cumulative Distribution Function