Some consequences of force model uncertainty on probability of collision with orbital debris
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This paper considers the problem of covariance propagation for a low-earth-orbit satellite when random fluctuations in the atmospheric density cause significant changes to the motion of the orbiting object. The standard deterministic model for spacecraft motion is supplemented by a stochastic model; the deterministic part of the drag acceleration is due to the usual exponential atmosphere, whereas the stochastic part is based on a first-order stationary Gauss-Markov process. Linear Error Theory is used to propagate the state error covariance. To demonstrate the efficacy of this approach, we discuss the problem of estimating the probability of collision between two orbiting objects for a given stochastic atmospheric model. In particular, the consequence of varying the correlation and the variance of the stochastic model is examined. It is seen that the variance and time-correlation of the stochastic density perturbations significantly influence the estimated value of the probability of collision and hence the resulting debris collision avoidance strategy.