Effect of atmospheric density uncertainty on collision probability

The purpose of this paper is to analyze the effects of the uncertainty in the atmospheric density on the probability of collision, PC, between the International Space Station (ISS) and another space object. The current method used by US Space Command for orbit determination is batch least squares which assumes a perfect dynamic model. This perfect dynamic model assumption results in an optimistic covariance, that is, the estimated covariance is too small. Atmospheric density fluctuations can cause significant drag effects on near-Earth satellites. In this paper, the atmospheric density uncertainty is characterized by N first order stationary Gauss-Markov processes. Four covariances are generated and compared to determine the error in the current covariance generated by non-linear least squares when using a stochastic density model. The first is the non-linear least squares covariance. The second is the covariance obtained from a Kalman filter. These covariances should represent the state errors. The third is the covariance determined numerically from a Monte Carlo analysis. The fourth covariance uses the Least Squares covariance at epoch, which is then propagated analytically using the state transition matrix from the Clohessy-Wiltshire equations. The effect of the error in the batch least squares covariance on Pc is then determined for a specific scenario.

Effect of atmospheric density uncertainty on collision probability Academic Article