Collision Probability Estimation

As small satellites become more common and are assigned increasingly sophisticated missions, their role in proximity operations is also increased. An estimate of the current relative state (position, velocity and often attitude) as well as a prediction of the future relative state is important in close proximity operations. However, it is often insufficient to rely solely on this estimate to predict a collision due to the errors involved in the state estimate. An alternative approach is to determine the probability of a collision. In order to do this, the covariance of the state estimate must also be taken into account. For this reason, it is therefore important to determine a measure of the uncertainty of the position and velocity of both spacecraft. One approach is to conduct a Monte Carlo analysis either onboard or on the ground. Implementing this approach is time consuming and most likely not feasible with current technology. This paper explores the possibility of using covariance propagation onboard a small satellite to perform this uncertainty analysis. Covariance propagation has been shown to be one or two orders of magnitude faster than Monte Carlo analysis. This paper will show how this type of analysis can be used by small satellites for hazard avoidance.