# Spacecraft Collision Probability Estimation for Rendezvous and Proximity Operations

The current version of this paper is available at: http://digitalcommons.usu.edu/etd/1398/

#### Abstract

The topic of this thesis is on-board estimation of spacecraft collision probability for orbital rendezvous and proximity operations. All of the examples shown in this work assume that the satellite dynamics are described by the Clohessy-Wiltshire equations, and that the spacecraft are spherical. Several collision probability metrics are discussed and compared. Each metric can be placed into one of three categories. The first category provides an estimate of the instantaneous probability of collision, and places an upper bound on the total probability of collision. The second category provides an estimate of total collision probability directly. The last category uses Monte Carlo analysis and a novel Pseudo Monte Carlo analysis algorithm to determine total collision probability. The metrics are compared and their accuracy is determined for a variety of on-orbit conditions. Lastly, a method is proposed in which the metrics are arranged in a hierarchy such that those metrics that can be computed quickest are calculated first. As the proposed algorithm progresses the metrics become more costly to compute, but yield more accurate estimates of collision probability. Each metric is compared to a threshold value. If it exceeds the limits determined by mission constraints, the algorithm computes a more accurate estimate by calculating the next metric in the series. If the threshold is not reached, it is assumed there is a tolerable collision risk and the algorithm is terminated. In this way the algorithm is capable of adapting to the level of collision probability, and can be sufficiently accurate without needless calculations being performed. This work shows that collision probability can be systematically estimated.

*This paper has been withdrawn.*