A Multistep Probability of Collision Computation Algorithm

The two-dimensional probability of collision calculation method is both widely
used and computationally efficient. However, Monte Carlo simulations show that
this method sometimes fails to provide sufficiently accurate estimates for Earthorbiting satellites. This study presents a multistep algorithm that calculates collision probabilities for all conjunctions, regardless if affected by curvilinear trajectory or time varying covariance dynamics. The algorithm sequentially applies increasingly accurate estimation methods, but only as required for efficiency. Evaluating usage violations for the two-dimensional probability of collision method
represents one of the most important steps. Extensive testing demonstrates the
efficiency and reliability of the multistep algorithm.