Satellite instantaneous collision probability computation using equivalent volume cuboids

In a study researchers propose an integrated, two-stage approach to effectively compute the satellite instantaneous collision probability. First, it uses the Gaussian mixture model (GMM) o approximate the relative position vector probability density function (PDF) for the two involved resident space objects (RSOs) at a future time, and the GMM is then integrated over the hard body sphere. The core of this integration involves evaluating the integral for a general 3-D Gaussian PDF over a sphere, in which researchers adopt the equivalent volume method to yield an analytic approximation.