This 30 minute presentation shows how collision probability is determined in Advanced Conjunction Analysis Tools (AdvCAT) using numerical computation and/or approximation methods. Collision probability analysis for spherical objects exhibiting linear relative motion is accomplished by combining covariances and physical object dimensions at the point of closest approach. The resulting covariance ellipsoid and hardbody can be projected onto the plane perpendicular to relative velocity when the relative motion is assumed linear.
Collision potential is determined from the object footprint on the projected, two-dimensional, covariance ellipse. The resulting double integral can be reduced to a single integral by various methods. Numerical methods or approximation can then be used to determine the true or maximum probability.