Accommodating Rectangular Objects in Probability Calculations

This work refines probability calculations for rectangular object shapes of unknown orientation and compares those results to their representations as spheres. Conjunction 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 then be projected onto the plane perpendicular to relative velocity. Collision potential is determined from the object's physical footprint on the projected, two-dimensional, probability density space. For rectangular objects, the attitude must be considered because the region of integration (footprint) changes. Ideally, the attitude of each object should be known to accurately assess this probability. In the absence of object attitude information, a footprint must be created that completely defines the region where the two objects might touch. This footprint can then be rotated to determine the orientation that produces the largest probability making it the most conservative estimate for the given conjunction conditions. For a rectangular object modeled as a circle, the representation is shown to be overly conservative, producing a larger probability than that of the rectangular shape.