<p>    </p> <p>Space has become ever more crowded since the launch of Sputnik. The need for predictions of possible collisions between space objects has only ever grown. The development of space, particularly around Earth, increases the density of space objects and skyrockets the number of close approaches between these objects, called conjunctions. This investigation is conducted in the context of probability dilution, a phenomenon leading to a false negative collision prediction where increasing positional uncertainty decreases the predicted likelihood of a collision. Dilution is investigated along two avenues: how to generate accurate collision predictions in an efficient manner and how to obtain better input data with which to make these predictions. Along the first avenue, this research presents a novel analytical rectan- gular probability of collision expression as well as a variety of new covariance scale factor formulations for maximum collision probability that indicate the maximum possible collision risk for any conjunction. Along the second avenue, this research tests new sensor tasking regimes to mitigate dilution, ultimately showing that while dilution can be reduced, shrink- ing the positional covariance through optimal measurement updates may not be enough to avoid false negatives in orbital conjunctions. </p>