Correlation of multiple singular observations and initial state estimation by means of probability distributions of high codimension

Optical observations of Earth-orbiting particles are singular in that multiple observations are required to determine the state of the object. It is generally uncertain, however, whether two arbitrary singular observations are of the same object, and solving this problem can be computationally intensive. In this paper, we propose a technique of correlating multiple singular observations and providing an initial estimate of the observed object's state by means of probability distributions in state space, provided the distributions have high codimension.