Directional distributions in tracking of space debris

Directional distributions play an important role in describing uncertainty in spherical coordinates. A review is given of some standard distributions on the sphere which arise as special cases of the Fisher-Bingham distribution. A new distribution, called the “extreme FB5” distribution, is introduced to describe semi-concentrated behavior on the sphere, that is, patterns of data that are unimodal and concentrated near a great circle. This behavior is particularly relevant to tracking problems. Properties of the new distribution are discussed and methods are given for simulation and estimation. Two simple error propagation illustrations are given to demonstrate the usefulness of the new model.