Geometric restructurization of the space object tracking problem for improved uncertainty representation

The problem of space debris tracking can be viewed as an example of Bayesian filtering. Examples of such filters include the classic Kalman filter, together with nonlinear variants such as the extended and unscented Kalman filters, and the computationally more expensive particle filters. The purpose of this paper is to show with a careful choice of coordinate system, the uncertainty in the space debris tracking problem can often be formulated in terms of a multivariate normal distribution, and hence filtering can be carried out using the Kalman Filter or one of its variant.