Fisher-Bingham-Kent Mixture Models for Angles-Only Observation Processing

The Fisher-Bingham-Kent (FBK) distribution was developed to describe uncertainty in angles-only observations when the distribution is concentrated near an arc of a great circle. It is a suitable model to describe the angular position of a propagated space object when the initial position and velocity are known up to small errors. However, in settings where the initial conditions are less constrained, e.g. when the maneuvering capabilities of the object are uncertain, it is of interest to fit a mixture of FBK distributions. In this paper we investigate how to fit such models using the expectation-maximization (EM) algorithm and and discuss a variety of space situational awareness applications.