  Detecting anomalous behaviour of satellites is an important goal within the
broader task of space situational awareness. The Two Line Element (TLE) data
published by NORAD is the only widely-available, comprehensive source of data
for satellite orbits. We present here a filtering approach for detecting
anomalies in satellite orbits from TLE data. Optimal proposal particle filters
are deployed to track the state of the satellites' orbits. New TLEs that are
unlikely given our belief of the current orbital state are designated as
anomalies. The change in the orbits over time is modelled using the SGP4 model
with some adaptations. A model uncertainty is derived to handle the errors in
SGP4 around singularities in the orbital elements. The proposed techniques are
evaluated on a set of 15 satellites for which ground truth is available and the
particle filters are shown to be superior at detecting the subtle in-track and
cross-track manoeuvres in the simulated dataset, as well as providing a measure
of uncertainty of detections.
