A spherical co-ordinate space parameterisation for orbit estimation

An interesting challenge in orbital estimation problems for space surveillance using optical sensors is that, since both the orbital mechanics and the sensor observation process are non-linear, the standard filtering solutions such as Kalman filters are inapplicable and lead to divergent results. Naïve particle filtering solutions also fail since they require many particles to accurately represent the posterior distribution. However, since the sensor observation noise is modelled as a multivariate Gaussian distribution, it may be expected that the same single-object probability distributions, once projected into the augmented sensor space (a full spherical frame centred on the sensor), assume a simpler form that can be approximated by a multivariate Gaussian distribution. In this paper, a sequential Monte Carlo filter is proposed for the orbital object estimation problem, which exploits the structure of the measurement likelihood probability by introducing a proposal distribution based on a linear Kalman filter update.