Gaussian Sum Filters for Space Surveillance: Theory and Simulations

While standard Kalman-based filters, Gaussian assumptions, and covariance-weighted metrics are very effective in data-rich tracking environments, their use in the data-sparse environment of space surveillance ismore limited. To properly characterize non-Gaussian density functions arising in the problem of long-term propagation of state uncertainties, a Gaussian sum filter adapted to the two-body problem in space surveillance is proposed and demonstrated to achieve uncertainty consistency. The proposed filter is made efficient by using only a onedimensional Gaussian sum in equinoctial orbital elements, thereby avoiding the expensive representation of a full six-dimensional mixture and hence the “curse of dimensionality.” Additionally, an alternate set of equinoctial elements is proposed and is shown to provide enhanced uncertainty consistently over the traditional element set. Simulation studies illustrate the improvements in theGaussian sumapproach over the traditional unscentedKalman filter and the impact of correct uncertainty representation in the problems of data association (correlation) and anomaly (maneuver) detection.