Satellite Cluster Tracking via Extent Estimation

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Clusters of closely-spaced objects in orbit present unique tracking and prediction challenges. Association of observations to individual objects is often not possible until the objects have drifted sufficiently far apart from one another. This dissertation proposes a new paradigm for initial tracking of these clusters of objects: instead of tracking the objects independently, the cluster is tracked as a single entity, parameterized by its centroid and extent, or shape. The feasibility of this method is explored using a decoupled centroid and extent estimation scheme. The dynamics of the centroid of a cluster of satellites are studied, and a set of modified equinoctial elements is shown to minimize the discrepancy between the motion of the centroid and the observation-space centroid. The extent estimator is formulated as a matrix-variate particle filter. Several matrix similarity measures are tested as the filter weighting function, and the Bhattacharyya distance is shown to outperform the others in test cases. Finally, the combined centroid and extent filter is tested on a set of three on-orbit breakup events, generated using the NASA standard breakup model and simulated using realistic force models. The filter is shown to perform well across low-Earth, geosynchronous, and highly-elliptical orbits, with centroid error generally below five kilometers and well-fitting extent estimates. These results demonstrate that a decoupled centroid and extent filter can effectively track clusters of closely-spaced satellites. This could improve spaceflight safety by providing quantitative tracking information for the entire cluster much earlier than would otherwise be available through typical means.