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Paris, France 2022

For a variety of mission-critical objectives in Space Domain Awareness (SDA), it is relevant to maintain estimates over large regions of state space using highly non-Gaussian distributions. This problem is broadly applicable in initial orbit determination, maneuver detection, and collision avoidance, and observing targets in this context often necessitates search over the feasible region. Often, this search process results in a large set of null detections. This paper explores methodologies for utilizing negative information in this context, with a special focus on the well-known admissible region. Given a Gaussian mixture representation of the admissible region, a novel methodology for splitting mixands in an arbitrary measurement space is presented. A mixand weight update is derived for the key scenario in which no detection is made at a measurement epoch. Merging methodologies are applied, and the resultant Gaussian sum filter is demonstrated for a representative case in which follow-on tracking of a geostationary object is desired.