Exploring an Alternative Approach to the Assessment of Collision Risk

This paper explores the construction of a collision assessment method exploiting an alternative to probability theory for the representation and quantification of uncertainty of the states for two anthropogenic space objects (ASOs). Propagated uncertainty in the position and velocity of an ASO depends on, for example, seemingly random measurement errors, systematic errors in the selection of and assumptions in the dynamics and measurement models, and their combined influence on an orbit determination solution. Using outer probability measures allows for a holistic treatment of random and systematic uncertainty, and to establish if the available information on the ASOs' states is sufficient to gauge the risk collision against an operational threshold through an upper and a lower bound on the probability of collision. The proposed method is illustrated in a context with similar hypotheses as Coppola's direct method: the upper probability, i.e., credibility, of a collision is derived and compared to Coppola's original probability of collision. It is shown that exploiting the credibility of collision is sufficient to derive a counterpart to Coppola's risk assessment that does not suffer from the probability dilution effect when the available information on the ASOs is scarce. The resulting approach is conservative (favors false alarms over missed detections) and potential alternatives are discussed.