CollisionCalc (TM)


CollisionCalc (TM) provides the critical missing step in satellite conjunction analysis: The transition from uncertain orbit estimates to a quantitatively meaningful metric representing the risk of collision between two conjuncting objects. It is a deceptively simple-seeming problem that has stumped satellite operators for decades. The traditional approach, computing an epistemic collision "probability", leads to low and misleading collision risk numbers. In fact, given two objects that are on a collision course, the actual probability of detecting an imminent collision using the traditional "probability" approach is practically zero. This is why so many practitioners have traditionally used the safer fixed-distance threshold approach. 

However, as LEO and MEO become more crowded over the next few years, the fixed-distance approach will prove untenable for many operators. It is safe but too conservative for the increasingly crowded operating environment. This is why satellite operators have been scrambling to find a new approach. What is needed is something that actually solves the conjunction risk assessment problem, and that is what CollisionCalc (TM) does. This is not merely a unique and useful algorithm.  CollisionCalc (TM) is an essential acquisition for anyone operating satellites in LEO, MEO, or even GEO.


CollisionCalc (TM) is a stand-alone piece of software that can work with data from JSpOC, ComSpOC, ESpOC or whatever space situational awareness service you use. As input, CollisionCalc (TM) takes the position, velocity, and associated uncertainties for both conjuncting objects at the estimated time of closest approach. The standard JSpOC Conjunction Data Message (CDM) explicitly reports this information; although, satellite operators often choose to generate their own estimate using their own tools and data. 

Given this input, CollisionCalc (TM) reports the risk of collision in the form of a statistical p-value on the hypothesis that the two objects are going to collide. If the reported risk is high, that doesn't mean that a collision is certain, or even near-certain, it simply means that the two objects are not far enough apart at closest approach, relative to the orbit uncertainties, to guarantee that they won't collide. However, a low reported risk does mean that your satellite is (relatively) safe. In a conjunction in which the two objects actually are on a collision course, for any fixed threshold, α, CollisionCalc (TM) will detect that imminent collision with a probability of at least 1-α. For example, suppose you set your risk threshold at 10-5; CollisionCalc (TM) will correctly detect an imminent collision in at least 99.999% of all conjunctions in which the two objects are on a collision course. More generally, this means that if CollisionCalc (TM) gives you a low risk number, you can be confident that your satellite is safe. This is what it means to report risk in quantitatively meaningful terms. CollisionCalc (TM) delivers it; no other available approach does.

Finally, it should also be noted that there is no dilution problem with the risk metric reported by CollisionCalc (TM). Satellite operators familiar with the traditional "probability" approach should know about a phenomenon called "probability dilution," in which lowering the quality of your data appears to make your satellite safer. Probability dilution is not a minor computational quirk, and it is certainly not a cosmic message telling us that ignorance is bliss. It is simply an artifact of having misapplied probabilistic mathematics. As a side-effect of delivering the correct solution to what is actually an inference problem, CollisionCalc (TM) eliminates this artifact.