When a maneuverable spacecraft confronts a potentially unsafe conjunction with another space object, its operators must decide whether to maneuver to mitigate the risk of a collision. Such decisions may not be straightforward, since the operators must balance their confidence in the predictions that detected the conjunction, the actual likelihood of a collision, any risk inherent in performing the maneuver, interruptions to the mission’s ongoing operations, and long-term consequences such as depletion of consumable propellant. The most common metric for assessing the risk associated with a conjunction is the collision probability.

This innovation provides an augmentation to such methods, based on the well-known Wald Sequential Probability Ratio Test (WSPRT). The WSPRT guides decisions based explicitly on false alarm and missed detection criteria. A WSPRT for conjunction assessment reduces to a simple likelihood ratio based on current and prior collision odds.

The algorithm uses sequential estimates of collision probability, such as are operationally available from an orbit determination process, in a simple WSPRT that explicitly accounts for decision-makers’ preferences, expressed in terms of three quantities: an acceptable rate of false alarms, an acceptable rate of missed detections, and a prior assessment of the risk of collision that is independent of the orbit determination process. The last of these three, interpreted as the base rate of collision over the ensemble of possible realizations of the encounter, plays a central role in the overall decision procedure. While the base rate is in principle unknowable, a suitable proxy may be a collision rate computed from a background debris flux.

The algorithm compares the likelihood ratio to two decision limits, which can be expressed in terms of limits on collision probability. If the lower limit is reached, the conjunction may be dismissed, while if the upper limit is reached, a risk reduction maneuver may be needed. When neither limit is exceeded, an owner/operator should, if possible, seek another observation. The procedure is therefore essentially similar to current operational practice. Unlike current practice, however, the test satisfies tolerances related to targeted false alarm and missed detection rates. Importantly, the test is indifferent to the method used to compute collision probability.

This work was done by J. Russell Carpenter and F. Landis Markley of Goddard Space Flight Center. For further information, contact the Goddard Technology Transfer Office at (301) 286-5810. GSC-16968-1

NASA Tech Briefs Magazine

This article first appeared in the June, 2015 issue of NASA Tech Briefs Magazine.

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