A New Method for Time of Critical Approach Calculation

Paper number

IAC-15,A6,7,4,x29137

Author

Mr. Elad Denenberg, TECHNION - Israel Institute of Technology, Israel

Coauthor

Prof. Pini Gurfil, Asher Space Research Institute (ASRI), Israel

Year

2015

Abstract

Satellite clusters constitute one of the future trends in space systems.
However, thus far, there has not been an efficient method for guaranteeing
a safe operation of clusters in debris-rich environments. This paper
suggests a method for a fast and accurate calculation of the Time
of Critical Approach (TCA) between each member of a cluster of satellites
and cataloged space debris. A cluster is a group of satellites flying
under minimum and maximum distance constraints. All members of a cluster
are in danger of collisions among themselves, as well as with other
orbiting objects, such as other spacecraft and debris. The TCA is
crucial in situational awareness; it is at that point in time in which
the maximum probability of collision and the evasive maneuver are
calculated. There are numerous methods today for finding the TCA between
two orbiting objects; these methods vary in accuracy and speed. However,
the problem of quickly calculating the TCA's of $N$ satellites belonging
to a cluster with $M$ exterior objects has not been addressed. In
this paper, we first suggest a method which is an effective compromise
between speed and accuracy for finding the TCA between two space objects.
The proposed method is a Surrogate Based Optimization algorithm (SBO),
using the Alfano/Negron Close Approach Software (ANCAS) as the surrogate
function. ANCAS fits a cubic polynomial to the relative speed, searching
for the minimum distance in the critical points where the speed is
null. As in SBO, the true position and speed are calculated at the
TCA estimated by ANCAS; if the error is too large, the information
of the new calculated point is used to fit a cubic polynomial and
repeat the process. The described method is compared with exiting
methods and the advantages are shown. Then, a generalization
of the search to large groups of objects is suggested based on the
known characteristics of the clusters members. The method is compared
with an all-on-all search that is currently in common use.

Abstract document

IAC-15,A6,7,4,x29137.brief.pdf

Manuscript document

IAC-15,A6,7,4,x29137.pdf (🔒 authorized access only).

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