Ellipsoid Targeting with Overlap

TLDR: In this article, the authors investigate the possibility of destroying a passive point target and determine the best targeting points in an area within which stationary or mobile targets are distributed uniformly or normally.

Abstract: First, we investigate the possibility of destruction of a passive point target. Subsequently, we study the problem of determination of best targeting points in an area within which stationary or mobile targets are distributed uniformly or normally. Partial results are given in the case in which the number of targeting points is less than seven or four, respectively. Thereafter, we study the case where there is no information on the enemy distribution. Then, the targeting should be organized in such a way that the surface defined by the kill radii of the missiles fully covers each point within a desired region of space-time. The problem is equivalent to the problem of packing ellipsoids of different sizes and shapes into an ellipsoidal container in \(\mathbb{R}^{4}\) so as to minimize a measure of overlap between ellipsoids is considered.