Diffuse Gaussian Multiple-Shot Patterns

Abstract

When multiple weapons are fired at a single target, it may not be best to fire all weapons directly at the target on account of errors common to all shote. The probability of hitting the target can sometimes be increased by firing the weapons in a pattern around the target, rather than at directly at it. This observation leads naturally to the problem of finding the optimal pattern. The optimization problem is in general difficult because even calculating the hit probability for a given pattern usually requires numerical integrals. One excpetion is when errors are noromally distributed and the damage function takes on a compatible "Diffuse Gaussian" form. In that case, the hit probability can be expressed as an analyric function of the pattern's aimpoints, and conventional methods used to optimize it. This paper describes the required mathematics for a general diffuse Gaussian form, thus generalizing previous work.