Optimal Sequential Aim Corrections for Attacking a Stationary Point Target

A battery of weapons is directed one at a time at a stationary point target. The impact points of each weapon have a common circular normal distribution centered an unknown distance from the target; however, the centering of this distribution can be altered by a known amount between one shot and the next, if desired. We derive the optimal corrections among all unbiasing corrections that are linear functions of earlier impact-point components, and give the corresponding maximum probability of target destruction for any number of weapons for two target destruction functions. Also, we determine how large the offset need be in order that the optimal scheme be less costly than a strategy that makes no adjustment to aim. Three other schemes that do adjust aim are compared to the optimal one for various battery sizes.