Numerical Estimation of Munitions Payload using Random Distributions

Abstract This mathematical research involves formulating mathematical explanations and solving discrete probabilistic problems related to the numerical estimation of target hits. These estimation formulas enable the cost estimation of operating and support funding for weapons payloads. Two of the three analytical problems involve estimating the probability that a target is hit after a tactical munitions is dispensed from an aircraft or missile launcher and the submunitions are ejected to clear a targeted area. The first problem entails determining the probability of hitting a target if a munitions may fall within a circle of radius r with a landing spread resembling a Gaussian or bivariate normal distribution, i.e., a two-dimensional probability distribution given jointly by (X,Y) ∼N(0, [sgrave]2); the second problem generalizes the first and assumes that a mine's true position and a munitions’ targeting are subject to random errors whose distributions are circular Gaussian; this problem is solved using discrete convolution techniques in the spatial domain and multiple integrals for the dispersing distribution. A third Poisson model is offered under some standard assumptions for multiple target hits.