Single shot hit probability estimation as a result of the numerical solution of double integrals using Mathcad - Khaikov, Vadim L. (Vojnotehnički glasnik / Military Technical Courier, 2018)
A geometric interpretation of single shot hit probability (Phit) is a volume of the 3D space under the surface f(y,z) described by the bivariate normal distribution and bounded from below by the YOZ plane with the target’s contour (T-region). The Phit is proposed to be estimated by a method based on the numerical integration of the double integral. The double integral integrand is the 2D normal distribution of the Y, Z system of random variables. The dispersion characteristics and the coordinates of the dispersion center are known in advance.The limits of the first and the second integral are described by the analytic functions which characterize the geometric shape of the T-region. The implementation of the offered method is as follows: the selected shooting target is partitioned into N geometric subregions and then analytic formula(s) for each subregion’s boundaries is/are determined and each double integral is defined. The Phit estimations are produced using a numerical integration in the computer software Mathcad. The results of the calculus of all Phit values (for subregions) are added up (or subtracted) depending on the geometric relationships between the regions. The schema for solving Phit numerically makes it possible to calculate the likelihood for targets with arbitrary geometric shapes and not just for rectangular-shaped silhouettes. For illustrating the operability of the proposed method, the Phit for two kinds of head-type shooting targets has been evaluated. The developed method has been compared with the already existing works.
Keywords: hit probability; numerical solution; shooting target; double integrals; shot dispersion; Mathcad