Circular Probable Error for Circular and Noncircular Gaussian Impacts

Report No. ARL-MR-830
Authors: David W. Webb
Date/Pages: September 2012; 16 pages
Abstract: Circular probable error (CEP), defined as the radius of a circle centered at the aimpoint, which has a 50% probability of hit, is one of many measures of precision used to characterize ballistic precision. When determining CEP for two-dimensional impact data in which both dimensions are assumed to be independent, the case where both dispersion components are equal is a straightforward application of the Rayleigh distribution. However, when the dispersion components differ, an approximate CEP formula is necessary. This document evaluates the accuracy of the approximate CEP formula using Monte-Carlo simulation and shows that its associated probability of hit is no more than 2.17% higher than the nominal value of 0.50.
Distribution: Approved for public release
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Last Update / Reviewed: September 1, 2012