Confidence Intervals for CEP When the Errors Are Elliptical Normal

A common parameter for describing the accuracy of a weapon is the circular probable error, generally referred to as CEP. CEP is simply the bivariate analog of the univariate probable error and measures the radius of a mean-centered circle which includes 50% of the bivariate probability. In the case of circular normal errors where the error variances are the same in both directions, CEP can be expressed as a function of the common miss distance standard deviation. Also, CEP can be expressed as a function of the common miss distance standard deviation. Also, CEP estimators based on observed miss distances are easily formulated and can be used to construct confidence intervals for CEP. In the case of elliptical normal errors, CEP cannot be expressed explicitly as a function of the miss distance standard deviations. Here, one must obtain CEP by numerical methods or by referring to tabular values. This has led to the development of a number of approximations by which CEP can be expressed as a function of the miss distance standard deviations. While CEP estimators based on observed miss distances are easily formulated from these approximations, their probability distributions are too complicated to be useful for CEP confidence intervals. In this report, these probability distributions are approximated with distributions which are more practical for the formulation and application of CEP confidence intervals. Approximate CEP confidence intervals are then formulated and their accuracy determined through Monte Carlo sampling.