A series representation of the spherical error probability integral

Abstract

The author derives an infinite series representation of the spherical error probability integral (SEPI). The SEPI characterizes missile miss distance distributions resulting from Monte Carlo simulations. The SEPI is used when these distributions occupy a three-dimensional region of space. Truncation of this series provides a computationally efficient tool for approximating the SEPI. A series convergence analysis is presented that provides an upper bound on the approximation accuracy. The accuracy bound may be used to determine a sufficient number of terms needed for approximation to any desired accuracy. Presentation of numerical results provides empirical confirmation of the validity of the series expression. Calculation of the truncated series and numerical integration of the SEPI generate the numerical results. It is shows that the SEPI converges to the circular error probability integral as the standard deviation of a given component approaches zero. Approximation error bounds, as a function of sigma, are derived. >