Four Methods of Solving for the Spherical Error Probable Associated with a Three-Dimensional Normal Distribution

摘要

When the predicted position of a satellite contains normally distributed errors, the position uncertainty can be described by a Spherical Error Probable or SEP. The SEP is calculated by integrating the three-dimensional normal probability density function over a spherical volume. The SEP is set equal to the radius of that volume which contains the satellite with 50% probability. In this report the authors present four methods for integrating the density function and finding the SEP. The three normal variates in the density function are assumed to be independent and unbiased with known variances. (Author)