Precise Computation of Position Accuracy in GNSS Systems
  Accuracy and Availability computations for a GNSS System - or combination of Systems - through Service Volume Simulations take considerable time. Therefore, the computation of the accuracy in 2D and 3D are often simplified by an approximate solution. The drawback is that such simplifications can lead to accuracy results that are too conservative (up to 25% in the 2D case and up to 43% in the 3D case, for a 95% confidence level), which in turn translates into pessimistic System Availability. This article presents a way to compute the exact accuracy, for any confidence level, for the one, two or three dimensional cases, through the derivation of corresponding factors. Using the factors introduced here, allows getting accurate results swiftly.   The generic mathematical solution to compute the accuracy is presented. The approximate and precise computations are described. Then, the exact factors that should be applied to obtain the accuracy at a typical confidence level (95%) are derived for the three cases. 
Juan Pablo Boyero Garrido
stat.CO