Relationship between navigation vertical error, VDOP, and pseudo-range error in GPS

At a specified position and time, vertical position error is related to satellite ranging errors by the relationship Z=VDOP*URE where URE is the user range equivalent error, VDOP is the vertical dilution of precision, and Z is the vertical position error. This relationship is developed and it is shown that it is statistically correct even when position and time are variables. Expressions are given for the density, cumulative distribution, and standard deviation of Z in terms of the distributions of VDOP and URE. Vertical position error is investigated at several locations and the results compared with published work. A simple method for converting VDOP distributions to distributions of vertical accuracy as an alternative to computer simulation is presented. >